任意边界及耦合条件下的多跨梁结构振动特性  

Vibration analysis of multi-span beam system under arbitrary boundary and coupling conditions

作　　者：郑超凡[1] 吴晓光[1] 张成[1] ZHENG Chaofan;WU Xiaoguang;ZHANG Cheng(National Key Laboratory on Ship Vibration and Noise,China Ship Development and Design Center,Wuhan 430064,China)

机构地区：[1]中国舰船研究设计中心船舶振动噪声重点实验室,湖北武汉430064

出　　处：《中国舰船研究》2017年第4期95-101,共7页Chinese Journal of Ship Research

基　　金：国家自然科学基金资助项目(61503354)

摘　　要：[目的]为了克服边界及耦合条件对多跨梁结构振动特性研究的束缚,[方法]基于欧拉梁理论模型,采用Rayleigh-Ritz法建立多跨梁结构振动计算模型,对其在任意边界和任意弹性耦合条件下的自由振动特性进行研究。在传统三角余弦级数的基础上,引入4项辅助正弦三角级数,改善以往求解过程中在边界处存在的不连续或者跳跃现象。将位移容许函数的未知傅里叶展开系数看作广义变量,结合Rayleigh-Ritz法对其求极值,将结构的振动特性问题转换为求解一个标准特征值问题。[结果]通过与有限元计算结果进行对比,验证了收敛速度与计算精度。[结论]所得结果可为多跨梁结构的工程应用提供理论参考。In order to overcome the difficulties of studying the vibration analysis model of a multi-span beam system under various boundary and coupling conditions,this paper constructs a free vibration analysis model of a multi-span beam system on the basis of the Bernoulli-Euler beam theory.The vibration characteristics of a multi-span beam system under arbitrary boundary supports and elastic coupling conditions are investigated using the current analysis model.Unlike most existing techniques,the beam displacement function is generally sought as an improved Fourier cosine series,and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions.On this basis,the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh-Ritz method,and the vibration problem of multi-span bean systems is converted into a standard eigenvalue problem concerning the unknown displacement expansion coefficient.By comparing the free vibration characteristics of the proposed method with those of the FEA method,the efficiency and accuracy of the present method are validated,providing a reliable and theoretical basis for multi-span beam system structure in engineering applications.

关 键 词：改进傅里叶级数 任意边界条件 Rayleigh-Ritz法 多跨梁 结构振动 

分 类 号：U661.44[交通运输工程—船舶及航道工程]