Abstract

This paper investigates nonlinear forced vibrations of homogeneous Euler-Bernoulli microbeams with clamped-clamped boundary conditions. Here, the nonlocal strain gradient theory is incorporated to achieve the governing nonlinear partial differential equation of motion, including mid-plane stretching and damping effects. Using the Galerkin approach, a reduced equation of motion is derived under a central harmonic force. The perturbation technique is employed to examine the nonlinear forced vibration behavior of microbeam. Frequency responses of microbeam are presented for primary, super-harmonic, and sub-harmonic resonances. Simulation results indicate role of size effect on the vibration behavior of microbeam. Moreover, the effects of different physical parameters on the vibration behavior of microbeam are studied. Finally, the proposed approach is compared with a numerical solution to demonstrate the accuracy and validity of the presented analytical solution.

摘要

本文研究具有边界条件的均质Euler-Bernoulli微束的非线性强迫振动。在这里，结合了非局部应变梯度理论来实现控制非线性偏微分运动方程，包括中平面拉伸和阻尼效应。使用Galerkin方法，可以在中心谐波力的作用下简化运动方程。摄动技术被用来检查微束的非线性强迫振动行为。提出了微束的频率响应，用于初级，超谐波和次谐波共振。仿真结果表明尺寸效应对微束振动行为的影响。此外，研究了不同物理参数对微束振动行为的影响。最后，