Modal Reduction of Viscoelastic Beam Cosidering Higher Order System

Abstract

Most of the finite element models are very large in size with thousands of degrees of freedom Modal reduction techniques are applied to reduce the size of large finite element models to give faster computations of the required dynamic characteristics. There are many model reduction techniques which are used to model the system with small amount of errors. A popular method of model reduction is balanced reduction method. The present work consists of the study of full modal and reduced modal vibrational dynamic characteristics of a simply supported beam considering higher order with viscoelastic materialistic nature which is based on Euler-Bernoulli beam theory. The typical characteristics of a viscoelastic material depends on temperature, strain, dynamic excitation, etc.., The main objective of this work is to do modal reduction of the higher order viscoelastic material using balanced truncation (or) reduction (or) realization and to compare the results with full modal. For this, a fourth order equation of motion is developed for a simply supported beam with viscoelastic linear damping for different temperatures. Frequency, time and transient responses of the beam are plotted by using MATLAB software. Model reduction is done via balanced truncation