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

张博宇,张伟

振动与冲击 ›› 2022, Vol. 41 ›› Issue (19) : 80-89.

PDF(1959 KB)
PDF(1959 KB)
振动与冲击 ›› 2022, Vol. 41 ›› Issue (19) : 80-89.
论文

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

  • 张博宇,张伟
作者信息 +

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

  • ZHANG Boyu, ZHANG Wei
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文章历史 +

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

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

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

Key words

Antisymmetric cross-ply / Bistable shell / Galerkin discretization / Nonlinear dynamics

引用本文

导出引用
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[J]. Journal of Vibration and Shock, 2022, 41(19): 80-89

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