An equivalent linearization method for nonlinear Van der Pol oscillator subjected to random vibration using orthogonal functions

关键词:  Nonlinear system, equivalent linearization, orthogonal functions, Van der Pol oscillator, random vibration

Key words:  Nonlinear system, equivalent linearization, orthogonal functions, Van der Pol oscillator, random vibration

摘要:

This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse (BP) function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.

Abstract:

This paper deals with the idea of the orthogonal functions in the equivalent linearization of the nonlinear systems. Block Pulse (BP) function gives effective tools to approximate complex problems. The aim of this work is on using properties of the BP function as an orthogonal function in process of linearization. The BP functions have been used to propose an equivalent linearization method in the time domain to determine the unknown linearization coefficients. The accuracy of the proposed method compared with the other equivalent linearization approaches, including the regulation linearization and the dual criterion linearization methods. This study exploited the nonlinear Van der Pol oscillator system under stationary random excitation to demonstrate the feasibility of the proposed method. The validity of the analytical method is verified by applying different values of nonlinearity and intensity of excitation. Besides, by comparing the mean square responses and frequency response functions of the linearized systems for a wide range of nonlinearity depicted the present method is in agreement with other methods.