黏弹性地基上欧拉梁的横向自由振动

摘要

研究了黏弹性三参数地基上有限长欧拉梁的横向自由振动.给出了简支边界条件下的频率方程和模态方程,进而推导出模型地基梁的固有频率和模态函数的解析表达式,提供了精确计算任意一阶频率和模态的简便方法.在具体算例中,运用推导出的公式能方便地计算出低阶和高阶频率的精确值,避免了以往数值方法带来的计算误差.同时通过具体算例分析了不同物理参数对黏弹性地基上欧拉梁的振动特性的影响.%This paper focuses on the free transverse vibration of an Euler-Bernoulli beam resting on three-parameter viscoelastic foundation.Under simply supported boundary conditions,the exact frequency equations and the modal functions are given,and the explicit formulae for natural frequencies and modal functions are derived.Therefore we provide a simple and convenient way to obtain analytical solution of any order natural frequencies and modal functions.In numerical examples,with the explicit formulae,the low and high order natural frequencies are calculated easily,avoiding calculation error from numerical methods.The effects of the different parameters of the Euler-Bernoulli beam and the viscoelastic foundation on the free vibration characteristics are also numerically demonstrated.