基于精细传递矩阵法的变厚度圆柱壳自由振动分析

江晨半1,王献忠2,3,左营营2,3

振动与冲击 ›› 2020, Vol. 39 ›› Issue (3) : 134-141.

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (3) : 134-141.
论文

基于精细传递矩阵法的变厚度圆柱壳自由振动分析

  • 江晨半1,王献忠2,3,左营营2,3
作者信息 +

Free vibration analysis for cylindrical shells with variable thickness based on precise transfer matrix method

  • JIANG Chenban1, WANG Xianzhong2,3, ZUO Yingying2,3
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摘要

结合精细积分和传递矩阵方法,对变厚度圆柱壳的自由振动进行计算分析。该方法基于圆柱壳的基本微分方程,推导得到关于位移内力向量的一阶齐次偏微分方程,采用精细积分求得场传递矩阵,将其进行组装得到总传递方程,根据边界条件求解总传递方程中系数矩阵的行列式,计算得到变厚度圆柱壳的固有频率。将计算结果与有限元结果进行对比,验证方法的准确性及有效性。同时探究了边界条件、厚度变化形式、厚度变化系数及长径比对自由振动的影响规律。

Abstract

Combining the precise integration and the transfer matrix method, free vibration of a cylindrical shell with variable thickness was calculated and analyzed.Based on basic equations of cylinder shells, first order homogeneous partial differential equations for a cylinder shell with variable thickness’s displacement and internal force vectors were derived to solve their field transfer matrices using the precise integration.The cylinder shell’s total transfer equation was assembled with the field transfer matrices obtained with precise integration.According to boundary conditions, natural frequencies of the cylindrical shell with variable thickness were calculated by solving determinant of coefficient matrix of the total transfer equation.The calculation results using the proposed method were compared with those using the finite element method to verify the correctness and effectiveness of the proposed method.Meanwhile, effect laws of boundary condition, thickness varying form, thickness variation coefficient and ratio of the cylinder shell’s length to diameter on its free vibration were explored.

关键词

精细积分 / 传递矩阵法 / 变厚度圆柱壳 / 自由振动

Key words

precise integration / transfer matrix method / cylindrical shells with variable thickness / free vibration

引用本文

导出引用
江晨半1,王献忠2,3,左营营2,3. 基于精细传递矩阵法的变厚度圆柱壳自由振动分析[J]. 振动与冲击, 2020, 39(3): 134-141
JIANG Chenban1, WANG Xianzhong2,3, ZUO Yingying2,3. Free vibration analysis for cylindrical shells with variable thickness based on precise transfer matrix method[J]. Journal of Vibration and Shock, 2020, 39(3): 134-141

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