基于传递矩阵法分析ACLD圆柱壳振动控制问题的一种完全力电耦合模型

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振动与冲击 ›› 2011, Vol. 30 ›› Issue (6) : 147-152.

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基于传递矩阵法分析ACLD圆柱壳振动控制问题的一种完全力电耦合模型

李晓妮1,2; 向宇1; 黄玉盈2; 袁丽芸1,2; 陆静1,2

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A fully coupled electro-mechanical model based on transfer matrix method for vibration control of circular cylindrical shell with active constrained layer damping

LI Xiao-ni1,2;XIANG Yu1;HUANG Yu-ying2;YUAN Li-yun1,2;LU Jing1,2

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摘要

目前在ACLD薄壳结构的动力学分析中，通常采用一种忽略压电约束层面内电场强度，仅考虑在厚度方向为常量分布的法向电场强度的简化力电耦合模型。文中首先从理论上分析了简化力电耦合模型的局限性，进而提出了一种新的完全力电耦合模型，以此为基础导出了该模型下ACLD圆柱壳的一阶常微分矩阵状态方程，并结合传递矩阵法和齐次扩容精细积分法求解该方程。相对于传统三维模型方法，所建立的新模型和求解方法不仅大幅度简化了计算，而且适用于分析部分覆盖和任意支承条件下ACLD圆柱壳的振动控制问题。最后通过数值算例对完全力电耦合模型和简化力电耦合模型进行了比较，结果表明：简化力电耦合模型仅适用于低频分析；完全力电耦合模型具有更宽的频率适应性

Abstract

The commonly used model for dynamics analysis of the shell with active constrained layer damping (ACLD) is a simply coupled electro-mechanical model (SCEM). In this model the electric field is assumed to be negligible in the in-plane directions of piezoelectric layer and to be constant throughout the thickness in the normal direction. The reason for ineffectiveness of SCEM is firstly analyzed theoretically. A fully coupled electro-mechanical model(FCEM) is further developed. Then a first-order differential matrix equation for FCFM of thin ACLD circular cylindrical shell is derived. A high precision and high efficiency transfer matrix method based on the extended homogeneous capacity precision integration approach is employed to solve the matrix equation. Compared with the classical 3D method, the proposed method can greatly simplify computation, and be applied to analyze the vibration control problems of thin circular cylindrical shell partially treated with ACLD under arbitrary boundary conditions as well. Numerical results are given to compare with two kinds of models(SCEM and FCEM) at a wider frequency range. Both models agree exactly in the low-frequency range, whereas differ significantly in the high-frequency range. This confirms sufficiently SCME is only applicable to low-frequency vibration problems while FCEM can be used at a wider frequency range

关键词

力电耦合 / 主动约束层阻尼 / 圆柱壳 / 传递矩阵法 / 振动控制

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李晓妮;向宇;黄玉盈;袁丽芸;陆静;. 基于传递矩阵法分析ACLD圆柱壳振动控制问题的一种完全力电耦合模型[J]. 振动与冲击, 2011, 30(6): 147-152

LI Xiao-ni;XIANG Yu;HUANG Yu-ying;YUAN Li-yun;LU Jing;. A fully coupled electro-mechanical model based on transfer matrix method for vibration control of circular cylindrical shell with active constrained layer damping[J]. Journal of Vibration and Shock, 2011, 30(6): 147-152