TY - JOUR ID - 15342 TI - Free in-plane vibration of heterogeneous nanoplates using Ritz method JO - Journal of Theoretical and Applied Vibration and Acoustics JA - TAVA LA - en SN - 2423-4761 AU - Faroughi, Shirko AU - Goushegir, Seyed Mohammad Hossein AD - Assistant Professor, Faculty of Mechanical Engineerng, Urmia University of Technology, Urmia, Iran AD - M.Sc. Student, Faculty of Mechanical Engineerng, Urmia University of Technology, Urmia, Iran Y1 - 2016 PY - 2016 VL - 2 IS - 1 SP - 1 EP - 20 KW - In-plane vibration KW - Rectangular heterogeneous nanoplate KW - Nonlocal elasticity theory KW - Ritz method DO - 10.22064/tava.2016.15342 N2 - In this paper, the Ritz method has been employed to analyze the free in-plane vibration of heterogeneous (non-uniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal polynomials are applied in the Ritz method in order to examine the nonlocal effect, aspect ratio, length of nanoplate and non-uniformity parameters on the vibrational behaviors of the nanoplate. Results are verified with the available published data and good agreements are observed. The outcomes confirm apparent dependency of in-plane frequency of nanoplate on the small scale effect, non-uniformity, aspect ratio and boundary conditions. For instance, frequency parameter decreases by increasing the nonlocal parameter in all vibration modes; the frequency parameters increase with length and aspect ratio of nanoplates. Furthermore, the effect of nonlocal parameters on the frequency parameter is more prominent at the higher aspect ratios. Finally, the effect of nonlocal parameter on the in-plane modes is also presented in this analysis. UR - https://tava.isav.ir/article_15342.html L1 - https://tava.isav.ir/article_15342_13964456d67a2be70d2e712d68470b24.pdf ER -