Block pulse transform method for linearization of nonlinear SDOF systems

Abstract

This paper addresses a linearization technique for a linearizable nonlinear SDOF system based on block pulse (BP) transform. BP transform method is a useful tool for giving a solution of difference equations with less computational costs. The main goal of this work is on reducing the costs of linearizing computation. It is necessary to compare the results obtained using this method with other traditional methods to verify the effectiveness of the proposed method. Therefore, the efficiency of BP transform method is compared with the traditional equivalent linearization (EL) method, used to linearize nonlinear systems. Two numerical simulations are applied to the Duffing oscillator system to demonstrate the feasibility of the proposed method based on BP transform. Finally, the results of comparison between existing approaches that have applied to the considered problem depicted the proposed method base on orthogonal functions is able to approximate the nonlinear system’s behavior and shows the superiority of the proposed approach in the sense that it is more accurate by computational advantageous.

Keywords

• linearization
• block pulse transform
• nonlinearity
• duffing oscillator