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

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摘要首先，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。其次，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。最后应用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接近于，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。
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

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	张博宇
	张伟

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

Abstract：Firstly, the nonlinear dynamic modeling of antisymmetric cross-ply bistable shallow shell in hot and humid environment is carried out. Based on the classical shell theory and considering the effects of temperature and humidity, the thermal expansion coefficient and wet expansion coefficient are added to the constitutive equation. Secondly, the compatible equation and the dynamic equilibrium equation are combined to establish a nonlinear dynamic model for the antisymmetric cross-ply laminated bistable shell. Finally, Galerkin discretization is conducted on the vibration partial differential equation to obtain the three-degree-of-freedom nonlinear ordinary differential equation. The averaged equation under the polar coordinate system and the averaged equation under the rectangular coordinate system is used to study the non-linear dynamics in the antisymmetric bistable shallow shell. The influence law of the external excitation parameters on the system is explored and the system’s non-linear dynamic behavior characteristics are explored when the main resonance is close to and the internal resonance is 1: 2: 2.
Keywords: Antisymmetric cross-ply; Bistable shell; Galerkin discretization; Nonlinear dynamics

Key words： Antisymmetric cross-ply Bistable shell Galerkin discretization Nonlinear dynamics

收稿日期: 2021-07-29 出版日期: 2022-10-15

引用本文:

张博宇，张伟. 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[J]. 振动与冲击, 2022, 41(19): 80-89.
ZHANG Boyu, ZHANG Wei. Modeling and nonlinear vibration response of antisymmetric cross-ply bistable shallow shell in humid and hot environment. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(19): 80-89.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I19/80

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