任意边界条件下弹性梁耦合振动特性分析

李海虹1,王昊1,郭山国2,刘志奇1,李王铎1

振动与冲击 ›› 2022, Vol. 41 ›› Issue (17) : 48-54.

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (17) : 48-54.
论文

任意边界条件下弹性梁耦合振动特性分析

  • 李海虹1,王昊1,郭山国2,刘志奇1,李王铎1
作者信息 +

Coupled vibration characteristics analysis of elastic beam under arbitrary boundary conditions

  • LI Haihong1, WANG Hao1, GUO Shanguo2, LIU Zhiqi1, LI Wangduo1
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摘要

采用谱几何法建立了任意边界条件下弹性梁横向、纵向和扭转耦合振动分析模型。将弹性梁的横向、纵向和扭转振动位移函数分别描述为一种辅助函数为三角级数的改进傅里叶级数;在弹性梁两端引入边界约束弹簧组,通过改变其刚度值模拟任意边界条件;应用Hamilton原理从能量角度推导整个结构的拉格朗日函数;采用Ritz法对其进行求解。计算了弹性梁模型不同边界下前6阶固有频率,与文献解对比最大误差为0.02%,验证了文中方法的正确性和较快的收敛性。该模型统一了弹性梁横向、纵向和扭转振动的位移函数表示形式和模态特性求解方程,通过改变边界约束弹簧刚度系数可以实现对弹性梁耦合振动特性进行调整,为弹性梁动力学性能优化提供了一种参数化的研究方法。
关键词:弹性梁;耦合振动;谱几何法;任意边界条件

Abstract

A coupled model was established to analyze the transverse, longitudinal, and torsional vibration of elastic beams under arbitrary boundary conditions based on the Spectro-Geometric method. The vibration displacement functions of elastic beams were respectively expressed as improved Fourier series whose auxiliary functions were trigonometric series. The boundary restraining springs were introduced at both ends of the beam and the stiffness value of springs was changed to simulate arbitrary boundary conditions. Hamilton’s principle was employed to derive the Lagrangian function of the structure and the Ritz method was used to get the solution. The first 6 order natural frequencies under different boundaries of beams were calculated, with the maximum error of 0.02% compared with literature solutions. The correctness and fast convergence of the method were validated. The displacement function representation form and modal characteristic solution equations of the transverse, longitudinal, and torsional vibration of elastic beams were unified. The results show that coupled vibration characteristics of elastic beams could be adjusted with changing boundary spring stiffness coefficients, which provides a method for parametric studies on the optimization of the dynamic performance of elastic beams.
Key words: elastic beams; coupled vibration; Spectro-Geometric method; arbitrary boundary conditions

关键词

弹性梁 / 耦合振动 / 谱几何法 / 任意边界条件

Key words

elastic beams / coupled vibration / Spectro-Geometric method / arbitrary boundary conditions

引用本文

导出引用
李海虹1,王昊1,郭山国2,刘志奇1,李王铎1. 任意边界条件下弹性梁耦合振动特性分析[J]. 振动与冲击, 2022, 41(17): 48-54
LI Haihong1, WANG Hao1, GUO Shanguo2, LIU Zhiqi1, LI Wangduo1. Coupled vibration characteristics analysis of elastic beam under arbitrary boundary conditions[J]. Journal of Vibration and Shock, 2022, 41(17): 48-54

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