轴向载荷条件下弹性边界约束梁结构振动特性分析

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摘要本文采用改进傅里叶级数展开建立了轴向载荷条件下弹性边界约束梁结构振动分析模型。通过在梁结构两端引入平动和旋转位移约束弹簧，相应设置约束弹簧刚度系数可以实现对任意边界条件及其组合的模拟。梁结构振动系统位移场采用傅里叶级数附加边界光滑函数进行构建，利用能量原理建立轴向载荷作用下梁结构总动能、总势能和外力做功项，并结合瑞利-里兹步骤获得系统特征矩阵方程。通过数值算例，验证了本文模型对不同边界条件、轴向载荷作用下梁结构振动特性分析的正确性与可靠性。在此基础上，研究了边界约束弹簧横向刚度、旋转刚度、轴向载荷等系统参数及激振力对梁结构振动特性的影响。本文模型具有高效、高精度等特点，为研究轴向载荷作用下复杂边界条件梁结构振动行为提供了有效分析手段。

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	赵雨皓
	杜敬涛
	许得水

关键词 ：轴向载荷, 梁结构振动, 弹性边界约束, 傅里叶级数

Abstract：In this paper, an improved Fourier series expansion is employed to establish the vibration analysis model of an axially loaded beam with elastic boundary restraints. Through the introduction of translational and rotational restraining springs at both ends, any types of classical boundary condition and their combination can be simulated by setting the stiffness coefficients accordingly. The vibrational displacement of beam structure is expanded as the superposition of Fourier series and boundary smoothed terms. According to the energy principle, the total kinetic energy, total potential energy and external force of the whole system are formulated, and the system characteristic matrix is obtained in combination with Rayleigh-Ritz procedure. Numerical examples are then given to verify the correctness and reliability of the proposed model for the vibration characteristics analysis of beam structure under different boundary conditions and axial loads. Based on this, the influence of system parameters, including boundary restraining stiffness, axial load and force excitation, on the vibration characteristics of beam structure is investigated. The proposed model has the advantages of high efficiency and precision, which can provide an effective analytical tool for studying the vibration behavior of axially loaded beam with complex boundary conditions.

Key words： Axially loaded Beam structural vibration Elastic boundary restraint Fourier series

收稿日期: 2019-04-10 出版日期: 2020-07-28

引用本文:

赵雨皓，杜敬涛，许得水. 轴向载荷条件下弹性边界约束梁结构振动特性分析[J]. 振动与冲击, 2020, 39(15): 109-117.
ZHAO Yuhao, DU Jingtao, XU Deshui. Vibration characteristics analysis for an axially loaded beam with elastic boundary restraints. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(15): 109-117.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I15/109

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