Analyzing dynamical snap-through of a size dependent nonlinear micro-resonator via a semi-analytic method

Document Type: Full Length Article


1 Asistant Professor School of Mechanical Engineering, Shiraz University, Shiraz, Islamic Republic of Iran

2 Ph.D. Student, Department of Solid Mechanics Engineering, School of Mechanical Engineering, Shiraz University



In the present paper, the dynamical snap-through of a preloaded micro-sensor is analyzed. This behavior is linked to analyzing bifurcation behavior of the micro structure in a suitable framework. Effects of the axial pre-stress and the excitation amplitude on the stability and sensitivity of the sensor are also discussed. In order to capture the size effects, the modified strain gradient theory is employed on an Euler-Bernoulli beam. Applying the Hamilton’s principle and utilizing the Galerkin’s method, the nonlinear governing equation for the vibration is obtained. The method of multiple scales (MMS) is then used to obtain the frequency-response equation and by using a mathematical approach, the bifurcation points and the jump heights of the micro-resonator are analyzed. The calculated analytic equation for frequency response, provides the conditions for obtaining the range of snap-through and studying the effects of different designing parameters on the multivaluedness range. The jump height of the micro-resonator is proposed to use as a criterion for sensing purposes. The simulations are illustrated and the results are verified with similar works


  • The modified strain gradient theory is used to capture size effects in a microbeam.
  • The effect of Poisson’s ratio is taken into account.
  • A mathematical framework is developed to find bifurcation points of the system.
  • The effects of excitation amplitude and preload on the bifurcation are studied.
  • Bifurcation behavior with the change of length scale parameters is studied.


Main Subjects

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