非线性软弹簧型Duffing方程的解析解

Analytical solution of nonlinear soft spring Duffing equation

针对单自由系统中物体受非线性软弹簧作用时的Duffing方程,利用Anstz方法,在没有任何假设和近似的前提下,引入一个二阶常微分方程及其解,经过推演和变换,得到了Duffing方程的解析解,通过将解回代原方程,证明了其解答的正确性,并讨论了解答的适用初始条件。该方法得到的解答准确,形式简洁,便于在其他非线性Duffing方程的求解中应用。

By introducing Ansatz method, the analytical solution of the Dulling equation in the SDOF system is derived. The solution is exact because it is derived without any approximation. In the induction, the solution for a second order ordinary differential equation is used. By substituting the solution into the Dulling equation, the correctness of the solution is proved. The initial conditions for the analytical solution are discussed. The results show that the solution is simple and correct; it can be used to solve other nonlinear vibration Dulling equation. 1 fig, 6 refs.