Highly Accurate Analytical Approximate Solutions to Mixed-Parity Duffing Equation

In this paper, a highly accurate analytical approximation solution method to a class of mixed-parity Duffing equation is proposed. The system may be attributed to the free vibration of laminated anisotropic plates or the simplified problem of particle vibration. The system is first analyzed qualitatively and subsequently, the analytic approximate periodic solution within the parametric range is constructed. The first approximate solution with a suitable initial condition can be obtained by using the proposed method. Subsequently, higher precision approximate solutions are constructed by combining Newton's method and harmonic balance method. These analytical solutions have excellent approximation accuracy as verified by numerical solutions derived from exact analytical expressions.

Automated summary

In this paper, a highly accurate analytical approximation solution method to a class of mixed-parity Duffing equation is proposed. The method first qualitatively analyzes the system and constructs an analytic approximate periodic solution within the parametric range. Higher precision approximate solutions are then obtained by combining Newton's method and harmonic balance method, showing excellent approximation accuracy compared to numerical solutions.