ThepresentpaperinvestigatesthedynamicresponseoffiniteTimoshenkobeamsrestingonasixparameterfoundationsubjectedtoamovingload.ItisforthefirsttimethattheGalerkinmethodanditsconvergencearestudiedfortheresponseofaTimoshenkobeamsupportedbyanonlinearfoundation.ThenonlinearPasternakfoundationisassumedtobecubic.Therefore,theefectsofthesheardeformablebeamsandthesheardeformationoffoundationsareconsideredatthesametime.TheGalerkinmethodisutilizedfordiscretizingthenonlinearpartialdifferentialgoverningequationsoftheforcedvibration.ThedynamicresponsesofTimoshenkobeamsaredeterminedviathefourth-orderRunge–Kuttamethod.Moreover,theefectsofdiferenttruncationtermsonthedynamicresponsesofaTimoshenkobeamrestingonacomplexfoundationarediscussed.ThenumericalinvestigationsshowsthatthedynamicresponseofTimoshenkobeamssupportedbyelasticfoundationsneedssuperhigh-ordermodes.Furthermore,thesystemparametersarecomparedtodeterminethedependenceoftheconvergencesoftheGalerkinmethod.
