渐硬恢复力型Duffing方程的精确解法

针对非线性振动分析中常见的渐硬恢复力型Duffing方程,首先建立了满足方程及初始条件的算子,运用相应的不动点理论,证明该算子在连续函数空间上有唯一不动点并可用迭代法求出.然后给出了该方程的精确解答及其迭代格式,并给出了对应的程序计算流程图.文末给出了该方法与Lindstedt-Poincaré(L-P)法计算结果.结果表明,该解答的不仅是正确的,而且迭代格式非常简洁,便于编程求解.此外,该方法可以应用于其他非线性系统Duffing方程的求解.

Exact solution of Duffing equation with hardening restoring force

In order to solve the Duffing equation with hardening restoring force, the operator that satisfies the equation and the initial condition is given. By using the fixed-point theorem, the uniqueness of solution in the space of continuous runetions is proven. The solution can be given by using iteration method. The iterative formulation and the flow chart of the program are listed. The numerical results of Lindstedt-Poincar6 method are given. The results show that the solution is correct and the computer program of this method is simple. This method can be used to solve other Dulling equation of nonlinear vibration.