Analysis of Forced Response of a Damped Oscillator with Inertia and Static Nonlinearity using a Modified Lindstedt-Poincaré Method
Md. Zahangir Alam, Md. Alal Hosen
Abstract
The study presents an analysis of periodic solutions of a highly nonlinear oscillator that includes both the inertia and static nonlinearity. In addition, the oscillator is subjected to an external excitation, thereby increasing the complexity of the system’s behaviour. Recently, Alam et al. have presented a generalized modified Lindstedt-Poincaré method that covers a wide variety of nonlinear oscillators, including nonlinear oscillators with inertia and static nonlinearity. However, their method is useless if an external force is applied to the system. In this paper, an alternative modified Lindstedt-Poincaré method is proposed to investigate a damped, forced oscillator characterized by both inertial and static nonlinearities. Moreover, the resonance behaviour for various system parameters is investigated. The method is valid for both weak and strong nonlinearities. Finally, the accuracy of the analytical results is verified by comparing them with harmonic balance method (HBM) results and numerical results obtained using the Runge-Kutta fourth-order (RK4) method.
Conclusion
A modified Lindstedt-Poincaré method is presented to find a steady-state solution for a damped forced oscillator with inertia and static nonlinearity. The present method is simpler and more effective than the existing Lindstedt-Poincaré method for investigating nonlinear oscillators with strong nonlinearities and various damping conditions. The approximate results determined by the present method show surprisingly good agreement with those obtained by the numerical method.
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