Nonlinear dynamics of microplates
Nonlinear dynamics of microplates
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DOI：
10.1016/j.ijengsci.2014.10.004
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发表时间：
2015-01-01
影响因子：
6.6
通讯作者：
Farokhi, Hamed
中科院分区：
文献类型：
--
作者：
Ghayesh, Mergen H.;Farokhi, Hamed
本文基于修正的偶应力理论，研究了微板的非线性动力学问题。采用von Karman板理论建立了保留面内位移和惯性的系统模型。在拉格朗日方程的基础上，用能量法推导了运动方程，得到了一组带耦合项的二阶非线性常微分方程组。将这些方程转化为一阶非线性常微分方程组，并利用伪弧长延拓技术进行求解。通过绘制系统的频率-响应和力-响应曲线，考察了系统的非线性动力学。着重讨论了系统参数对共振响应的影响。讨论了基于修正的偶应力理论和经典偶应力理论建立的系统响应幅值的差异。(C)2014爱思唯尔有限公司。保留所有权利。
In this paper, the nonlinear dynamics of a microplate is investigated based on the modified couple stress theory. The von Karman plate theory is employed to model the system by retaining in-plane displacements and inertia. The equations of motion are derived via an energy method based on the Lagrange equations, yielding a set of second-order nonlinear ordinary differential equations with coupled terms. These equations are recast into a set of first-order nonlinear ordinary differential equations and the resulting equations are solved by means of the pseudo-arclength continuation technique. The nonlinear dynamics is examined through plotting the frequency-response and force-response curves of the system. The influence of system parameters on the resonant responses is highlighted. The differences in the response amplitude of the system modelled based on the modified couple stress theory and the classical one are discussed. (C) 2014 Elsevier Ltd. All rights reserved.