黏弹性三参数地基上Timoshenko梁横向自由振动

摘要

The complex modal analysis was developed to study the transverse vibration of a Timoshenko beam rested on three-parameter viscoelastic foundation. Complex frequency equations and modal function expressions were obtained for the beam with both ends pin-connected. The effects of foundation parameters on natural frequencies and modal functions were analyzed in numerical examples, and the characteristics of the Timoshenko beam were compared with those of a corresponding Euler-Bernoulli beam. The results show that all the natural frequencies increase with the increasing of the stiffness and the shearing parameters, and decreasing of the viscoelastic coefficients. The natural frequencies of the Timoshenko beam are slightly less than those of the Euler-Bernoulli beam.%运用复模态分析方法研究了黏弹性三参数地基上Timoshenko梁的横向振动特征，得到简支边界条件下的频率方程以及模态函数表达式。通过具体算例，分析了各项地基参数对固有频率和模态函数的影响，比较了相同地基上作用的Timoshenko梁和Euler-Bernoulli梁的振动特征。结果表明，随着地基刚度、剪切参数的增大以及黏性系数的减小，各阶固有频率值均增大；Timoshenko梁的固有频率略低于Euler-Bernoulli梁。