噪声与振动控制2019，Vol.39Issue(1)：10-15,6.DOI:10.3969/j.issn.1006-1355.2019.01.003
改进傅里叶方法在梁结构振动特性分析中的应用
Application of Improved Fourier Series Method in Vibration Analysis of Beam Structures
摘要
Abstract
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.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Key words
vibration and wave/improved Fourier series/beam structure/vibration characteristics/spring stiffness/forced vibration分类
通用工业技术引用本文复制引用
肖伟,霍瑞东,李海超,高晟耀,庞福振..改进傅里叶方法在梁结构振动特性分析中的应用[J].噪声与振动控制,2019,39(1):10-15,6.基金项目
国家重点研发计划课题资助项目(2016YFC0303406) （2016YFC0303406）
哈尔滨工程大学博士研究生科研创新基金资助项目(HEUJIP201801) （HEUJIP201801）
总装预研基金资助项目(6140210020105) （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) （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) （HEUCFD1515）
海军预研基金资助项目等. （）
