The pulse response of non-linear systems

The response of a non-linear, non-conservative, single degree of freedom system subjected to a pulse excitation is analysed. A transformation of the displacement variable is effected. The transformation function chosen is the solution of the linear problem subjected to the same pulse. With this transformation the equation of motion is brought into a form where Anderson's ultraspherical polynomial approximation is applicable for the solution of the problem. The method is applied to a cubic Duffing oscillator subjected to various pulses. The pulses considered are cosine, exponentially decaying and the step function. The analytical results are compared with the digital solution obtained on an IBM 360/344 system by using a Runge-Kutta fourth order method. The analytical results compare well with the digital solution.