第2章简谐激励受迫振动理论的应用

§2-5简谐激励受迫振动理论的应用(测振原理))sin(sin,0)()(2tYytYmymkzzczmthenyxzLetyxcyxkxm222222222)(1)()()()sin(pppcmkmYZtZz22)(1)(2tanppmkc§2-5简谐激励受迫振动理论的应用(隔振原理)yxm2k2kcF12YXn当22221nTkXXckXF220021,sinnnkFXtFF当YXFFTRnnDT2222121:传递率11,2nTR忽略阻尼时12122gfTRgmknXckXFXm2§2-4-5等效粘性阻尼(EquivalentViscousDamping)EnergyDissipatedbyDamping(阻尼对系统能量的耗散作用)Dampingispresentinallsystem(阻尼无处不在)internalmolecularfriction–结构阻尼Structuraldampingslidingfriction–库仑阻尼Coulombdampingfluidresistance–粘性阻尼ViscousdampingSincemathematicaldescriptionofdampingisquitecomplicate,simplifieddampingmodalsuchasviscoushasbeendevelopedtoevaluatethesystemresponse.等效阻尼(Equivalentdamping)Ceq:equatetheenergydissipatedbytheviscousdampingtothatofthenonviscousdampingforcewithassumedharmonicmotion22ddeqeqWWCXCXtheamplitudeofsystematresonant0nFXc结构阻尼(StructuralDamping)Fromexperimentsofmoststructuralmetals,dampingisindependentofthefrequencyandproportionaltothesquareoftheamplitudesindeqeqWXCXCmxxkxFt220,:,:ititititxXexiXeixmxkixFekmxkixFekiFXkmik0001complexstiffnessassumeharmonicmotionstructuraldampingfactorcomplexstiffnesskFX0,resonanceAtComparetoviscousdampingatresonance220kFX2222222201,1111,yrxiyxiFXHpwhereFRFLetiHyxyx1,0,1,2121222resonanceAtsin,tanmxcxkxFtpXkFppp02222021112021H()-yx,:.resnresresFXkXXX012107072whenSidebandshalfpowerpointsresXkXkFFppppp222002222222211222128141221ppppppp1212122212222212242121211Let0XX12212221p1211212QfffQnndampingstructuralFor