Structural Dynamics(1).pdf

Dynamics of Structures
For graduate student
Zhou Ke-min
******@hqu.
Main reference
(Structural Dynamics)
《Vibration problem in engineering》
2. 杨茀康《结构动力学》
3. 俞载道《结构动力学基础》
4. 李东旭《高等结构动力学》
5. R. W. Clough 《 Dynamics of Structures 》
6. 克拉夫《结构动力学》
Chapter 1 Introduction
§1-1 Fundamental objective of
structural dynamics analysis
To Analyze stresses and deflections of given structure
subjected to an arbitrary dynamic loading.
Dynamic loading: its magnitude, and/or direction,
position varies with time
Structural response (resulting stresses and deflections)
is time-varying, or dynamic.
Deterministic analysis:
The time variation of loading is fully known
Non deterministic analysis :
The time variation of loading is pletely
known, but can be defined in a statistical sense
(random dynamic loading).
First phase: Displacement time-histories
Secondary: Stresses, strains, internal forces
§1-2 Types of Prescribed Loadings
Periodic: Simple harmonic plex loading
F F
t t
Unbalanced rotating machine in building Gas engine
Any periodic loading can be represented as sum of a series of
simple ponents by Fourier analysis
Nonperiodic: impulsive loading long –duration loading
F t F t
Bomb blast pressure on building Earthquake on building
§1-3 Essential Characteristics of
Dynamic Problem
1. Response vary with time
2. Inertial force produced by acceleration
§1-4 Methods of Discretization
Formulated in term of Partial Differential Equations
Lumped-Mass Procedure
F(t)
Intertial forces
F(t)
fI1 fI2 fI3 Initertial forces
The number of dynamic degrees of freedom
of the structures
Three masses are fully concentrated, corresponding
mass points translate only in a vertical direction:
Three-Degree-Of-Freedom (3 DOF) system
F(t)
fI1 fI2 fI3
Initertial forces
Rotational displacement of three point are considered: 6DOF
A system with continuously distributed mass:
infinite number of degrees of freedom
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