矩形薄板动力响应的DQ半解析法研究

DQ Semi-analytic Method of Dynamic Response on Thin Rectangular plates

针对矩形薄板的动力响应问题,提出了一种有效的方法:DQ半解析法,本方法针对矩形薄板的振动控制微分方程,在空间域采用DQ法,即微分求积法(differential quadrature method),在时间域取级数,采用时域配点的方法,得到求解以板各节点动力响应位移场为全部待定参数的线性方程组,只需一次求解该方程组即得到全部待定参数,进而得到各节点的动力响应位移场,再由高阶Lagrange插值得到全域内的动力响应位移场.算例结果表明,本方法具有很高的精度和极佳的计算效率,且不受边界条件约束.

Based on the vibration theory of the rectangular plates, the issue about the dynamic response of plates is researched with a new method , which is called differential quadrature semi-analytic method . It adopts differential quadrature method in space domain and series in time domain on the basis of controlling partial differential equation, and gets DQ linear equations for solving all parameters of the displacement-field by adding timepoints, with that,it gets the dynamic response of the plates.