In-plane free vibration analysis of multi-span curved beams with elastic support and connecting boundary conditions

Q4 Energy

哈尔滨工程大学学报 Pub Date : 2012-06-01 DOI:10.3969/J.ISSN.1006-7043.201107007

Haijun Zhou, Wanyou Li, Binglin Lü, Wenlong Li

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引用次数: 0

Abstract

According to the vibration problem of a curved beam with elastic support boundary conditions,the in-plane free vibration characteristics of multi-span curved beams were analyzed using an improved Fourier series method.The transverse and tangential displacement functions were sought as a Fourier cosine series,and an auxiliary polynomial function was introduced to take all the relevant discontinuities of the elastic boundaries.The Rayleigh-Ritz method was used to solve Hamilton's equation,which is based on the energy principle,and a standard eigenvalue problem concerning the unknown displacement amplitudes was derived from which the natural frequencies and mode shapes can be solved.The results of single-span and two-span curved beams with free,simple supported,clamped,and elastic supported boundary conditions were obtained and compared with the results acquired from the finite element method(FEM) to validate the correctness of the presented method.Furthermore,the effect of the connecting stiffnesses between two-span curved beams on the first four frequencies was described.

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具有弹性支承和连接边界条件的多跨弯曲梁面内自由振动分析

针对具有弹性支承边界条件的弯曲梁的振动问题，采用改进的傅立叶级数法分析了多跨弯曲梁的面内自由振动特性。将横向位移函数和切向位移函数求为傅里叶余弦级数，并引入辅助多项式函数取弹性边界的所有相关不连续点。采用基于能量原理的瑞利-里兹法求解Hamilton方程，导出了包含未知位移幅值的标准特征值问题，并由此求解了固有频率和模态振型。分别对自由、简支、固支和弹性支边界条件下的单跨和双跨弯曲梁进行了计算，并与有限元法计算结果进行了比较，验证了所提方法的正确性。进一步分析了两跨弯曲梁连接刚度对前4个频率的影响。

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来源期刊

哈尔滨工程大学学报 Energy-Nuclear Energy and Engineering

CiteScore

0.90

自引率

0.00%

发文量

6802

期刊介绍：