Modal Analysis of Undamped MDOF Vibratory System

This paper deals with the numerical estimation of natural frequencies and mode shapes using basic vibration theory for two and three Degree of freedom (DOF) vibratory system. The procedure can be extended to an ‘n’ DOF vibratory system easily. The equations of motion are dependent on each coordinate. The principle of orthogonality of mode shapes is used to convert the physical coordinate system into a generalised coordinate system which gives rise to an n-uncoupled differential equations. Response for free vibrations for each DOF can be obtained for different initial conditions to analyse the system. It can be realised that the response for an arbitrary initial displacement to the masses is the superposition of responses for each mode of vibration.