湿热环境下反对称正交铺设双稳态扁壳的建模与非线性振动响应研究  

Modeling and nonlinear vibration response of antisymmetric cross-ply bistable shallow shell in humid and hot environment

作　　者：张博宇 张伟[1] ZHANG Boyu;ZHANG Wei(Beijing Municipal Key Lab of Nonlinear Vibrations and Strength of Mechanical Structures,Department of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China)

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

出　　处：《振动与冲击》2022年第19期80-89,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(11832002)。

摘　　要：对湿热环境下的反对称正交铺设双稳态扁壳进行了非线性动力学建模。在经典壳理论的基础上,考虑温度和湿度的影响,在本构方程中加入热膨胀系数和湿膨胀系数;联立相容方程和动力平衡方程以建立模型,得到了反对称正交铺设双稳态扁壳的偏微分运动控制方程;应用Galerkin方法对系统偏微分运动控制方程进行三阶离散,得到了三自由度的常微分运动控制方程。通过双稳态系统在主共振Ω接近于ω,内共振为1∶2∶2条件下的六维极坐标系和直角坐标系下的平均方程,得到了外激励幅值变化对反对称正交铺设条件下双稳态系统的非线性动力学特性的影响规律。Here,firstly,the nonlinear dynamic model of antisymmetric cross-ply bistable shallow shell in humid and hot environment was established.Based on the classical shell theory,considering effects of temperature and humidity,thermal expansion coefficient and wet expansion coefficient were added to the shell’s constitutive equation.Secondly,the model was established by combining the compatibility equation and the dynamic equilibrium equation,and the shell’s partial differential motion control equation was obtained.Finally,Galerkin method was used to discretize the system’s partial differential motion control equations,and ordinary differential motion control equations with 3-DOF were obtained.Through using average equations in a 6-D polar coordinate system and a rectangular coordinate system under the condition of the main resonanceΩof the bistable system being close toωand the internal resonance being 1∶2∶2,influence laws of amplitude variation of external excitation on nonlinear dynamic characteristics of the bistable system under the condition of antisymmetric cross-ply were obtained.

关 键 词：反对称正交铺设 双稳态壳 伽辽金离散 非线性动力学 

分 类 号：O322[理学—一般力学与力学基础]