摘要
针对单自由度自治系统中常见的一类非线性振动Duffing方程,在没有任何假设和近似的前提下,引入anstz,利用一个2阶常微分方程及其解,经过等价变换,给出了该类方程的精确解法。本文以软弹簧型Duffing方程为例,通过将解回代原方程,证明了解答的正确性。还讨论了不同初始条件下软弹簧型Duffing方程精确解的形式。研究表明:该方法还可应用于其它非线性振动Duffing方程的求解。
Exact solution for a class of nonlinear vibration Duffing equation is derived. This kind of equation usually appears in an autonomous system with single degree of freedom. By introducing ansatz method and using the solution for a second order ordinary differential equation, we give an accurate solution method for this kind of equation. As an example, we derive the solution for the soft-spring type Duffing equation. This solution is exact because it is derived without any approximation. By substituting the solution into the Duffing equation, its correctness is proved. Moreover, different solutions for soft-spring type Duffing equation under different initial conditions is discussed. Research reveals the feasibility of the method. It can be used to solve other nonlinear vibration Duffing equation.
出处
《机械科学与技术》
CSCD
北大核心
2008年第6期764-765,共2页
Mechanical Science and Technology for Aerospace Engineering
