A CLOSED-FORM SOLUTION PROCEDURE TO THE VIBRA TlON OF NON-CLASSICALLY DAMPED SYSTEMS SUBJECTED TO HARMONIC LOADS

Abstract

The dynamic response of a multi-degree-offreedom  (MOP) sy"tem wIth non-proportional dampmg Juh)I'Cted /0 harmonic iooru iJ consIdered. Modal substituttOf1 is emplo~d to transform the coup/tid differentIal equation, of motiOn from geometric to modal coordinates. A.r
might be expected, the modal trans/ormotion does nOf uncouple the differential equations of motion because of the innl!renl lion proportional damping, but transforms them mto a system of coupled
olgebrOlc equations of convenient form Jor solul/On. The modal cOQrdmalu are Jhen easily deunnmed wIth the help of cooven/lOnal
techniques for solvmg systems of coupled equations. The method presented gives a dosed form sol,lIlOn witham the need to resort to iterative procedures, whIch wOtlld olh.erwlse be necessary
for other types of more Irregular excllGllOnJ like earthquake ground motrons Besides, I I presenled a /.whmque of compllmg th~ damp/TIg matrix of MDF $}'steml exhibiting dljJerem mechanisms of energy
d,ss/palron In dljJerfmt regions The application of the method IS Illus/roled on a two-ma.s.s sy.slem, whose foundollon mteracts ""ilh the supportmg SOil - a phenomenon ruulllllg to/ally to a four-degreeof
-freedom syslt!m