不同阶外激励下压电纤维复合材料悬臂板的内共振特性分析  

THE INFLUENCE OF DIFFERENT ORDER EXCITATIONS ON RESPONSES OF PIEZOELECTRIC FIBRE COMPOSITE PLATES WITH MULTI INNER RESONANCE

作　　者：郭翔鹰[1,2] 段梦烨 Guo Xiangying;Duan Mengye(Department of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China;Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures,Beijing 100124,China)

机构地区：[1]北京工业大学材料与制造学部,北京100124 [2]非线性振动与机械结构强度北京市重点实验室,北京100124

出　　处：《动力学与控制学报》2021年第5期23-32,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11572006,11772010)。

摘　　要：本文研究了不同阶横向激励作用下压电纤维复合材料(MFC)悬臂板的非线性动力学特性.基于Reddy一阶剪切板理论,引入von Kármán几何非线性理论,利用Hamilton原理建立了结构的非线性动力学控制方程.讨论在不同结构尺寸下的前三阶固有频率,利用Galerkin方法将系统离散为三自由度的非线性常微分方程.考虑主参数共振-1:3:5内共振,分析不同阶外激励作用下压电纤维复合悬臂板的非线性振动响应.数值模拟结果表明,复合材料板几何尺寸增大时结构的固有频率降低.此外,不同阶的横向激励幅值对结构的非线性振动影响很大,为实际工程应用提供理论支持.The paper investigates nonlinear dynamical characteristic of a macro fibre composite(MFC)plate subjected to transversal excitations. Nonlinear governing equations for the MFC plate are established based on Reddy’s first-order shear deformation theory,von Karman geometrical nonlinear kinematics and Hamilton’s principle. To analyze complex inner resonance phenomenon of the MFC plate,the first three order natural frequencies and the relationships of various internal resonances with different physical dimensions are discussed under different order excitations,and Galerkin’s approach is employed to discretize the partial differential governing equations into a three-degree-of-freedom nonlinear system. Then,stability analysis is conducted to investigate influences of related parameters on nonlinear behaviors of the composite plate. The results of numerical simulation show that increase of plate size will lead to decrease of both the natural frequencies and dynamic stability of the plate. Moreover,the different order transversal excitation has great effects on the nonlinear dynamics of the structure. The results will provide theoretical supports for practical engineering applications.

关 键 词：压电纤维复合材料 非线性 稳定性分析 内共振 

分 类 号：TB33[一般工业技术—材料科学与工程]