弹性边界梁振动特性模拟与人工弹簧刚度适配性研究

Simulation of Vibration Characteristics of Elastic Boundary Beams and Study on Adaptability of Artificial Spring Stiffness

边界条件是梁、板、壳结构振动特性求解与分析的重要条件,基于弹性边界梁的振动方程模拟任意边界条件是目前分析的热点,对梁的动力学分析也具有更重要的意义。本文基于能量法,采用人工弹簧技术,构建任意边界条件下欧拉梁结构动力学模型。选取改进的傅里叶级数作为梁结构位移容许函数,通过瑞利里兹程序进行求解,得到欧拉梁结构的振动特性。通过与有限元(ANSYS)计算结果对比,验证方法的准确性。在此基础上,研究人工弹簧刚度值与结构刚度值的对应关系,对人工弹簧刚度取值给出建议,实现弹簧刚度与结构刚度的合理适配。

Boundary conditions are important conditions for solving and analyzing the vibration characteristics of beams,plates,and shell structures.Simulating arbitrary boundary conditions based on the vibration equation of elastic boundary beams is a hot spot in current research,and it is also of greater significance for the dynamic analysis of beams.Based on the energy method and using artificial spring technology,this paper constructed a dynamic model of the Euler beam structure under arbitrary boundary conditions.The improved Fourier series was selected as the displacement allowable function of the beam structure and solved by the Rayleigh Ritz method to obtain the vibration characteristics of the Euler beam structure.The accuracy of the method was verified by comparing the results with the calculation results from the finite element code ANSYS.On this basis,the corresponding relationship between the artificial spring stiffness and the structural stiffness was studied,a reasonable value of the artificial spring stiffness was suggested,and the reasonable match of the spring stiffness and structural stiffness was obtained.