梁振动方程的多辛Preissman格式

Multi-Symplectic Preissman Scheme for Solving Vibration Equation of Beams

考虑梁振动方程的一个多辛形式 ,并利用中点公式得到一个等价于多辛Preissman积分的新格式 ,用Fourier分析法 ,证明该格式是无条件稳定的 .最后给出数值例子 .数值例子表明 ,文中所给的格式是有效的 。

For solving vibration equation of beams, a symplectic form is considered; and a new scheme equivalent to multi-symplectic Preissman integrator is obtained by using midpoint formula; and the scheme is proved to be unconditionally stable by using the method of Fourier analysis. The scheme is effective and theoretical analysis coincides with actual calculation, as shown by numerical examples which are given finally.