黏弹性地基梁振动的微分求积法分析

探讨了黏弹性地基上有限长Euler-Bernoulli梁的横向振动.主要研究梁的固有频率和简谐均布荷载作用下的动力响应.将微分求积方法(DQ)直接应用于自由与受迫振动控制方程中.在简支边界条件下,得到横向自由振动的固有频率,并与复模态分析方法的结果进行比较.数值结果表明DQ与复模态分析方法得到的前七阶频率值高度吻合,但随着阶数的增长,两种方法数值间的微小差异值增大.数值结果还表明, 在均布简谐荷载作用下,经过短暂的瞬态响应后,梁的振动频率与外部荷载振动频率一致.

Differential quadrature method for vibration analysis of beams on viscoelastic foundations

This paper investigates transverse vibrations of finite Euler-Bernoulli beams resting on viscoelastic foundations.It studies natural frequencies and dynamic response of an elastic beam subjected to a harmonic load.The differential quadrature methods(DQ) are applied directly to the governing equations of the free and the forced vibrations that are two partial differential equations.Under the simple supported boundary condition,the natural frequencies of the transverse vibrations are calculated,and compared with the results of the complex modal analysis method.The natural frequencies and dynamic response are numerically studied.The numerical results obtained with the DQ are in good agreement with that of the complex mode analysis methods for the first seven orders,but with the growth of the orders,the small quantitative differences between them increase.Numerical results also illustrate that the beam vibrates with same frequency of external load under harmonic motion,after a short transient response.