悬臂Rayleigh梁横向振动固有频率

摘要

Considering the rotary inertia based on the Euler-Bernoulli beams,the transverse vibration of a cantilever beam is studied.The widely applicable integral equation method is employed to obtain the approximate solutions of characteristic equation and then the natural frequencies of a cantilever beam.Comparison of the numerical solutions obtained through integral equation method,stress function method,and ritz method shows the effectiveness of the integral equation method.%在Euler-Bernoulli梁基础上考虑转动惯量,研究悬臂梁的横向振动问题.采用广泛适用的积分方程方法求解该问题,求出悬臂梁自由振动特征方程的近似解,获得悬臂梁振动固有频率的数值解答.积分方程方法与应力函数法、瑞兹法所得数值结果进行对比,表明了该方法的有效性.