State Space Method to Predict the Modal Model of a Five Degree of Freedom Spring Mass Vibratory System

Abstract

AbstractIn this paper, a state space method is used to predict the modal model of a five degree of spring-mass vibratory system. To predict the modal model, various MATLAB commands such as ‘lsim’ to obtain the response in time domain and ‘freqresp’ to obtain the response in the frequency domain are used. In this work, state space formulation is used to convert the five degree coupled equations into single degree an un-coupled second order differential equations. Then the state space entities such as system matrix, input matrix, output matrix and direct transmission matrix will be predicted. The main objective of this work is to predict the response of the system at different masses by applying unit impulsive load excitations. To solve the Eigen value problem MATLAB ‘eig’ command is used. It is observed that the state space formulation is very simple and easy to apply for n-degree of freedom system model. Also, it can be concluded that the state space method formulation along with MATLAB commands is very effective to predict the response of the system either in time domain or in frequency domain.KeywordsState space methodCoupled equationsTime domainFrequency domainVibrationsModal analysis