Direct Method for the Determination of Coefficients of Characteristic Equation of a MDOF System

Abstract

Dynamic response of any single degree of freedom (SDOF) vibratory system is studied by evaluating its natural frequencies whereas that of any multi degree of freedom (MDOF) vibratory system is studied by evaluating its natural frequencies and corresponding mode shapes. Efficient method to determine the natural frequencies and mode shape of a MDOF system is to determine its dynamic matrix and to calculate its eigen-values and eigen-vectors. As the number of degree of freedom (DOF) of the system increases, the size of the dynamic matrix increases and the use of a computer program or package become essential. Hence this paper proposes a new method to directly calculate the coefficients of characteristic equation of any degree of freedom system from which eigen-values and then natural frequencies can be determined.