功能梯度矩形板的强非线性共振分析

针对陶瓷-金属功能梯度矩形板,在给出非均匀材料应力-应变关系及非线性几何方程的基础上,应用虚功原理导出了横向简谐激励力作用下功能梯度板的非线性振动偏微分方程。对于四边简支约束功能梯度矩形板,通过位移函数的设定,利用伽辽金积分法推得了关于时间自变量的达芬型强非线性振动方程。针对强非线性系统的主共振问题,应用改进的多尺度法进行解析求解,得到了稳态运动下的幅频响应方程。通过数值算例,给出了功能梯度矩形板共振下的幅频曲线图和相图,讨论了激励幅值及频率等参数对系统非线性振动特性的影响,并对改进多尺度法和经典多尺度法的结果进行了比较。

STRONGLY NONLINEAR RESONANCE ANALYSIS OF FUNCTIONALLY GRADED MATERIAL RECTANGULAR PLATES

A ceramic/metal functionally graded rectangular plate is considered in this study.Based on the stress-strain relationship and nonlinear geometric equations,the nonlinear partial differential equations of a FGM plate subjected to a transverse harmonic excitation are derived by using the principle of virtual work.For the simply supported rectangular plate,the Duffing strongly nonlinear vibration equation is obtained by using Galerkin method.Using the modified multi-scale method,the strongly nonlinear primary resonance is solved and the amplitude-frequency response equation is obtained.The stationary frequency-response curves and phase trajectory of the functionally graded plate are plotted.The effects of different parameters are discussed.Also,the results by modified multi-scale method are contrasted with those by a classical multi-scale method.