弹性支承半无限直杆中的波动

Analysis of Wave Motion in Elastic-bearing Supported Half-infinite Straight Rod

由本构方程和动力学平衡条件,建立弹性直杆的波动方程.通过Fourier变换,将其变换到其频域.在频域中,求得了考虑线性滞回阻尼时杆的波动解,最后施行Fourier反变换,得到时域解.结果表明,对于线性参数体系的弹性支承半无限直杆,采用频域分析方法可以容易地处理具有复杂时域本构模型的问题,从而获得不同时刻杆振动的全貌.

Based on the constitutive equation and dynamic equilibrium condition of the straight elastic rod,the wave motion equation is established firstly,and then,through Fourier transform,the equation is converted into frequency domain.In the frequency domain,tooking the linear hysteretic damping of the rod into account,the wave motion solution is obtained in detail.Finally,the time domain solution is got via inverse Fourier transform.The results show that,for the linear parameter system of elastic-bearing supported straight half-infinite rod,by adopting the frequency domain analysis method,it is easy to treat the problem with complicated time domain constitutive relatives,thereby the full view of the rod vibration at different time can be taken.A new treatment method is provided to vibration in rod,and helps to the understand problems further such as the wave motion of the soil embeded pile subjected to hammering loads.