(a) 2019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
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)
known as d'Alembert's principle
CHAPTER 1. OVERVIEW 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. 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.
制作人 Jilu Bridge(in Taiwan) in Jiji Earthquake of 2019
(a) 2019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 2019
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.
FIGURE 1-3 Sine-series representation of simple beam deflection.
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
Discrete Models
FIGURE 1-4 (a) 2019年台湾集集地震集鹿大桥破坏状态 Lumped-mass idealization of a simple beam.
Dynamics of Structures
Junjie Wang Dept. of Bridge Engineering 2019.01
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
1.1 BACKGROUND
(a) simple harmonic; (b) complex;
(a) 2019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
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
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
1.3 SOLUTIONS TO A DYNAMIC PROBLEM
Continuous Models (partial differential equations; generalized displacement, sum of a series)
(a) 2019年台湾集集地震集鹿大桥破坏状态
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
(a) 2019年台湾集集地震集鹿大桥破坏状态
Sunshine Skyway Bridge Tampa Bay, Florida (1980)
Tasman Bridge Derwent River, Hobart, Australia (1975)
(c) impulsive;
(d) long-duration.
FIGURE 1-1 Characteristics and sources of typical dynamic loadings
CHAPTER 1. OVERVIEW OF STRUCTURAL DYNAMICS
集鹿大桥
制作人：同济大学桥梁工程系 孙利民