基于改进傅里叶级数法的任意边界下梁横振特性分析

Transverse Vibration Characteristics Analysis of Beam with General Boundary Conditions Based on Improved Fourier Series Method

【目的】船舶工程、海洋工程、汽车工程等相关领域涉及大量的梁结构,其振动特性直接关系到整体结构的振动控制。【方法】将梁结构横向振动位移采用一种改进傅里叶级数展开,运用Rayleigh-Ritz能量法进行求解,建立任意弹性边界条件下梁横向振动特性统一求解模型;在此基础上,分析不同边界条件对梁结构振动特性的影响规律。【结果与结论】基于改进傅里叶级数,利用Rayleigh-Ritz能量法建立的梁结构振动的求解模型与解析解基本相同,具有良好的准确性,且优于Ansys仿真解。本研究可为船海工程等梁结构振动机理研究与优化提供参考。

【Objective】Beam structure is widely used in various engineering occasions,such as ship engineering,ocean engineering,automobile engineering etc.,and its vibration characteristics have a directs influence on the vibration control of the whole structure.【Method】The transverse vibration displacement of the beam structure is expanded by a modified Fourier series and solved by the Rayleigh-Ritz energy method to establish a unified solution model for the transverse vibration characteristics of the beam under general elastic boundary conditions.With the model developed,the influence of different boundary conditions on the vibration characteristics of beam system is studied and discussed.【Result and Conclusion】Based on the improved Fourier series,the beam vibration model established by Rayleigh-Ritz energy method is basically the same as the analytical solution,with good accuracy and surpasses the Ansys simulation solution.The study provides a very important reference for the research and vibration optimization of beam structures in ship and ocean engineering.