Normal modes in damped systems

Abstract

A general review of normal mode theory as applied to the vibration of linear damped lumped parameter bilateral systems is presented. It is shown that systems possessing classical damping may always be solved by the method developed by Rayleigh. However, for more general type non-classical damping the method proposed by F. A. Foss must be used, The main differences between classical and non-classical normal modes are noted. A non-classically damped system which does not possess a mode type solution is solved by La place Transform techniques. The effect of damping on the natural frequencies of a linear system is discussed. It is shown that in classically damped systems increasing the damping decreases the natural frequencies of the system, With non-classical damping some of the natural frequencies of the damped system may be greater than the corresponding natural frequencies of the undamped system. From the perturbation analysis, used in determining the effect of damping on the natural frequencies of the system, the concept of equivalent classical damping for non-classically damped systems is derived. Experimental techniques needed to determine the mode shapes, natural frequencies, mass spring and damping matrices of classically damped systems are presented. By the use of the concept of equivalent classical damping an estimate of the damping matrix in non-classical systems may be obtained. Experimental results supporting the theory are presented.