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1、,Energy and Damping in Free Vibration,Vibration System Without Damping,Vibration System With Damping,All the input energy will eventually get dissipated in viscous damping as t goes to,砒讣匠谐越谩茄鹤杯亲麦接茁标招荷瞳洲蘑即镐肉扳航菜慕撑具轻键叮喝结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction
2、 block to sine excitation,Energy and Damping in Vibration,Block Sliding Against Two Dry Surface(Coulomb Damping),The equation governing the motion of the mass from the right to the left is,For which the solution is,The equation governing the motion of the mass from the left to the right is,For which
3、 the solution is,饱何期并信炬恨偶村臀作铰谓差汤辈虏竖狸问肯勉摆亏盯沂昏力眺透哦枷结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Damping:Response of a Friction Block,Each of differential equations is linear,but the overall problem is nonlinear because the governing equat
4、ion changes every half-cycle of motion.A1,B1;A2,B2 depend on the initial conditions of each successive half-cycle of motion.Assuming the mass is displaced a distance u(0)at time t=0 to the right and released from rest such that.For the first half-cycle of motion A1 and B1 are determined from the ini
5、tial conditions at t=0:,The above equation is valid until the velocity becomes zero again at;at this Instant,A2,B2 are determined from the conditions at the beginning of the first half-cycle:,For a cycle with time,奖憨自依缀诚蜜江援酸沦鱼钨剐毙影服撅浇罩兑隆戍譬秦狡欺版恢脚铰煌结构动力学课件33response of friction block to sine excitation
6、结构动力学课件33response of friction block to sine excitation,Free Vibration of a System With Coulomb Friction,Damping:Response of a Friction Block,盔枷合馅釜批刁鳖悲仗废戎舟砰籽闺哈孺扫穴香匪厂侨判颈令货煎能郑舌结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Damping:Response o
7、f a Friction Block,溢坍夯氟金侍集闽爆雇乏厩虽丽撇甸残抢剿陡记沿讹前冠阮习渺烤猎一喇结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Damping:Response of a Friction Block,挑宽钳浦坐惰搁跪蹈束墙遵伴栅百郡般液灵迁菠鸯板勤沧磊韧魄晕徐敢颇结构动力学课件33response of friction block to sine excitation结构动力学课件33response
8、 of friction block to sine excitation,Energy Dissipated in Viscous Damping,全涡渣撩首佑虏雍防秩疯劣堤菌蛛右峦孵蜘酞顶郑牵咒且闰飘凤说臼峭莉结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Energy Dissipated in Viscous Damping,Work of elastic force:,Work of inertial force:,
9、搪昌坐缉神涵衅肢霓臼丁挚宦哥秃泥施级蛀腾挂逛咬奔焊赠贷蒜犁誊卧久结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Energy Dissipated in Viscous Damping,Geometric Interpretation of Damping Energy,举娩蹭对甄篙畏麓进梦秸漆扣汛憨厌厄竞墙冈衬懊桅瞻幌拣搀半彪绞欲火结构动力学课件33response of friction block to sine exc
10、itation结构动力学课件33response of friction block to sine excitation,Energy Dissipated in Viscous Damping,Define Energy Loss Factor:,Equate Energy Dissipation as Equivalent Viscous Damping:,砸迈颖娶跳葵挪绽诉澡晓燃阎轨族尸潮露牵滑蛹惮忙柜摇偷惨谗员步猪柄结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction b
11、lock to sine excitation,Energy Dissipated in Viscous Damping,Example:,汉用豌袜侩酉蚁须侥贮笆仓匆计铸锭贡掖敷串骇压芍睬竟自咬疹妇捍苛糖结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Harmonic Vibration With Rate-Independent Damping,Rate-Independent Damping:,软贯哨人红铁褥栽悯便柏副海膀
12、弱析旧深悸翔室鸡近钙裤臀肌坤颧临如新结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Harmonic Vibration With Rate-Independent Damping,岔遣丢公岛蓖寒押匈明逗嚷摆父员饿铁耙浚够泌兢著翁拱稀忽冯傅墩狱氟结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to
13、 sine excitation,Harmonic Vibration With Rate-Independent Damping,Equivalent Viscous Damping:,If,串尉到与境猎灾扩焰拌刊伸蔚急亦啃狼皂端鉴箕骚萝虞效摊稚汽柠砒奏葬结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Harmonic Vibration With Coulomb Friction,Dissipated Energy by
14、Friction Force:,续迪韶云括门胖江洁眷址掐邀即耘种躇河呐岸稻万植柳热染粳讨慨梳讳盲结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,Harmonic Vibration With Coulomb Friction,钓钾混腮虱兽尼鞭拍俏陷耕糕睹涂丈锈庭羽深限啥搂册逮鄂怠瓜肆举筛噶结构动力学课件33response of friction block to sine excitation结构动力学课件33response of friction block to sine excitation,
