摘要
为了获得任意边界条件下单跨梁结构的振动特性,采用改进傅里叶级数方法建立振动模型。由于传统傅里叶级数在边界处存在导数不连续和收敛性较差的问题,使用改进傅里叶级数可以有效改善其解的收敛性与准确性。在梁的两端边界处引入横向约束弹簧与旋转约束弹簧以通过改变其刚度值来模拟任意边界条件。在求解过程中首先建立梁的能量表达式,再通过瑞利-里兹法对其进行求解,最后使用数值计算软件对其进行数值仿真验证,并与已有文献的结果进行比较。该文所提方法合理,误差可控制在极小范围内,当边界条件改变时不需要对理论推导与数学计算过程重新推导,从而实现了单跨梁结构振动特性最为一般情况的预报。
Considering the bad convergence and discontinuities of displacement derivatives of traditional Fourier series at boundary points,we constructed an improved Fourier series to enhance the convergence and correctness of the series solution as a single-span beam free vibration analysis model with arbitrary boundary conditions was built. Linear and rotational springs were settled at both ends of the beam and the stiffness constants of springs were set to simulate arbitrary boundary conditions. In the solving process,we described the beam system based on energy principle and used the Rayleigh-Ritz method. Finally,we implemented numerical simulations to validate the method and compared the results with those in the existing literature. The results show that this method is reasonable and takes good accuracy. Therefore,when the boundary conditions change,there is no need to reformulate the theoretical model or modify the simulation in forecasting the vibration characteristics of single-span beam structure.
作者
鲍四元
曹津瑞
BAO Siyuan;CAO Jinrui(School of Civil Engineering,SUST,Suzhou 215011,China)
出处
《苏州科技大学学报（自然科学版）》
CAS
2019年第1期16-20,47,共6页
Journal of Suzhou University of Science and Technology（Natural Science Edition）
基金
国家自然科学基金资助项目(11202146)
关键词
任意边界条件
改进傅里叶级数法
振动特性
梁
瑞利-里兹法
arbitrary boundary condition
improved Fourier series
vibration characteristics
beam
Rayleigh-Ritz method
作者简介
鲍四元(1980-),男,安徽六安人,副教授,博士,研究方向:动力学与控制。
