Amethodtocalculatethestationaryrandomresponseofanon-classicallydampedstructureisproposedthatfeaturesclearly-definedphysicalmeaningandsimpleexpression.Themethodisdevelopedinthetrequencydomain.Theexpressionoftheproposedmethodconsistsofthreeterms,i.e.,modalvelocityresponse,modaldisplacementresponse,andcoupled(betweenmodalvelocityandmodaldisplacementresponse).Numericalresultsfromtheparametricstudyandthreeexamplestructuresrevealthatthemodalvelocityresponsetermandthecoupledtermareimportanttostructuralresponseestimatesonlyforadynamicsystemwithatunedmassdamper.Intypicalcases,themodaldisplacementtermcanprovideresponseestimateswithsatisfactoryaccuracybyitself,sothatthemodalvelocitytermandcoupledtermmaybeignoredwithoutlossofaccuracy.Thisisusedtosimplifvtheresponsecomputationofnon-classicallydampedstructures.Forthewhitenoiseexcitation,threemodalcorrelationcoefficientsmclosedformarederived.Toconsiderthemodalvelocityresponsetermandthecoupledterm,asimplifiedapproximationbasedonwhitenoiseexcitationisdevelopedforthecasewhenthemodalvelocityresponseisimportanttothestructuralresponses.Numericalresultsshowthattheapproximateexpressionbasedonwhitenoiseexcitationcanprovidestructuralresponseswithsatisfactoryaccuracy.
