MODIFIED ENERGY METHOD FOR A CLASS OF STRONGLY NONLINEAR VIBRATION SYSTEM

The energy method is a approximately analytical approach frequently used in solving strongly nonlinear systems. The calculation is simplified due to ignoring the affection of instantaneous work done by exciting and damping force. But it will generate biggish error when the system suffers high disturbance. The cause of the error is unveiled and the classical energy method is improved in the paper. A new analytical approach, modified energy method(MEM), is developed at last. Analytical solution of strongly nonlinear nonautonomous systems is proposed based on MEM for dynamic foundations, and numerical calculation is carried out with Runge-Kutta method for the system. The results of numerical analysis show that MEM is more accurate than classical energy method, even under subharmonic vibration with high disturbance.