结构动力学—1dyanmics of structures-ch1 ch
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For most problems in structural dynamics it may be assumed that mass does not vary with time, in which case Eq. (13) may be written
the second term is called the inertial force resisting the acceleration of the mass.
The equation of motion for the simple system is most easily formulated by directly expressing the equilibrium of all forces acting on the mass using d'Alembert's principle.
FIGURE 1-3 Sine-series representation of simple beam deflection.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
Discrete Models
FIGURE 1-4 Lumped-mass id(ea)a1l9i9z9a年t台io湾n集o集f地a震集si鹿m大p桥l破e坏b状e态am.
(a) 1999年台湾集集地震集鹿大桥破坏状态
Tasman Bridge Derwent River, Hobart, Australia (1975)
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.2 ESSENTIAL CHARACTERISTICS OF A DYNAMIC PROBLEM • timevarying nature of the dynamic problem • inertial forces (more fundamental distinction)
Dynamics of Structures
Junjie Wang Dept. of Bridge Engineering
2005.01
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.1 BACKGROUND
(a) simple harmonic; (b) complex; (c) impulsive; (d) long-duration.
known as d'Alembert's prinIEW OF STRUCTURAL DYNAMICS
1.4.2 Principle of Virtual Displacements
However, if the structural system is 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 equilibrium 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.
1.3 SOLUTIONS TO A DYNAMIC PROBLEM
Continuous Models (partial differential equations; generalized displacement, sum of a series)
(a) 1999年台湾集集地震集鹿大桥破坏状态
The principle of virtual displacements may be expressed as follows. If a system which is in equilibrium under the action of a set of externally applied forces is subjected to a virtual displacement, i.e., a displacement pattern compatible with the system's constraints, the total work done by the set of forces will be zero.
FIGURE 1-1 Characteristics and sources of typical dynamic loadings
CHAPTER 1. OVERVIEW OF 集 鹿 大 桥 STRUCTURAL DYNAMICS
The Damages 制作人：同济大学桥梁工程系 孙利民 of Jilu Bridge(in Taiwan) in Jiji Earthquake of 1999
制作人：同济大学桥梁工程系 孙利民
(a) 1999年台湾集集地震集鹿大桥破坏状态
The Damages of Kobe Bridge(Japan) in Kobe Earthquake of 1995
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
Sunshine Skyway Bridge Tampa Bay, Florida (1980)
1.4.3 Hamilton's principle
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.5 ORGANIZATION OF THE TEXT
Part I－SDOF
Basic Conceptions Basic Methods
Part II－ Discrete MDOF
Structural Properties (Mass, Damping, Stiffness) Modal Superposition Eigen Problem Selection of Dynamic DOF Step by Step Methods
DYNAMICS
Part III－Distributed Parameter Systems
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
FEM Athird method of expressing the displacements of any given structure in terms of a nite number of discrete displacement coordinates, which combines certain features of both the lumpedmass and the generalizedcoordinate procedures
FIGURE 2-1 Idealized SDOF system: (a) basic components; (b) forces in equilibrium.
CHAPTER 2. ANALYSIS OF FREE VIBRATION
22 EQUATION OF MOTION OF THE BASIC DYNAMIC SYSTEM
1.4.1 Direct Equilibration Using d'Alembert's Principle
The equations of motion of any dynamic system represent expressions of Newton's second law of motion, which states that the rate of change of momentum of any mass particle m is equal to the force acting on it. This relationship can be expressed mathematically by the differential equation
(a) 1999年台湾集集地震集鹿大桥破坏状态
FIGURE 1-2 Basic difference between static and dynamic loads: (a) static loading; (b) dynamic loading.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
(a) 1999年台湾集集地震集鹿大桥破坏状态
FIGURE 1-5 Typical finite-element beam coordinates.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.4 FORMULATION OF THE EQUATIONS OF MOTION
Part V－ Special Focuses
Earthquake Engineering Ship-Bridge Collision Vehicle-Forces Vibration
PART I
SINGLE DEGREE OF FREEDOM SYSTEMS
CHAPTER 2. ANALYSIS OF FREE VIBRATION
The equation of motion is merely an expression of the equilibrium of these forces as given by
In accordance with d'Alembert's principle, the inertial force is the product of the mass and acceleration
Partial Differential Equation of Motion Analysis of Undamped Free Vibration Analysis of Dynamic Response
Part IV－ Random Vibration
Probability Theory Random Process Stochastic Response of SDOF Systems Stochastic Response of MDOF Systems
21 COMPONENTS OF THE BASIC DYNAMIC SYSTEM
The 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 (exibility 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.
the second term is called the inertial force resisting the acceleration of the mass.
The equation of motion for the simple system is most easily formulated by directly expressing the equilibrium of all forces acting on the mass using d'Alembert's principle.
FIGURE 1-3 Sine-series representation of simple beam deflection.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
Discrete Models
FIGURE 1-4 Lumped-mass id(ea)a1l9i9z9a年t台io湾n集o集f地a震集si鹿m大p桥l破e坏b状e态am.
(a) 1999年台湾集集地震集鹿大桥破坏状态
Tasman Bridge Derwent River, Hobart, Australia (1975)
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.2 ESSENTIAL CHARACTERISTICS OF A DYNAMIC PROBLEM • timevarying nature of the dynamic problem • inertial forces (more fundamental distinction)
Dynamics of Structures
Junjie Wang Dept. of Bridge Engineering
2005.01
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.1 BACKGROUND
(a) simple harmonic; (b) complex; (c) impulsive; (d) long-duration.
known as d'Alembert's prinIEW OF STRUCTURAL DYNAMICS
1.4.2 Principle of Virtual Displacements
However, if the structural system is 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 equilibrium 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.
1.3 SOLUTIONS TO A DYNAMIC PROBLEM
Continuous Models (partial differential equations; generalized displacement, sum of a series)
(a) 1999年台湾集集地震集鹿大桥破坏状态
The principle of virtual displacements may be expressed as follows. If a system which is in equilibrium under the action of a set of externally applied forces is subjected to a virtual displacement, i.e., a displacement pattern compatible with the system's constraints, the total work done by the set of forces will be zero.
FIGURE 1-1 Characteristics and sources of typical dynamic loadings
CHAPTER 1. OVERVIEW OF 集 鹿 大 桥 STRUCTURAL DYNAMICS
The Damages 制作人：同济大学桥梁工程系 孙利民 of Jilu Bridge(in Taiwan) in Jiji Earthquake of 1999
制作人：同济大学桥梁工程系 孙利民
(a) 1999年台湾集集地震集鹿大桥破坏状态
The Damages of Kobe Bridge(Japan) in Kobe Earthquake of 1995
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
Sunshine Skyway Bridge Tampa Bay, Florida (1980)
1.4.3 Hamilton's principle
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.5 ORGANIZATION OF THE TEXT
Part I－SDOF
Basic Conceptions Basic Methods
Part II－ Discrete MDOF
Structural Properties (Mass, Damping, Stiffness) Modal Superposition Eigen Problem Selection of Dynamic DOF Step by Step Methods
DYNAMICS
Part III－Distributed Parameter Systems
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
FEM Athird method of expressing the displacements of any given structure in terms of a nite number of discrete displacement coordinates, which combines certain features of both the lumpedmass and the generalizedcoordinate procedures
FIGURE 2-1 Idealized SDOF system: (a) basic components; (b) forces in equilibrium.
CHAPTER 2. ANALYSIS OF FREE VIBRATION
22 EQUATION OF MOTION OF THE BASIC DYNAMIC SYSTEM
1.4.1 Direct Equilibration Using d'Alembert's Principle
The equations of motion of any dynamic system represent expressions of Newton's second law of motion, which states that the rate of change of momentum of any mass particle m is equal to the force acting on it. This relationship can be expressed mathematically by the differential equation
(a) 1999年台湾集集地震集鹿大桥破坏状态
FIGURE 1-2 Basic difference between static and dynamic loads: (a) static loading; (b) dynamic loading.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
(a) 1999年台湾集集地震集鹿大桥破坏状态
FIGURE 1-5 Typical finite-element beam coordinates.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.4 FORMULATION OF THE EQUATIONS OF MOTION
Part V－ Special Focuses
Earthquake Engineering Ship-Bridge Collision Vehicle-Forces Vibration
PART I
SINGLE DEGREE OF FREEDOM SYSTEMS
CHAPTER 2. ANALYSIS OF FREE VIBRATION
The equation of motion is merely an expression of the equilibrium of these forces as given by
In accordance with d'Alembert's principle, the inertial force is the product of the mass and acceleration
Partial Differential Equation of Motion Analysis of Undamped Free Vibration Analysis of Dynamic Response
Part IV－ Random Vibration
Probability Theory Random Process Stochastic Response of SDOF Systems Stochastic Response of MDOF Systems
21 COMPONENTS OF THE BASIC DYNAMIC SYSTEM
The 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 (exibility 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.