基于转换矩阵法的中间带弹性支撑Rayleigh梁自由振动

摘要

以中间带弹性支撑Rayleigh梁模型为基础,采用转换矩阵法,推导得到跨度不同、单位长度质量不同、各跨刚度不同、中间带弹性支承、不同边界条件下Rayleigh连续梁的特征方程.通过算例分析中间弹性支承刚度与边界条件对连续Rayleigh梁模态的影响,给出了Rayleigh梁在不同跨高比和振型阶数下的频率与欧拉梁的差别.%Based on the model of the Rayleigh beam with intermediate elastic support, the paper derived the characteristic equation of Rayleigh continuous beam with different span,mass of unit length,stiffness,intermediate elastic support and boundary conditions,by the transfer matrix method. Then it analyzed the effect of stiffness of the intermediate elastic support and boundary conditions on the mode of continuous Rayleigh beam by an example,and showed the difference of the frequency between the Rayleigh beam and the Euler beam under different span depth ratio and vibration order.