ORIGINAL_ARTICLE
Optimal characteristics determination of engine mounting system using TRA mode decoupling with emphasis on frequency responses
It is possible to improve vehicle vibration by tuning the parameters of engine mounting system. By optimization of mount characteristics or finding the optimal position of mounts, vibration of the engine and transmitted force from the engine to the chassis can be reduced. This paper examines the optimization of 6-degree-of-freedom engine mounting system based on torque roll axis (TRA) mode decoupling, so that TRA direction coincides with one of the natural modes of vibration. This is achieved by determination of optimal location and stiffness of mounts. In order to find feasible results, physical constraints are taken into account in optimization process. A detailed procedure of optimization problem is explained. Finally, by comparing the frequency and time responses of the optimal design with the original configuration, it is concluded that TRA decoupling is a proper objective function in engine mounting optimization and can greatly improve the vibration behavior of the engine. Achieving decoupled system, the optimal configuration has a better chance of placing dominant natural frequency below the operation range. Also, the forces transmitted through the mounts are reduced noticeably in the optimal design.
https://tava.isav.ir/article_29616_241067396488ebc7dfc53749bcfca281.pdf
2017-07-01
111
126
10.22064/tava.2017.45671.1053
Vibration
Engine mounting system
Torque roll axis
Mode decoupling
Rahime
Naseri
rahime.naseri@gmail.com
1
MSc, Mechanical Engineering Department, Amirkabir University of Technology
AUTHOR
Abdolreza
Ohadi
a_r_ohadi@aut.ac.ir
2
Professor, Mechanical Engineering Department, Amirkabir University of Technology
AUTHOR
Vahid
Fakhari
v_fakhari@sbu.ac.ir
3
Assistant Professor, Faculty of Mechanical and Energy Engineering, Shahid Beheshti University
LEAD_AUTHOR
Heidar Ali
Talebi
alit@aut.ac.ir
4
Department, Electrical Engineering Amirkabir University of Technology
AUTHOR
[1] R. Racca, How to select power-train isolators for good performance and long service life, in, SAE Technical Paper, 1982.
1
[2] P.E. Geck, R.D. Patton, Front wheel drive engine mount optimization, in, SAE Technical Paper, 1984.
2
[3] T. Jeong, R. Singh, Analytical methods of decoupling the automotive engine torque roll axis, Journal of Sound and Vibration, 234 (2000) 85-114.
3
[4] M.S. Foumani, A. Khajepour, M. Durali, Optimization of engine mount characteristics using experimental/numerical analysis, Modal Analysis, 9 (2003) 1121-1139.
4
[5] P. Diemer, M.G. Hueser, K. Govindswamy, T. D'Anna, Aspects of powerplant integration with emphasis on mount and bracket optimization, in, SAE Technical Paper, 2003.
5
[6] J.S. Sui, C. Hoppe, J. Hirshey, Powertrain mounting design principles to achieve optimum vibration isolation with demonstration tools, in, SAE Technical Paper, 2003.
6
[7] A. Akanda, C. Adulla, Engine mount tuning for optimal idle and road shake response of rear-wheel-drive vehicles, in, SAE Technical Paper, 2005.
7
[8] A. El Hafidi, B. Martin, A. Loredo, E. Jego, Vibration reduction on city buses: Determination of optimal position of engine mounts, Mechanical Systems and Signal Processing, 24 (2010) 2198-2209.
8
[9] S.U. Kolte, D. Neihguk, A. Prasad, S. Rawte, A. Gondhalekar, A particle swarm optimization tool for decoupling automotive powertrain torque roll axis, in, SAE Technical Paper, 2014.
9
[10] F. Dai, W. Wu, H. Wang, Q. Liu, F. Ma, F. Zhao, Study on Mount Matching Optimization for Removing Powertrain Abnormal Low Frequency Vibration, in: Proceedings of the FISITA 2012 World Automotive Congress, Springer, 2013, pp. 417-429.
10
[11] B. Angrosch, M. Plöchl, W. Reinalter, Mode decoupling concepts of an engine mount system for practical application, Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 229 (2015) 331-343.
11
[12] J.Y. Park, R. Singh, Role of spectrally varying mount properties in influencing coupling between powertrain motions under torque excitation, Journal of Sound and Vibration, 329 (2010) 2895-2914.
12
[13] J. Hu, W. Chen, H. Huang, Decoupling analysis for a powertrain mounting system with a combination of hydraulic mounts, Chinese Journal of Mechanical Engineering, 26 (2013) 737-745.
13
[14] J.F. Hu, R. Singh, Improved torque roll axis decoupling axiom for a powertrain mounting system in the presence of a compliant base, Journal of Sound and Vibration, 331 (2012) 1498-1518.
14
[15] J. Liette, J.T. Dreyer, R. Singh, Critical examination of isolation system design paradigms for a coupled powertrain and frame: Partial torque roll axis decoupling methods given practical constraints, Journal of Sound and Vibration, 333 (2014) 7089-7108.
15
[16] B. Sakhaei, M. Durali, Vehicle Interior Vibration Simulation-a Tool for Engine Mount Optimization, International Journal of Automotive Engineering, 3 (2013) 541-554.2013.
16
[17] Y. Rasekhipour, A. Ohadi, A Study on Performance of Simplified Vehicle Models in Optimization of Hydraulic Engine Mounts in Comparison with Full-Vehicle Model, International Journal of Automotive Engineering, 1 (2011).
17
[18] M.Z.R. Khan, A.K. Bajpai, Genetic algorithm and its application in mechanical engineering, International Journal of Engineering Research & Technology, 2 (2013) 677-683.
18
[19] V. Fakhari, A. Ohadi, Robust control of automotive engine using active engine mount, Journal of Vibration and Control, 19 (2013) 1024-1050.
19
[20] J.Y. Park, R. Singh, Effect of non-proportional damping on the torque roll axis decoupling of an engine mounting system, Journal of Sound and Vibration, 313 (2008) 841-857.
20
[21] V. Fakhari, A. Ohadi, Optimization and control of an active engine mount system to improve vibration behaviour of the vehicle, in, Amirkabir University of Technology 2013.
21
ORIGINAL_ARTICLE
An analytical approach for the nonlinear forced vibration of clamped-clamped buckled beam
Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framework for verification of numerical results. In this paperHomotopy analysis method and Homotopy Pade technique which are approximate analytical methods, are used to obtain nonlinear forced vibration response of Euler-Bernoulli clamped-clamped buckled beam subjected to an axial force and transverse harmonic load for the first time. Analytical solutions for nonlinear frequency are derived via Homotopy analysis method, Homotopy Pade technique and Runge Kutta method and the results are compared with experimental results of literature. Also the time response of the beam is obtained for free and forced vibration via analytical and numerical methods. In addition, the frequency response is drawn. Comparison of analytical results with numerical results and literature results reveals that Homotopy analysis method and Homotopy Padetechnique have excellent accuracy for wide range of nonlinear parameters and predict system behavior precisely.
https://tava.isav.ir/article_29617_428bb5e27871862b9b3001678edae07a.pdf
2017-07-01
127
144
10.22064/tava.2017.50057.1065
Nonlinear vibration
Forced Vibration
Euller-Bernoulli beam
Homotopy analysis method
Homotopy Pade method
Shahin
Mohammadrezazadeh
sh.mrezazadeh@email.kntu.ac.ir
1
Ph.D. student, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran.
AUTHOR
Ali-Asghar
Jafari
ajafari@kntu.ac.ir
2
Proffesor, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
LEAD_AUTHOR
Mohammad Saeid
Jafari
saeid_jafari@email.kntu.ac.ir
3
MSc student, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
AUTHOR
[1] M.T. Ahmadian, M. Mojahedi, Free vibration analysis of a nonlinear beam using homotopy and modified lindstedt-poincare methods, Journal of Solid Mechanics, 1 (2009).
1
[2] L. Azrar, R. Benamar, R.G. White, Semi-analytical approach to the non-linear dynamic response problem of S–S and C–C beams at large vibration amplitudes part I: General theory and application to the single mode approach to free and forced vibration analysis, Journal of Sound and Vibration, 224 (1999) 183-207.
2
[3] J.H. He, Α Review on Some New Recently Developed Nonlinear Analytical Techniques, International Journal of Nonlinear Sciences and Numerical Simulation, 1 (2000) 51-70.
3
[4] J.H. He, Modified Lindstedt–Poincare methods for some strongly non-linear oscillations: Part I: expansion of a constant, International Journal of Non-Linear Mechanics, 37 (2002) 309-314.
4
[5] N. Mohammadi, Nonlinear vibration analysis of functionally graded beam on Winkler-Pasternak foundation under mechanical and thermal loading via perturbation analysis method, Technology, 3 (2015) 144-158.
5
[6] A.H. Nayfeh, Introduction to perturbation techniques, Wiley-Interscience, New York, (1981).
6
[7] S.R.R. Pillai, B.N. Rao, On nonlinear free vibrations of simply supported uniform beams, Journal of sound and vibration, 159 (1992) 527-531.
7
[8] M.I. Qaisi, Application of the harmonic balance principle to the nonlinear free vibration of beams, Applied Acoustics, 40 (1993) 141-151.
8
[9] H.M. Sedighi, K.H. Shirazi, J. Zare, An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method, International Journal of Non-Linear Mechanics, 47 (2012a) 777-784.
9
[10] H.M. Sedighi, K.H. Shirazi, A. Noghrehabadi, Application of recent powerful analytical approaches on the non-linear vibration of cantilever beams, International Journal of Nonlinear Sciences and Numerical Simulation, 13 (2012b) 487-494.
10
[11] J.N. Reddy, I.R. Singh, Large deflections and large‐amplitude free vibrations of straight and curved beams, International Journal for numerical methods in engineering, 17 (1981) 829-852.
11
[12] B.S. Sarma, T.K. Varadan, Lagrange-type formulation for finite element analysis of non-linear beam vibrations, Journal of sound and vibration, 86 (1983) 61-70.
12
[13] Y. Shi, C. Mei, A finite element time domain modal formulation for large amplitude free vibrations of beams and plates, Journal of Sound and Vibration, 193 (1996) 453-464.
13
[14] S.J. Liao, An approximate solution technique not depending on small parameters: a special example, International Journal of Non-Linear Mechanics, 30 (1995) 371-380.
14
[15] S. Liao, Beyond perturbation: introduction to the homotopy analysis method, CRC press, 2003.
15
[16] S.J. Liao, A.T. Chwang, Application of homotopy analysis method in nonlinear oscillations, Journal of applied mechanics, 65 (1998) 914-922.
16
[17] S. Li, S.J. Liao, An analytic approach to solve multiple solutions of a strongly nonlinear problem, Applied Mathematics and Computation, 169 (2005) 854-865.
17
[18] E.B. Saff, R.S. Varga, Padé and Rational Approximation: Theory and Applications: Proceedings of an International Symposium Held at the University of South Florida, Tampa, Florida, December 15-17, 1976, Academic Press, 1977.
18
[19] L. Wuytack, Commented bibliography on techniques for computing Padé approximants, Padé Approximation and its Applications, (1979) 375-392.
19
[20] M.H. Kargarnovin, R.A. Jafari-Talookolaei, Application of the homotopy method for the analytic approach of the nonlinear free vibration analysis of the simple end beams using four engineering theories, Acta Mechanica, 212 (2010) 199-213.
20
[21] T. Pirbodaghi, M.T. Ahmadian, M. Fesanghary, On the homotopy analysis method for non-linear vibration of beams, Mechanics Research Communications, 36 (2009a) 143-148.
21
[22] T. Pirbodaghi, S.H. Hoseini, M.T. Ahmadian, G.H. Farrahi, Duffing equations with cubic and quintic nonlinearities, Computers & Mathematics with Applications, 57 (2009b) 500-506.
22
[23] M. Fooladi, S.R. Abaspour, A. Kimiaeifar, M. Rahimpour, On the analytical solution of Kirchhoff simplified model for beam by using of homotopy analysis method, World Applied Sciences Journal, 6 (2009) 297-302.
23
[24] S.H. Hoseini, T. Pirbodaghi, M.T. Ahmadian, G.H. Farrahi, On the large amplitude free vibrations of tapered beams: an analytical approach, Mechanics Research Communications, 36 (2009) 892-897.
24
[25] A.A. Motallebi, M. Poorjamshidian, J. Sheikhi, Vibration analysis of a nonlinear beam under axial force by homotopy analysis method, Journal of Solid Mechanics Vol, 6 (2014) 289-298.
25
[26] R.A. Jafari-Talookolaei, M.H. Kargarnovin, M.T. Ahmadian, M. Abedi, An investigation on the nonlinear free vibration analysis of beams with simply supported boundary conditions using four engineering theories, Journal of Applied Mathematics, 2011 (2011).
26
[27] A. Fereidoon, D.D. Ganji, H.D. Kaliji, M. Ghadimi, Analytical solution for vibration of buckled beams, International Journal of Research and Reviews in Applied Sciences, 4 (2010) 17-21.
27
[28] W. Lacarbonara, A.H. Nayfeh, W. Kreider, Experimental validation of reduction methods for nonlinear vibrations of distributed-parameter systems: analysis of a buckled beam, Nonlinear Dynamics, 17 (1998) 95-117.
28
[29] A.M. Abou-Rayan, A.H. Nayfeh, D.T. Mook, M.A. Nayfeh, Nonlinear response of a parametrically excited buckled beam, Nonlinear Dynamics, 4 (1993) 499-525.
29
[30] A.A. Afandeh, R.A. Ibrahim, Nonlinear response of an initially buckled beam with 1: 1 internal resonance to sinusoidal excitation, Nonlinear Dynamics, 4 (1993) 547-571.
30
[31] S.A. Ramu, T.S. Sankar, R. Ganesan, Bifurcations, catastrophes and chaos in a pre-buckled beam, International Journal of Non-Linear Mechanics, 29 (1994) 449-462.
31
[32] W. Kreider, A.H. Nayfeh, Experimental Investigation of Single-Mode Reponses in a Fixed-Fixed Buckled Beam, Nonlinear Dynamics, 15 (1998) 155-178.
32
[33] A.H. Nayfeh, W. Kreider, T.J. Anderson, Investigation of natural frequencies and mode shapes of buckled beams, AIAA journal, 33 (1995) 1121-1126.
33
[34] J.C. Ji, C.H. Hansen, Non-linear response of a post-buckled beam subjected to a harmonic axial excitation, Journal of Sound and Vibration, 237 (2000) 303-318.
34
[35] W. Lestari, S. Hanagud, Nonlinear vibration of buckled beams: some exact solutions, International Journal of Solids and Structures, 38 (2001) 4741-4757.
35
[36] G.B. Min, J.G. Eisley, Nonlinear vibration of buckled beams, Journal of Engineering for Industry, 94 (1972) 637-645.
36
[37] W.Y. Tseng, J. Dugundji, Nonlinear vibrations of a buckled beam under harmonic excitation, Journal of applied mechanics, 38 (1971) 467-476.
37
[38] W. Lacarbonara, A theoretical and experimental investigation of nonlinear vibrations of buckled beams, Virginia Polytechnic Institute and State University. http://scholar. lib. vt. edu/theses/public/etd-441520272974850/wlacarbo. pdf, (1997).
38
[39] J.G. Eisley, Large amplitude vibration of buckled beams and rectangular plates, AIAA Journal, 2 (1964) 2207-2209.
39
[40] T. Smelova-Reynolds, E.H. Dowell, The role of higher modes in the chaotic motion of the buckled beam—I, International journal of non-linear mechanics, 31 (1996) 931-939.
40
[41] T. Smelova-Reynolds, E.H. Dowell, The role of higher modes in the chaotic motion of the buckled beam—II, International journal of non-linear mechanics, 31 (1996) 941-950.
41
[42] D.M. Tang, E.H. Dowell, On the threshold force for chaotic motions for a forced buckled beam, Journal of Applied Mechanics, 55 (1988) 190-196.
42
[43] F. Tajaddodianfar, M.R. Hairi-Yazdi, H. Nejat-Pishkenari, Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method, Microsystem Technologies, 23 (2017) 1913-1926.
43
[44] M. Rezaee, M. Minaei, A theoretical and experimental investigation on large amplitude free vibration behavior of a pretensioned beam with clamped–clamped ends using modified homotopy perturbation method, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230 (2016) 1615-1625.
44
ORIGINAL_ARTICLE
Isogeometric analysis: vibration analysis, Fourier and wavelet spectra
This paper presents the Fourier and wavelet characterization of vibration problem. To determine the natural frequencies, modal damping and mass participation factors of bars, a rod element is established by means ofisogeometric formulation. The non-uniform rational Bezier splines (NURBS) is presented to characterize the geometry and the deformation field in isogeometric analysis (IGA). Non-proportional damping has been used to measure the real-state energy dissipation in vibration. Therefore, the stiffness, damping and mass matrices are derived by the NURBS basis functions. The efficiency and accuracy of the present isogeometric analysis is demonstrated by using classical finite element method (FEM) models and closed-form analytical solutions. The frequency content, modal excitation energy and damping are measured as basis values. Results show that the present isogeometric formulation can determine the modal frequencies and inherent damping in anaccurate way. Damping as an inherent characteristics of viscoelastic materials is treated in a realistic way in IGA method using non-proportional form. Based on results, k-refinement technique has enhanced the accuracy convergence with respect to other refinement methods. In addition, the half-power bandwidth method givesmodal damping for the IGA solution with appropriate accuracy with respect to FEM. Accuracy difference between quadratic and cubic NURBS is significant in IGA h-refinement
https://tava.isav.ir/article_29802_d7afd2df46ff7e43f813f54bdd0679b2.pdf
2017-07-01
145
164
10.22064/tava.2018.60256.1073
Fourier Spectrum
Isogeometric Analysis
NURBS
Wavelet Spectrum
Vibration Analysis
Erfan
Shafei
e.shafei@ut.ac.ir
1
Assistant Professor Civil Engineering Faculty, Urmia University of Technology
AUTHOR
Shirko
Faroughi
sh.farughi@uut.ac.ir
2
Mechanic, Urmia University of Technology, Urmia , Iran
LEAD_AUTHOR
[1] T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer methods in applied mechanics and engineering, 194 (2005) 4135-4195.
1
[2] C. Boor, A Practical Guide to Splines, Springer-Verlag New York, 1978.
2
[3] J.A. Cottrell, T.J.R. Hughes, Y. Bazilevs, Isogeometric analysis: toward integration of CAD and FEA, John Wiley & Sons, 2009.
3
[4] A. Buffa, G. Sangalli, R. Vázquez, Isogeometric analysis in electromagnetics: B-splines approximation, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 1143-1152.
4
[5] M.H. Aigner, Ch. Heinrich, C., Jüttler, B., Pilgerstorfer, E., Simeon, B., Vuong, A.-V, Swept volume parametrization for isogeometric analysis, In: Hancock, E., Martin, R. (Eds.), The Mathematics of Surfaces. MoS XIII, 2009 Springer., (2009).
5
[6] T.J.R. Hughes, A. Reali, G. Sangalli, Efficient quadrature for NURBS-based isogeometric analysis, Computer methods in applied mechanics and engineering, 199 (2010) 301-313.
6
[7] Y. Bazilevs, V.M. Calo, T.J.R. Hughes, Y. Zhang, Isogeometric fluid-structure interaction: theory, algorithms, and computations, Computational mechanics, 43 (2008) 3-37.
7
[8] Y. Bazilevs, V.M. Calo, J.A. Cottrell, J.A. Evans, T.J.r.R. Hughes, S. Lipton, M.A. Scott, T.W. Sederberg, Isogeometric analysis using T-splines, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 229-263.
8
[9] M.R. Dörfel, B. Jüttler, B. Simeon, Adaptive isogeometric analysis by local h-refinement with T-splines, Computer methods in applied mechanics and engineering, 199 (2010) 264-275.
9
[10] S. Lipton, J.A. Evans, Y. Bazilevs, T. Elguedj, T.J.R. Hughes, Robustness of isogeometric structural discretizations under severe mesh distortion, Computer Methods in Applied Mechanics and Engineering, 199 (2010) 357-373.
10
[11] V.P. Nguyen, C. Anitescu, P.A. Bordas, T. Rabczuk, Isogeometric analysis: an overview and computer implementation aspects, Mathematics and Computers in Simulation, 117 (2015) 89-116.
11
[12] T.J.R. Hughes, A. Reali, G. Sangalli, Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS, Computer methods in applied mechanics and engineering, 197 (2008) 4104-4124.
12
[13] D. Wang, W. Liu, H. Zhang, Novel higher order mass matrices for isogeometric structural vibration analysis, Computer Methods in Applied Mechanics and Engineering, 260 (2013) 92-108.
13
[14] C.H. Thai, H. Nguyen‐Xuan, N. Nguyen‐Thanh, T.H. Le, T. Nguyen‐Thoi, T. Rabczuk, Static, free vibration, and buckling analysis of laminated composite Reissner–Mindlin plates using NURBS‐based isogeometric approach, International Journal for Numerical Methods in Engineering, 91 (2012) 571-603.
14
[15] O. Weeger, U. Wever, B. Simeon, Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations, Nonlinear Dynamics, 72 (2013) 813-835.
15
[16] S. Shojaee, E. Izadpanah, N. Valizadeh, J. Kiendl, Free vibration analysis of thin plates by using a NURBS-based isogeometric approach, Finite Elements in Analysis and Design, 61 (2012) 23-34.
16
[17] L.V. Tran, A.J.M. Ferreira, H. Nguyen-Xuan, Isogeometric analysis of functionally graded plates using higher-order shear deformation theory, Composites Part B: Engineering, 51 (2013) 368-383.
17
[18] C.H. Thai, A.J.M. Ferreira, E. Carrera, H. Nguyen-Xuan, Isogeometric analysis of laminated composite and sandwich plates using a layerwise deformation theory, Composite Structures, 104 (2013) 196-214.
18
[19] P. Phung-Van, M. Abdel-Wahab, K.M. Liew, S.P.A. Bordas, H. Nguyen-Xuan, Isogeometric analysis of functionally graded carbon nanotube-reinforced composite plates using higher-order shear deformation theory, Composite structures, 123 (2015) 137-149.
19
[20] F. Tornabene, N. Fantuzzi, M. Bacciocchi, A new doubly-curved shell element for the free vibrations of arbitrarily shaped laminated structures based on Weak Formulation IsoGeometric Analysis, Composite Structures, 171 (2017) 429-461.
20
[21] T. Yu, S. Yin, T. Bui, S. Xia, S. Tanaka, S. Hirose, NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method, Thin-Walled Structures, 101 (2016) 141-156.
21
[22] N. Fantuzzi, G. Della Puppa, F. Tornabene, M. Trautz, Strong Formulation IsoGeometric Analysis for the vibration of thin membranes of general shape, International Journal of Mechanical Sciences, 120 (2017) 322-340.
22
[23] S. Yin, T. Yu, T. Bui, P. Liu, S. Hirose, Buckling and vibration extended isogeometric analysis of imperfect graded Reissner-Mindlin plates with internal defects using NURBS and level sets, Computers & Structures, 177 (2016) 23-38.
23
[24] L. Dedè, C. Jäggli, A. Quarteroni, Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation, Computer Methods in Applied Mechanics and Engineering, 284 (2015) 320-348.
24
[25] MATLAB 7.04 User’s Manual., MathWorks, USA., 2005.
25
[26] C.R.W. Farrar, K., An introduction to structural health monitoring, Philosophical Transactions of the Royal Society of London A, Mathematical, Physical and Engineering Sciences, 365 (2007) 303-315.
26
[27] P.C. Chang, S.C. Liu, Recent research in nondestructive evaluation of civil infrastructures, Journal of materials in civil engineering, 15 (2003) 298-304.
27
[28] S.L. Chen, H.C. Lai, K.C. Ho, Identification of linear time varying systems by Haar wavelet, International journal of systems science, 37 (2006) 619-628.
28
[29] ASTM, A568-Standard, "Specification for Steel Sheet, Carbon, and High Strength Low-Alloy, Hot-Rolled and Cold-Rolled".
29
[30] Y. Kitada, Identification of nonlinear structural dynamic systems using wavelets, Journal of Engineering Mechanics, 124 (1998) 1059-1066.
30
[31] K.M. Liew, Q. Wang, Application of wavelet theory for crack identification in structures, Journal of engineering mechanics, 124 (1998) 152-157.
31
ORIGINAL_ARTICLE
Free vibration and wave propagation of thick plates using the generalized nonlocal strain gradient theory
In this paper, a size-dependent first-order shear deformation plate model is formulated in the framework of the higher-order generalized nonlocal strain-gradient (GNSG) theory. This modelemploys two nonlocal parameters and a strain-gradient coefficient to capture the both higher-order nonlocal stress-gradient and strain-gradient effects in nanostructures. The presence of these different scale parameters renders a unified model, which is able to predict both increase and reduction of stiffness in nanoplates. The governing equations are developed for freevibration of first-order shear deformation plates using Ritz method. The dispersion relations for the GNSG plate model is also derived. Several numerical examples are studied to show the efficiency, competence and accuracy of the proposed model. To ensure the applicability of the presented GNSG plate model, the results are compared with the experimental data available in the scientific literature. It is found that the effects of scale parameters on the wave frequencies are significant at high wavenumbers and ratio of any pair of these parameters is the main criterion for the correct study of size effects. The results show that the reduced nonlocal strain-gradient (RNSG) model and the GNSG model diverge in higher vibration modes.
https://tava.isav.ir/article_30106_6034579e0206ddec6cfac0c8c91e344f.pdf
2017-07-01
165
198
10.22064/tava.2018.68796.1085
Free vibration
first-order shear deformation plate
wave propagation
higher-order nonlocal strain-gradient model
Ritz method
Seyed Mohammad Hossein
Goushegir
smh.goushegir@mee.uut.ac.ir
1
Faculty of Mechanical Engineering, Urmia University of Technology
LEAD_AUTHOR
Shirko
Faroughi
sh.farughi@uut.ac.ir
2
Faculty of Mechanical Engineering, Urmia University of Technology
AUTHOR
[1] J.A. Ruud, T.R. Jervis, F. Spaepen, Nanoindentation of Ag/Ni multilayered thin films, Journal of Applied Physics, 75 (1994) 4969-4974.
1
[2] P. Ball, Roll up for the revolution, Nature, 414 (2001) 142-144.
2
[3] R.H. Baughman, A.A. Zakhidov, W.A. De Heer, Carbon nanotubes--the route toward applications, science, 297 (2002) 787-792.
3
[4] B.H. Bodily, C.T. Sun, Structural and equivalent continuum properties of single-walled carbon nanotubes, International Journal of Materials and Product Technology, 18 (2003) 381-397.
4
[5] C. Li, T.W. Chou, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures, 40 (2003) 2487-2499.
5
[6] R. Liu, L. Wang, Thermal vibration of a single-walled carbon nanotube predicted by semiquantum molecular dynamics, Physical Chemistry Chemical Physics, 17 (2015) 5194-5201.
6
[7] G. Shi, P. Zhao, A new molecular structural mechanics model for the flexural analysis of monolayer graphene, Computer Modeling in Engineering & Sciences(CMES), 71 (2011) 67-92.
7
[8] P.L. De Andres, F. Guinea, M.I. Katsnelson, Density functional theory analysis of flexural modes, elastic constants, and corrugations in strained graphene, Physical Review B, 86 (2012) 245409.
8
[9] A.C. Eringen, Nonlocal polar elastic continua, International journal of engineering science, 10 (1972) 1-16.
9
[10] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, 54 (1983) 4703-4710.
10
[11] A.C. Eringen, Nonlocal continuum field theories, Springer Science & Business Media, 2002.
11
[12] W.H. Duan, C.M. Wang, Y.Y. Zhang, Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics, Journal of applied physics, 101 (2007) 024305.
12
[13] Q. Wang, Q.K. Han, B.C. Wen, Estimate of material property of carbon nanotubes via nonlocal elasticity, Advanced Theoretical Applied Mechanics, 1 (2008) 1-10.
13
[14] L.Y. Huang, Q. Han, Y.J. Liang, Calibration of nonlocal scale effect parameter for bending single-layered graphene sheet under molecular dynamics, Nano, 7 (2012) 1250033.
14
[15] Y. Liang, Q. Han, Prediction of nonlocal scale parameter for carbon nanotubes, Science China Physics, Mechanics and Astronomy, 55 (2012) 1670-1678.
15
[16] A.A. Pisano, A. Sofi, P. Fuschi, Nonlocal integral elasticity: 2D finite element based solutions, International Journal of Solids and Structures, 46 (2009) 3836-3849.
16
[17] W.H. Duan, C.M. Wang, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory, Nanotechnology, 18 (2007) 385704.
17
[18] P. Lu, P.Q. Zhang, H.P. Lee, C.M. Wang, J.N. Reddy, Non-local elastic plate theories, in: Proceedings of the royal society of london a: Mathematical, physical and engineering sciences, The Royal Society, 2007, pp. 3225-3240.
18
[19] R. Aghababaei, J.N. Reddy, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration, 326 (2009) 277-289.
19
[20] H.T. Thai, A nonlocal beam theory for bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, 52 (2012) 56-64.
20
[21] T. Murmu, S.C. Pradhan, Small-scale effect on the free in-plane vibration of nanoplates by nonlocal continuum model, Physica E: Low-dimensional Systems and Nanostructures, 41 (2009) 1628-1633.
21
[22] S. Faroughi, S.M.H. Goushegir, Free in-plane vibration of heterogeneous nanoplates using Ritz method, Journal of Theoretical and Applied Vibration and Acoustics, 2 (2016) 1-20.
22
[23] Y.Z. Wang, F.M. Li, K. Kishimoto, Flexural wave propagation in double-layered nanoplates with small scale effects, Journal of Applied Physics, 108 (2010) 064519.
23
[24] L. Wang, H. Hu, Flexural wave propagation in single-walled carbon nanotubes, Physical Review B, 71 (2005) 195412.
24
[25] B.o. Wang, Z. Deng, H. Ouyang, J. Zhou, Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory, Physica E: Low-dimensional Systems and Nanostructures, 66 (2015) 283-292.
25
[26] M.A. Eltaher, M.A. Hamed, A.M. Sadoun, A. Mansour, Mechanical analysis of higher order gradient nanobeams, Applied Mathematics and Computation, 229 (2014) 260-272.
26
[27] C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78 (2015) 298-313.
27
[28] H.M. Ma, X.L. Gao, J.N. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56 (2008) 3379-3391.
28
[29] N. Challamel, C.M. Wang, The small length scale effect for a non-local cantilever beam: a paradox solved, Nanotechnology, 19 (2008) 345703.
29
[30] N. Challamel, Z. Zhang, C.M. Wang, J.N. Reddy, Q. Wang, T. Michelitsch, B. Collet, On nonconservativeness of Eringen’s nonlocal elasticity in beam mechanics: correction from a discrete-based approach, Archive of Applied Mechanics, 84 (2014) 1275-1292.
30
[31] C.M. Wang, S. Kitipornchai, C.W. Lim, M. Eisenberger, Beam bending solutions based on nonlocal Timoshenko beam theory, Journal of Engineering Mechanics, 134 (2008) 475-481.
31
[32] D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51 (2003) 1477-1508.
32
[33] E.C. Aifantis, On the role of gradients in the localization of deformation and fracture, International Journal of Engineering Science, 30 (1992) 1279-1299.
33
[34] F.A.C.M. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39 (2002) 2731-2743.
34
[35] J.N. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59 (2011) 2382-2399.
35
[36] H. Askes, E.C. Aifantis, Gradient elasticity and flexural wave dispersion in carbon nanotubes, Physical Review B, 80 (2009) 195412.
36
[37] B. Akgöz, Ö. Civalek, Application of strain gradient elasticity theory for buckling analysis of protein microtubules, Current Applied Physics, 11 (2011) 1133-1138.
37
[38] W. Xu, L. Wang, J. Jiang, Strain gradient finite element analysis on the vibration of double-layered graphene sheets, International Journal of Computational Methods, 13 (2016) 1650011.
38
[39] H.X. Nguyen, T.N. Nguyen, M. Abdel-Wahab, S.P.A. Bordas, H. Nguyen-Xuan, T.P. Vo, A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory, Computer Methods in Applied Mechanics and Engineering, 313 (2017) 904-940.
39
[40] Y.S. Li, E. Pan, Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory, International Journal of Engineering Science, 97 (2015) 40-59.
40
[41] L.i. Li, Y. Hu, Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory, Computational materials science, 112 (2016) 282-288.
41
[42] L.i. Li, Y. Hu, L. Ling, Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 75 (2016) 118-124.
42
[43] L.i. Li, Y. Hu, Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory, International Journal of Engineering Science, 97 (2015) 84-94.
43
[44] A. Farajpour, M.R.H. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, (2016) 1-19.
44
[45] L.i. Li, Y. Hu, L. Ling, Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory, Composite Structures, 133 (2015) 1079-1092.
45
[46] L.i. Li, X. Li, Y. Hu, Free vibration analysis of nonlocal strain gradient beams made of functionally graded material, International Journal of Engineering Science, 102 (2016) 77-92.
46
[47] F. Ebrahimi, M.R. Barati, A. Dabbagh, A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science, 107 (2016) 169-182.
47
[48] S. Faroughi, S.M.H. Goushegir, H.H. Khodaparast, M.I. Friswell, Nonlocal elasticity in plates using novel trial functions, International Journal of Mechanical Sciences, 130 (2017) 221-233.
48
[49] L. Behera, S. Chakraverty, Effect of scaling effect parameters on the vibration characteristics of nanoplates, Journal of Vibration and Control, 22 (2016) 2389-2399.
49
[50] L. Behera, S. Chakraverty, Free vibration of nonhomogeneous Timoshenko nanobeams, Meccanica, 49 (2014) 51-67.
50
[51] S. Chakraverty, L. Behera, Free vibration of rectangular nanoplates using Rayleigh–Ritz method, Physica E: Low-dimensional Systems and Nanostructures, 56 (2014) 357-363.
51
[52] R.D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, 16 (1964) 51-78.
52
[53] R.D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1 (1965) 417-438.
53
[54] C.M. Wang, J.N. Reddy, K.H. Lee, Shear deformable beams and plates: Relationships with classical solutions, Elsevier, 2000.
54
[55] M.R.K. Ravari, H. Zeighampour, Vibration analysis of functionally graded carbon nanotube-reinforced composite nanoplates using Mindlin’s strain gradient theory, Composite Structures, 134 (2015) 1036-1043.
55
[56] M. Mohr, J. Maultzsch, E. Dobardžić, S. Reich, I. Milošević, M. Damnjanović, A. Bosak, M. Krisch, C. Thomsen, Phonon dispersion of graphite by inelastic x-ray scattering, Physical Review B, 76 (2007) 035439.
56
[57] L.E. Shen, H.S. Shen, C.L. Zhang, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Computational Materials Science, 48 (2010) 680-685.
57
ORIGINAL_ARTICLE
Study on different solutions to reduce the dynamic impacts in transition zones for high-speed rail
One of the most important factors influencing the track maintenance is the transitions between parts of the track with different vertical stiffness. The dynamic forces in the super-structure, i.e. from rail to ballast/slab and subgrade, including every layer under ballast/slab until natural ground, are influenced by the type of materials, layer configuration and geometry. One way to mitigate track transition problems is to have a more gradual transition with a reduced stiffness differential. The aim of this research is to reduce vertical transient stresses and displacements under track supports at track transition areas by combining different structural configurations. For this purpose, the train-track dynamic interaction in the transition zones with different vertical stiffness values is analysed using a finite element software. A high-speed train moving on a slab and ballasted track is considered travelling in both directions. The effect of different structural track designs is studied in realistic operation scenarios. The results allow concluding that the sleeper displacements and ballast stresses can be significantly reduced in the transition zones by making small changes in the track structural elements.
https://tava.isav.ir/article_30707_3ffaca457b5d43f6eace8f256c745a9c.pdf
2017-07-01
199
222
10.22064/tava.2018.80091.1095
Track design
Transition zones
High-speed rail operations
Sleepers displacement
Track stresses
Finite elements method
Track dynamic behavior
Roberto
Sañudo
roberto.sanudo@unican.es
1
Department of Transport and Technology of Projects and Process, University of Cantabria, Spain
AUTHOR
Valeri
Markine
v.l.markine@tudelft.nl
2
Section of Railway Engineering, Delft University of Technology, The Netherlands
AUTHOR
João
Pombo
j.c.pombo@hw.ac.uk
3
School of Energy Geoscience, Infrastructure and Society, Heriot Watt University, UK & LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Portugal & ISEL/IPL, Lisboa, Portugal
LEAD_AUTHOR
[1] J.N. Varandas, P. Hölscher, M.A. Silva, Dynamic behaviour of railway tracks on transitions zones, Computers & structures, 89 (2011) 1468-1479.
1
[2] P. Hölscher, The dynamics of foundations for high speed lines on soft soils, International Journal of Railway Technology, 1 (2012) 147-166.
2
[3] B. Indraratna, S. Nimbalkar, C. Rujikiatkamjorn, Modernisation of rail tracks for higher speeds and greater freight, (2013).
3
[4] E. Fortunato, A. Paixão, R. Calçada, Railway track transition zones: design, construction, monitoring and numerical modelling, International Journal of Railway Technology, 2 (2013) 33-58.
4
[5] S.C. d’Aguiar, E. Arlaud, R. Potvin, E. Laurans, C. Funfschilling, Railway Transitional Zones: A case History from Ballasted to Ballastless Track, International Journal of Railway Technology, 2 (2014).
5
[6] J. Varandas, A. Paixão, E. Fortunato, P. Hölscher, R. Calçada, Numerical modelling of railway bridge approaches: influence of soil non-linearity, The International Journal of Railway Technology, 3 (2014) 73-95.
6
[7] P. Taforel, M. Renouf, F. Dubois, J.C. Voivret, Finite element-discrete element coupling strategies for the modelling of ballast-soil interaction, International Journal of Railway Technology, 4 (2015) 73-95.
7
[8] C. Voivre, V.H. Nhu, R. Peralès, Discrete Element Method Simulation as a Key Tool Towards Performance Design of Ballasted Tracks, International Journal of Railway Technology, 5 (2016) 83-98.
8
[9] Y. Momoya, T. Nakamura, S. Fuchigami, T. Takahashi, Improvement of degraded ballasted track to reduce maintenance work, International Journal of Railway Technology, 5 (2016) 31-54.
9
[10] P.K. Woodward, O. Laghrouche, S.B. Mezher, D.P. Connolly, Application of coupled train-track modelling of critical speeds for high-speed trains using three-dimensional non-linear finite elements, International Journal of Railway Technology, 4 (2015) 1-35.
10
[11] H. Wang, V. Markine, Modelling of the long-term behaviour of transition zones: Prediction of track settlement, Engineering Structures, 156 (2018) 294-304.
11
[12] S.B. Mezher, D.P. Connolly, P.K. Woodward, O. Laghrouche, J. Pombo, P.A. Costa, Railway critical velocity–Analytical prediction and analysis, Transportation Geotechnics, 6 (2016) 84-96.
12
[13] J. Pombo, T. Almeida, H. Magalhães, P. Antunes, J. Ambrósio, Finite Element Methodology for Flexible Track Models in Railway Dynamics Applications, International Journal of Vehicle Structures & Systems, 5, No.2, pp. 43-52 (DOI: 10.4273/ijvss.5.2.01)..
13
[14] N. Kuka, R. Verardi, C. Ariaudo, J. Pombo, Impact of maintenance conditions of vehicle components on the vehicle–track interaction loads, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, (2017) (DOI: 10.1177/0954406217722803)..
14
[15] R. Sañudo, L. Dell'Olio, J.A. Casado, I.A. Carrascal, S. Diego, Track transitions in railways: A review, Construction and Building Materials, 112 (2016) 140-157.
15
[16] C.D. Sasaoka, D. Davis, Implementing track transition solutions for heavy axle load service, in: Proceedings, AREMA 2005 Annual Conference, Chicago, IL, Citeseer, 2005.
16
[17] D. Read, D. Li, Design of track transitions, TCRP Research Results Digest, (2006).
17
[18] A. Namura, T. Suzuki, Evaluation of countermeasures against differential settlement at track transitions, Quarterly Report of RTRI, 48 (2007) 176-182.
18
[19] B.E.Z. Coelho, P. Hölscher, F.B.J. Barends, Dynamic behaviour of transition zones in railways, in: Proceedings of the 21st European Young Geotechnical Engineers' Conference, Rotterdam, 2011, pp. 133-139.
19
[20] Y. Du, M. Bai, Y. Chen, D. Yi, Vertical Displacement Distributions of Double-Track High-Speed Railways' Ballastless Track Infrastructure, in: Application of Nanotechnology in Pavements, Geological Disasters, and Foundation Settlement Control Technology, 2014, pp. 117-124.
20
[21] P.A. Lopez, The vertical stiffness of the track and the deterioration of high speed lines[La rigidez vertical de la via y el deterioro de las lineas de alta velocidad], Revista de Obras Publicas, 148 (2001) 7-26.
21
[22] A.L. Pita, P.F. Teixeira, F. Robusté, High speed and track deterioration: the role of vertical stiffness of the track, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 218 (2004) 31-40.
22
[23] E. Berggren, Railway track stiffness: dynamic measurements and evaluation for efficient maintenance, in, KTH, 2009.
23
[24] R. Sañudo, V. Markine, L. Dell'Olio, Improving Track Transitions of High-Speed Lines. In: Tsompanakis, in: Topping (eds.) Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing. Creta, Greece, 2011.
24
[25] J.A. Zakeri, V. Ghorbani, Investigation on dynamic behavior of railway track in transition zone, Journal of Mechanical Science and Technology, 25 (2011) 287-292.
25
[26] M. Banimahd, P.K. Woodward, 3-Dimensional finite element modelling of railway transitions, in: In Proceedings of 9 th International Conference on Railway Engineering, 2007.
26
[27] D. Li, J. Hyslip, T. Sussmann, S. Chrismer, Railway geotechnics, CRC Press, 2002.
27
[28] I. Gallego, Heterogeneidad resistente de las vías de Alta Velocidad: Transición terraplén-estructura, (2006).
28
[29] I. Gallego Giner, A. López Pita, Numerical simulation of embankment—structure transition design, Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 223 (2009) 331-343.
29
[30] S. ADIF, Recomendaciones sobre las cuñas de transición. Sistema de Gestion de la Calidad, in, 2008.
30
[31] M. Banimahd, P.K. Woodward, J. Kennedy, G.M. Medero, Behaviour of train–track interaction in stiffness transitions, in: Proceedings of the Institution of Civil Engineers-Transport, Thomas Telford Ltd, 2012, pp. 205-214.
31
[32] A.W.M. Kok, Moving loads and vehicles on a rail track structure: RAIL User’s Manual, in, Report, 1998.
32
[33] V.L. Markine, J.M. Zwarthoed, C. Esveld, Use of numerical optimisation in railway slab track design, in: OM Querin (Ed.): Engineering Design Optimization Product and Process Improvement. Proceedings of the 3rd ASMO UK/ISSMO conference, Harrogate, North Yorkshire, UK, 9th–10th July 2001, 2001.
33
[34] A. Man, survey of dynamic railway track properties and their quality (Doctoral dissertation), in: PhD. Thesis, , U Delft, DUP–Science, Delft, The Netherlands, 2002.
34
[35] C. Esveld, V.L. Markine, Assessment of high-speed slab track design, European Railway Review, 12 (2006) 55-62.
35
[36] J.J. Kalker, Wheel–rail rolling contact theory, in: Mechanics and Fatigue in Wheel/Rail Contact, Elsevier, 1991, pp. 243-261.
36
[37] A.D. Kerr, L.A. Bathurst, A Method for Upgrading the Performance at Track Transitions for High-Speed Service, in, 2003.
37
[38] R. Sañudo, V. Markine, L. Dell'olio, The Effect of Increasing Train Speed on Track Transition Performance, in: J. In. Pombo, ed. (Ed.) Third International Conference on Railway Technology: Research, Development and Maintenance., Sardinia, Italy., 2016.
38
[39] J. Choi, Influence of track support stiffness of ballasted track on dynamic wheel-rail forces, Journal of transportation engineering, 139 (2013) 709-718.
39
[40] U.-E.S. . UNE_EN_13848-5 Geometric quality levels., in, 2011.
40
[41] C. Esveld, Modern railway track, (2001).
41
[42]B. Lichtberger, (2011). Manual de vía. Eurailpress, DVV Media Group.
42
ORIGINAL_ARTICLE
A periodic folded piezoelectric beam for efficient vibration energy harvesting
Periodic piezoelectric beams have been used for broadband vibration energy harvesting in recent years. In this paper, a periodic folded piezoelectric beam (PFPB) is introduced. The PFPB has special features that distinguish it from other periodic piezoelectric beams. The Adomian decomposition method (ADM) is used to calculate the first two band gaps andtwelve natural frequencies of the PFPB. Results show that this periodic beam has wide band gaps at low frequency ranges and the band gaps are close to each other. Results also show that the PFPB can efficiently generate voltage from the localized vibration energy over the band gaps. The natural frequencies of the PFPB are close to each other and most of them are out of the band gaps. Therefore, the PFPB can also generate the maximum voltage over a relatively wide frequency range out of the band gaps. In order to show these features better, the voltage output of the PFPB over a wide frequency range is calculated using the ANSYS software and compared with that of a conventional piezoelectric energy harvester. The ANSYS is also used to validate the analytical results and good agreement is found.
https://tava.isav.ir/article_30810_93af25076cf94798217c34bd2a07be82.pdf
2017-07-01
223
238
10.22064/tava.2018.69901.1087
Vibration energy harvesting
Periodic folded piezoelectric beam
Vibration Band gap
Adomian decomposition method
finite element simulation
Mohammad
Hajhosseini
m.hajhosseini@stu.yazd.ac.ir
1
Department of Mechanical Engineering, Yazd University, Yazd 89195-741, Iran
AUTHOR
Mansour
Rafeeyan
rafeeyan@yazd.ac.ir
2
Department of Mechanical Engineering, Yazd University, Yazd 89195-741, Iran
LEAD_AUTHOR
Saeed
Ebrahimi
ebrahimi@yazd.ac.ir
3
Department of Mechanical Engineering, Yazd University, Yazd 89195-741, Iran
AUTHOR
[1] X.D. Xie, Q. Wang, N. Wu, Energy harvesting from transverse ocean waves by a piezoelectric plate, International Journal of Engineering Science, 81 (2014) 41-48.
1
[2] M.H. Ansari, M.A. Karami, Modeling and experimental verification of a fan-folded vibration energy harvester for leadless pacemakers, Journal of Applied Physics, 119 (2016) 1-10.
2
[3] A.G.A. Muthalif, N.H.D. Nordin, Optimal piezoelectric beam shape for single and broadband vibration energy harvesting: Modeling, simulation and experimental results, Mechanical Systems and Signal Processing, 54-55 (2015) 417-426.
3
[4] M.S. Chow, J. Dayou, W.Y.H. Liew, Increasing the output from piezoelectric energy harvester using width-split method with verification, International Journal of Precision Engineering and Manufacturing, 14 (2013) 2149-2155.
4
[5] C. Eichhorn, F. Goldschmidtboeing, P. Woias, A frequency tunable piezoelectric energy converter based on a cantilever beam, Proceedings of PowerMEMS, 9 (2008) 309-312.
5
[6] T. Reissman, E.M. Wolff, E. Garcia, Piezoelectric resonance shifting using tunable nonlinear stiffness, in: Active and Passive Smart Structures and Integrated Systems 2009, International Society for Optics and Photonics, 2009, pp. 72880G.
6
[7] S.M. Shahruz, Design of mechanical band-pass filters for energy scavenging, Journal of sound and vibration, 292 (2006) 987-998.
7
[8] E.D. Nobrega, F. Gautier, A. Pelat, J.M.C. Dos Santos, Vibration band gaps for elastic metamaterial rods using wave finite element method, Mechanical Systems and Signal Processing, 79 (2016) 192-202.
8
[9] Z.-J. Wu, F.-M. Li, Y.-Z. Wang, Study on vibration characteristics in periodic plate structures using the spectral element method, Acta Mechanica, 224 (2013) 1089-1101.
9
[10] H. Shu, W. Liu, S. Li, L. Dong, W.Q. Wang, S. Liu, D. Zhao, Research on flexural wave band gap of a thin circular plate of piezoelectric radial phononic crystals, Journal of Vibration and Control, 22 (2016) 1777-1789.
10
[11] Z.B. Cheng, Y.G. Xu, L.L. Zhang, Analysis of flexural wave bandgaps in periodic plate structures using differential quadrature element method, International Journal of Mechanical Sciences, 100 (2015) 112-125.
11
[12] M. Hajhosseini, M. Rafeeyan, S. Ebrahimi, Vibration band gap analysis of a new periodic beam model using GDQR method, Mechanics Research Communications, 79 (2017) 43-50.
12
[13] J. Wen, G. Wang, D. Yu, H. Zhao, Y. Liu, X. Wen, Study on the vibration band gap and vibration attenuation property of phononic crystals, Science in China Series E: Technological Sciences, 51 (2008) 85-99.
13
[14] Z. Chen, Y. Yang, Z. Lu, Y. Luo, Broadband characteristics of vibration energy harvesting using one-dimensional phononic piezoelectric cantilever beams, Physica B: Condensed Matter, 410 (2013) 5-12.
14
[15] M. Hajhosseini, M. Rafeeyan, Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting, Applied Mathematics and Mechanics, 37 (2016) 1053-1066.
15
[16] S.S. Rao, Vibration of continuous systems, John Wiley & Sons, 2007.
16
[17] C. Kittel, Introduction to Solid State Physics 8th ed,(2005), in, John Wiley & Sons, Inc., New York, 2005.
17
[18] G. Adomian, Solving frontier problems of physics: the decomposition method, Kluwer-Academic Publishers, Boston, MA, 1994.
18
[19] Q. Mao, Free vibration analysis of multiple-stepped beams by using Adomian decomposition method, Mathematical and computer modelling, 54 (2011) 756-764.
19
[20] D. Adair, M. Jaeger, Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method, Applied Mathematical Modelling, 40 (2016) 3230-3241.
20
[21] A. Erturk, D.J. Inman, On mechanical modeling of cantilevered piezoelectric vibration energy harvesters, Journal of Intelligent Material Systems and Structures, 19 (2008) 1311-1325.
21