哈工大课件机械系统动力学DynamicsofMechanicalSyst18748.pptx

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1、机械系统动力学机械系统动力学机电工程学院机电工程学院 机械设计系机械设计系ChenZhaobo(陈照波)Tel:86412057E-mail:机械楼一楼1020室参考书1.闻邦椿等闻邦椿等机械振动理论及应用机械振动理论及应用 高等教育出版社高等教育出版社2.胡海岩胡海岩 机械振动基础机械振动基础 北京航空航天大学出版社北京航空航天大学出版社 3.师汉民师汉民 机械振动系统机械振动系统 华中科技大学出版社华中科技大学出版社4.W.T.Thomson 振动理论及应用振动理论及应用 清华大学出版社清华大学出版社考核办法累加式1.大作业大作业1 10%2.大作业大作业2 10%3.平时表现平时表现 1

2、0%4.期终考试期终考试 70%PrefaceWhatisdynamics？Dynamicsfocusesonunderstandingwhyobjectsmovethewaytheydo.Dynamics=Kinematics+KineticsKinematicsisthestudyofthemotionofpointmassesorrigidbodies.Kinetics isthestudyoftheforceswhichcauseandaffectmotion.Whatismechanicalsystem?lStructurelMechanismlMachineDevelopments

3、tagesofdynamicsofmechanicalsystems:lStaticanalysislKineto-staticanalysislDynamicanalysislElasto-dynamicanalysisWhytostudydynamicsofmechanicalsystem?lHigherspeedlHigherprecisionlMoreflexiblelMorecomplicatedResonanceWhenaforcingfrequencyisequaltoanaturalfrequencyPrerequisites:Themostimportantprerequis

4、iteisordinarydifferentialequations.Youshouldbepreparedtoreviewundergraduatedifferentialequationsifnecessary.COURSE GOALS:1.Tobecomeproficientatmodelingvibratingmechanicalsystems.2.ToperformdynamicanalysissuchasfreeandforcedresponseofSDOFandMDOFsystems.3.Tounderstandconceptsofmodalanalysis.4.Tounders

5、tandconceptsinpassiveandactivevibrationcontrolsystems.Chapter1SingledegreeoffreedomsystemsObjectivesRecognizeaSDOFsystemBeabletosolvethefreevibrationequationofaSDOFsystemwithandwithoutdampingUnderstandtheeffectofdampingonthesystemvibrationApplynumericaltoolstoobtainthetimeresponseofSDOFsystemSingled

6、egreeoffreedomsystemsWhenone variablecandescribethemotionofastructureorasystemofbodies,thenwemaycallthesystema1-D system orasingledegreeoffreedom(SDOF)system.LkmxmstUnloadedSpringBody inequilibrium(at rest)Body in motionAt equilibrium,kst=mgUndampedSpring-MassSystemk(st+x)x mg=mx.FreeBodyDiagramEqua

7、tionsofmotionSumforces:Rearrangetoyieldthefamiliarequationofmotion:PhysicalmodelMathematicalmodellRestoringforcelDampingforceUndampedFreeVibrationDifferentialequationSolvingODElProposedsolution:lIntoODEyougetthecharacteristicequation:lGiving:lTheproposedsolutionbecomes:lForsimplicity,letsdefine:lGiv

8、ing:LetsmanipulatethesolutionRecallManipulatingthesolutionlSolutionwehave:lRewriting:lGiving:FurthermanipulationlSolutionwehave:lLet:lGiving:DifferentformsofthesolutionNote!NaturalfrequencylInthepreviouslyobtainedsolution:lThefrequencyofvibrationislItdependsonlyonthecharacteristicsofthevibrationsyst

9、em.Thatiswhyitiscalledthenatural frequencyofvibration.Naturalfrequencylnaturalfrequencyfromstaticdeflection.lnaturalfrequencyfromenergymethod.Recall:InitialConditionsAmplitude&phasefromICsUndampedfreeresponseAddingDampingDampingoDampingissomeformoffriction!oInsolids,frictionbetweenmoleculesresultind

10、ampingoInfluids,viscosityistheformofdampingthatismostobservedoInthiscourse,wewillusetheviscousdampingmodel;i.e.dampingproportionaltovelocitySpring-mass-dampersystemsFromNewtonsLaw:Solution(datesto1743byEuler)DividetheequationofmotionbymWherethedampingRatioisgivenby:(dimensionless)Whichisnowanalgebra

11、icequationin&substituteintoequationofmotionHerethediscriminant,determinesthenatureoftheroots.1)Rootsarerepeated&equal.Threepossibilities:CalledcriticallydampedNooscillationoccurs.CriticalDampingOver-DampingMostInterestingCase!Under-dampingDampednaturalfrequencyUnder-DampedfreeresponseUnder-Dampedfre

12、eresponseLogarithmicdecrementLogarithmicdecrementisnaturallogarithmofratioofanytwosuccesiveamplitudesandisequaltofollowingformDampingestimatesHomework#11.Theamplitudeofvibrationofanundampedsystemismeasuredtobe1mm.thephaseshiftismeasuredtobe2radandthefrequency5rad/sec.Calculatetheinitialconditions.2.

13、Usingtheequation:evaluatetheconstantA1andA2intermsoftheinitialconditions.3.Anautomobileismodeledas1000kgmasssupportedbyastiffnessk=400000N/m.Whenitoscillates,themaximumdeflectionis10cm.whenloadedwiththepassengers,themassbecomes1300kg.calculatethechangeinthefrequency,velocityamplitude,andacceleration

14、ifthemaximumdeflectionremain10cmHomework#14.UsethegivendatatoplottheresponseoftheSDOFsystem5.SolvetheequationAndplottheresponse.单自由度线性系统的强迫振动单自由度线性系统的强迫振动简谐激励简谐激励 激励力随时间的变化规律为正弦或余弦函数。周期激励周期激励 非周期激励非周期激励简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫

15、振动则有则有令令简谐激励下的强迫振动简谐激励下的强迫振动00.511.52-20-10010203040rX(dB)z=0.01z=0.1z=0.3z=0.5z=1幅频特性幅频特性 r=1附近发生共振附近发生共振lz z=0时时,r=1 共振共振 z z 增大，共振点增大，共振点 r 1简谐激励下的强迫振动简谐激励下的强迫振动相频特性相频特性00.511.5200.511.522.533.5rPhase(rad)z=0.01z=0.1z=0.3z=0.5z=1简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动简谐激励下的强迫振动00.20.40.60.8051015202530z00

16、.20.40.60.800.20.40.60.81zrpeak上图显示共振峰值随阻尼的上图显示共振峰值随阻尼的减小而增大减小而增大下图显示共振频率随阻尼的减下图显示共振频率随阻尼的减小而增大小而增大注意共振峰值只有当注意共振峰值只有当 z zti)F(ti)脉冲激励脉冲激励j jthth 脉冲激励作用下的脉冲激励作用下的t t时刻响应时刻响应ti xi t非周期激励下的强迫振动非周期激励下的强迫振动 脉冲响应函数法脉冲响应函数法 卷积积分的性质卷积积分的性质脉冲响应函数法应用示例脉冲响应函数法应用示例无阻尼系统无阻尼系统 无阻尼系统单位脉冲响应函数无阻尼系统单位脉冲响应函数mkx(t)t1t2

17、F00初始条件引起的响应初始条件引起的响应外力作用期间的响应外力作用期间的响应脉冲响应函数法应用示例脉冲响应函数法应用示例无阻尼系统无阻尼系统 脉冲响应函数法应用示例脉冲响应函数法应用示例无阻尼系统无阻尼系统 00脉冲响应函数法应用示例脉冲响应函数法应用示例无阻尼系统无阻尼系统 总的响应总的响应0246810-0.100.10.20.3Time(s)Displacement x(t)是静态变形的2倍作作 业业 3 计算单自由度系统的响应：计算单自由度系统的响应：1 一个有阻尼的弹簧质量系统，已知一个有阻尼的弹簧质量系统，已知m=196kg,k=19600N/m,c=2940Ns/m,作用在质量

18、块上的激振力为作用在质量块上的激振力为F(t)=160sin（19t）N，试求忽略阻尼及考虑阻尼的两种情况中，试求忽略阻尼及考虑阻尼的两种情况中，系统的振幅放大因子及位移。系统的振幅放大因子及位移。2 计算单自由度无阻尼系统对如图计算单自由度无阻尼系统对如图所示矩形激励力的响应：所示矩形激励力的响应：谢谢观看/欢迎下载BY FAITH I MEAN A VISION OF GOOD ONE CHERISHES AND THE ENTHUSIASM THAT PUSHES ONE TO SEEK ITS FULFILLMENT REGARDLESS OF OBSTACLES.BY FAITH I BY FAITH