改进傅里叶方法在梁结构振动特性分析中的应用

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英文篇名：Application of Improved Fourier Series Method in Vibration Analysis of Beam Structures 作者：肖伟 ; 霍瑞东 ; 李海超 ; 高晟耀 ; 庞福振 英文作者：XIAO Wei;HUO Ruidong;LI Haichao;GAO Shengyao;PANG Fuzhen;China Ship Development and Design Center;School of Ship Engineering,Harbin Engineering University;92578 Troops,People's Liberation Army; 关键词：振动与波 ; 改进傅里叶级数 ; 梁结构 ; 振动特性 ; 弹簧刚度 ; 受迫振动 英文关键词：vibration and wave;;improved Fourier series;;beam structure;;vibration characteristics;;spring stiffness;;forced vibration 中文刊名：ZSZK 英文刊名：Noise and Vibration Control 机构：中国舰船研究设计中心;哈尔滨工程大学船舶工程学院;中国人民解放军92578部队; 出版日期：2019-02-18 出版单位：噪声与振动控制 年：2019 期：v.39 基金：国家重点研发计划课题资助项目(2016YFC0303406);; 哈尔滨工程大学博士研究生科研创新基金资助项目(HEUJIP201801);; 总装预研基金资助项目(6140210020105);; 工信部高技术船舶重大创新专项课题资助项目;; 国家自然科学基金资助项目(51209052);; 工信部高技术船舶资助项目;; 中央高校基本科研业务费资助项目(HEUCFD1515);; 中国博士后基金资助项目(2014M552661);; 海军预研基金资助项目等 语种：中文; 页：ZSZK201901004 页数：6 CN：01 ISSN：31-1346/TB 分类号：15-20

摘要

对一般边界条件下Euler-Bernoulli梁的振动特性展开研究。首先基于改进傅里叶法建立了梁结构的位移函数表达式,其中位移函数被表示为傅里叶余弦级数展开式与辅助多项式函数的叠加,其后基于最小势能原理建立拉格朗日方程,并通过Rayleigh-Ritz法进行求解,得到其固有模态及强迫振动响应。通过讨论旋转方向和横向弹簧刚度取值对计算结果收敛性的影响,验证了本方法的数值稳定性,得到用于模拟经典边界条件的弹簧刚度值。将计算结果与有限元法对比,验证了本方法的有效性。在此基础上对一般边界条件下梁结构受迫振动的响应特性进行研究,给出弹簧刚度值等参数对梁结构振动特性的影响规律。
        The vibration characteristics of Euler-Bernoulli beam under general boundary conditions are studied. Firstly,the displacement function expression of the beam structure is established based on the modified Fourier method. The displacement function is expressed as a superposition of a Fourier cosine series expansion and an auxiliary polynomial function,and the Lagrange equation is established using the principle of minimum potential energy. Then, the equation is solved by Rayleigh-Ritz method, and the characteristic equation of the beam structure is obtained. The natural frequency and mode shape of the beam structure can be obtained by solving the characteristic equation. By discussing the influence of rotation and lateral spring stiffness on the convergence of the calculation results, the numerical stability of the method is verified, and the spring stiffness values used to simulate several classical boundary conditions are obtained. The computation results of this method are in good agreement with those of the finite element method. Thus the accuracy of the method is verified. On this basis, the response characteristics of the forced vibration of the beam structure under different boundary conditions are compared mutually. Finally, the influences between the effects of the rotation direction and the stiffness of the transverse spring on the vibration characteristics of the beam structure are discussed.

引文

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