Abstract

The objective of this study is to investigate the size-dependent nonlinear forced vibrations of homogeneous and functionally graded micro resonators with axially immovable ends. According to the power law distribution, for the functionally graded micro resonators, the material properties are changed in the thickness direction. Considering the damping and mid-plane stretching effects, the governing nonlinear partial differential equations of homogeneous and functionally graded micro resonators are achieved based on the nonlocal strain gradient theory. The nonlinear ordinary differential equations, including nonlinear external forces such as electrostatic actuation and Casimir force, are derived for homogeneous and functionally graded micro resonators by employing Galerkin approach. The static DC and harmonic AC voltages are combined to apply as the electrostatic actuator voltage. The frequency responses of the homogeneous and functionally graded micro resonators are studied by applying the multiple scales method. Finally, the effects of damping coefficient, amplitude of excitation, and nonlocal strain gradient parameters are investigated for the frequency responses of the homogeneous and functionally graded micro resonators.

摘要

本研究的目的是研究具有轴向固定端的均质且功能渐变的微型谐振器的尺寸相关的非线性强迫振动。根据幂律分布，对于功能梯度微谐振器，材料特性在厚度方向上会发生变化。考虑到阻尼和中平面拉伸效应，基于非局部应变梯度理论，得到了均质和功能梯度微谐振器的控制非线性偏微分方程。通过采用Galerkin方法，为均匀且功能梯度的微谐振器推导了非线性常微分方程，包括非线性外力，如静电激励和卡西米尔力。静态直流电压和谐波交流电压被组合起来用作静电执行器电压。通过应用多尺度方法研究了均质和功能梯度微谐振器的频率响应。最后，研究了阻尼系数，激励幅度和非局部应变梯度参数对均质和功能梯度微谐振器的频率响应的影响。