求解悬臂梁受迫振动的时域DQ法

Forced Vibration of Cantilever Beams by Time-domain Differential Quadrature

针对悬臂梁分别施加突加荷载F(x,t)=Q与交变荷载F(x,t)=Q·sinωt时的定解问题,提出对控制微分方程及定解条件直接进行离散求解的时域DQ法.该方法在空间域和时间域均采用离散的DQ法,得到全部离散点挠度的可解线性方程组,求解该线性方程组即可得到全域位移场.算例分析结果表明,时域DQ法比有限元法速度快且精度高.

Aiming at the definite solution problems for suddenly applied load and alternative load put on cantilever beams,a time-domain DQ（ differential quadrature） method is presented in this paper which directly makes discrete solution to governing partial differential equation and definite condition.This method adopts discrete DQ both in space domain and time domain and obtains the system of linear equations of all the discrete point deflection. Solving this system of linear equations can obtain the whole domain displacement-field. The numerical examples show that the computational accuracy and efficiency of time-domain DQ method are better than that of finite element method.