任意边界条件下带集中质量的连续多跨梁自振特性分析  

Analysis of Natural Vibration Characteristics of Continuous Multi-span Beams with Concentrated Mass under Arbitrary Boundary Conditions

作　　者：吴宗欢 王亚波 李冰冰 闻保健 马乾瑛[1] WU Zonghuan;WANG Yabo;LI Bingbing;WEN Baojian;MA Qianying(Department of Architecture and Civil Engineering,Chang'an University,Xi′an 710061,China)

机构地区：[1]长安大学建筑工程学院,西安710061

出　　处：《噪声与振动控制》2024年第1期52-58,85,共8页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(51208041);陕西省自然科学基金资助项目(2020SF-382,2014JM2-5080)。

摘　　要：提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hamilton原理得到频率特征矩阵,通过求解广义特征值求得自振频率及位移振型。随后,对所提出的方法的收敛性和精度进行讨论,与现有文献中的方法对比,该方法具有计算精度较高、收敛性好、收敛速度快等特点。讨论不同边界条件下截断数、跨数以及频率阶数之间的关系。最后通过工程中的实际案例说明该方法的实用性,与现有文献对比可知,其精度可达99.9%以上,由此验证了该方法的可靠性以及适用性。该方法易于通过编程实现快速计算,可为工程运用提供便捷有效的理论支撑。A method for solving the natural vibration characteristics of continuous multi-span beams with arbitrary concentrated mass under arbitrary boundary conditions is proposed.Firstly,the improved Fourier series method(IFSM)is used to determine the displacement shape functions of the beam,and the Lagrange equation of the beam is obtained by using Rayleigh-Ritz method.Then,the frequency characteristic matrix is obtained by Hamilton principle.By solving the generalized eigenvalue,the natural frequency and displacement mode shape are obtained.Finally,the convergence and accuracy of the proposed method are discussed.Compared with the existing literature,it is found that this method has the characteristics of high calculation accuracy,good convergence and fast convergence speed.The relations among truncation number,span number and frequency order under different boundary conditions are discussed.The practicability of the method is illustrated through practical engineering cases.Compared with the existing literature and methods,the accuracy of this method can reach more than 99.9%,which verifies the reliability and applicability of this method.The proposed method can realize the programming easily for fast calculation,which has provided a convenient and effective theoretical support for practical engineering application.

关 键 词：振动与波 连续多跨梁 集中质量 自振特性 IFSM法 Rayleigh-Ritz法 

分 类 号：O323[理学—一般力学与力学基础]