结构动力学课件-1dyanmicsofstructures-ch1ch.ppt
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1、Dynamics of StructuresDynamics of Structures Junjie WangJunjie WangDept.of Bridge EngineeringDept.of Bridge Engineering2005.012005.01(a)simple harmonic;(b)complex;(c)impulsive;(d)longduration.FIGURE 11Characteristics and sources of typical dynamic loadings1.1 BACKGROUNDCHAPTER 1.OVERVIEW OF STRUCTUR
2、AL DYNAMICS(a)1999年台湾集集地震集鹿大桥破坏状态The Damages of Jilu Bridge(in Taiwan)in Jiji Earthquake of 1999 The Damages of Kobe Bridge(Japan)in Kobe Earthquake of 1995 CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS(a)1999年台湾集集地震集鹿大桥破坏状态Sunshine Skyway BridgeTampa Bay,Florida(1980)Tasman BridgeDerwent River,Hobart,A
3、ustralia(1975)CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS(a)1999年台湾集集地震集鹿大桥破坏状态1.2 ESSENTIAL CHARACTERISTICS OF A DYNAMIC PROBLEM timevarying nature of the dynamic problem inertial forces(more fundamental distinction)FIGURE 12Basic difference between static and dynamic loads:(a)static loading;(b)dynam
4、ic loading.CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS(a)1999年台湾集集地震集鹿大桥破坏状态1.3 SOLUTIONS TO A DYNAMIC PROBLEMContinuous Models(partial differential equations;generalized displacement,sum of a series)FIGURE 13Sineseries representation of simple beam deflection.CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS
5、(a)1999年台湾集集地震集鹿大桥破坏状态Discrete ModelsFIGURE 14Lumpedmass idealization of a simple beam.CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS(a)1999年台湾集集地震集鹿大桥破坏状态FEMAthird method of expressing the displacements of any given structure in terms ofa nite number of discrete displacement coordinates,which combines c
6、ertain featuresof both the lumpedmass and the generalizedcoordinate proceduresFIGURE 15Typical finiteelement beam coordinates.CHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS1.4 FORMULATION OF THE EQUATIONS OF MOTION1.4.1 Direct Equilibration Using dAlemberts PrincipleThe equations of motion of any dynamic
7、 system represent expressions of Newtons second law of motion,which states that the rate of change of momentum of anymass particle m is equal to the force acting on it.This relationship can be expressedmathematically by the differential equationFor most problems in structural dynamics it may be assu
8、med that mass does notvary with time,in which case Eq.(13)may be writtenthe second term is called the inertial force resisting the acceleration of the mass.known as dAlemberts principleCHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS1.4.2 Principle of Virtual DisplacementsHowever,if the structural system i
9、s reasonably complex involving a number of interconnected mass points or bodies of finite size,the direct equilibration of all the forces acting in the system may be difficult.Frequently,the various forces involved may readily be expressed in terms of the displacement degrees of freedom,but their eq
10、uilibrium relationships may be obscure.In this case,the principle of virtual displacements can be used to formulate the equations of motion as a substitute for the direct equilibrium relationships.The principle of virtual displacements may be expressed as follows.If a system which is in equilibrium
11、under the action of a set of externally applied forces is subjected to a virtual displacement,i.e.,a displacement pattern compatible with the systems constraints,the total work done by the set of forces will be zero.1.4.3 Hamiltons principleCHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICS1.5 ORGANIZATION O
12、F THE TEXTCHAPTER 1.OVERVIEW OF STRUCTURAL DYNAMICSDYNAMICSPart ISDOFPart II Discrete MDOFPart IIIDistributed Parameter SystemsPart IV Random VibrationPart V Special FocusesBasic ConceptionsBasic MethodsStructural Properties(Mass,Damping,Stiffness)Selection of Dynamic DOFModal SuperpositionStep by S
13、tep MethodsPartial Differential Equation of MotionAnalysis of Undamped Free VibrationAnalysis of Dynamic ResponseProbability TheoryRandom ProcessEigen ProblemStochastic Response of SDOF SystemsShipBridge CollisionStochastic Response of MDOF SystemsEarthquake EngineeringVehicleForces VibrationPART IS
14、INGLE DEGREE OF FREEDOM SYSTEMSCHAPTER 2.ANALYSIS OF FREE VIBRATION21 COMPONENTS OF THE BASIC DYNAMIC SYSTEMThe essential physical properties of any linearly elastic structural or mechanical system subjected to an external source of excitation or dynamic loading are its mass,elastic properties(exibi
15、lity or stiffness),and energyloss mechanism or damping.In the simplest model of a SDOF system,each of these properties is assumed to be concentrated in a single physical element.A sketch of such a system is shown in Fig.21a.FIGURE 21Idealized SDOF system:(a)basic components;(b)forces in equilibrium.
16、CHAPTER 2.ANALYSIS OF FREE VIBRATION22 EQUATION OF MOTION OF THE BASIC DYNAMIC SYSTEMThe equation of motion for the simple system is most easily formulated by directly expressing the equilibrium of all forces acting on the mass using dAlemberts principle.The equation of motion is merely an expressio
17、n of the equilibrium of these forces as given byIn accordance with dAlemberts principle,the inertial force is the product of the mass and accelerationAssuming a viscous damping mechanism,the damping force is the product of the damping constant c and the velocityFinally,the elastic force is the produ
18、ct of the spring stiffness and the displacementCHAPTER 2.ANALYSIS OF FREE VIBRATION23 INFLUENCE OF GRAVITATIONAL FORCESFIGURE 22Influence of gravity on SDOF equilibrium.CHAPTER 2.ANALYSIS OF FREE VIBRATIONif the total displacement v(t)is expressed as the sum of the static displacement caused by the
19、weight W plus the additional dynamic displacement as shown in Fig.22c,i.e.,then the spring force is given bythen we have and noting that leads tonoting that does not vary with time,it is evident that and then we have It demonstrates that the equation of motion expressed with reference to the statice
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