Wuhan University of TechnologyPart ISingle-degree-of-freedom systems(SDOF)Chapter2Analysis of free vibrations3-1
3-1 Wuhan University of Technology Chapter 2 Analysis of free vibrations Part I Single-degree-of-freedom systems (SDOF)
Wuhan University of TechnologyContents2.1 Introduction2.2 Components of the basic dynamic system2.3 Equation of motion of the basic dynamic system2.4 Influence of gravitational forces2.5 Influence of support excitation2.6 Analysisof undampedfree vibrations2.7Damped free vibrations2.8 Review and problems3-2
3-2 Wuhan University of Technology 2.1 Introduction 2.2 Components of the basic dynamic system 2.3 Equation of motion of the basic dynamic system 2.4 Influence of gravitational forces 2.5 Influence of support excitation 2.6 Analysis of undamped free vibrations 2.7 Damped free vibrations 2.8 Review and problems Contents
Wuhan University of Technology2.1 IntroductionThis chapter will discuss thefree vibration of SDOF system;Theknowledgeof partial differential equationstudied inadvancedmathematicsarebasicallyreviewed.Inthediscussionoffreevibrationsofstructures,threescenariosare involved:(a) Critically-damped systems;(b) Undercritically-damped systems;(c)Overcritically-dampedsystems.3-3
3-3 Wuhan University of Technology 2.1 Introduction This chapter will discuss the free vibration of SDOF system; The knowledge of partial differential equation studied in advanced mathematics are basically reviewed. In the discussion of free vibrations of structures, three scenarios are involved: (a) Critically-damped systems; (b) Undercritically-damped systems; (c) Overcritically-damped systems
Wuhan University of Technology2.2 Components of the basic dynamic systemThe essential physical properties of any linearly elasticstructural or mechanical system subjected to an externalexcitation ordynamic loading are its mass, elastic properties(flexibility or stiffness), and energy-loss mechanism or damping;InthesimplestmodelofaSDOFsystem,eachoftheseproperties is assumed to be concentrated in a single physicalelement.3-4
3-4 Wuhan University of Technology 2.2 Components of the basic dynamic system The essential physical properties of any linearly elastic structural or mechanical system subjected to an external excitation or dynamic loading are its mass, elastic properties (flexibility or stiffness), and energy-loss 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
Wuhan Universityof Technology2.2Componentsof the basicdynamicsystemA sketch of such a system is shown in following Figy(t)Cp(t)m500000kBasiccomponentsofaidealizedSDoFsystem3-5
3-5 Wuhan University of Technology 2.2 Components of the basic dynamic system A sketch of such a system is shown in following Fig. Basic components of a idealized SDOF system y ( t ) c m p ( t ) k