Structural Dynamics Lecture 8 Generalized SDOF Systems 闺 同桥大学 土本之程手院
Structural Dynamics Lecture 8 Generalized SDOF Systems
Contents General comments on generalized SDOF Generalized properties:assemblages of rigid bodies Generalized properties:distributed flexibility Vibration analysis by Rayleigh's method Selection of the Rayleigh's vibration shape 目 土本品程学院
Contents General comments on generalized SDOF Generalized properties: assemblages of rigid bodies Generalized properties: distributed flexibility Vibration analysis by Rayleigh’s method Selection of the Rayleigh’s vibration shape
Discrete system: All properties are modeled as discrete,such as dynamic response at spatial coordinates,both mass and stiffness,as well as damping ==>In matrix from =>ODE (Ordinary Differential Equations) Distributed system: Physical properties are modeled as distributed characteristics.Also called continuous system, distributed-parameter system =>Infinite number of DOF ==>PDE(Partial Differential Equations) 目 土亦工鞋季悦
Discrete system: All properties are modeled as discrete, such as dynamic response at spatial coordinates, both mass and stiffness, as well as damping ==>In matrix from ==> ODE (Ordinary Differential Equations) Distributed system: Physical properties are modeled as distributed characteristics. Also called continuous system, distributed-parameter system ==>Infinite number of DOF ==> PDE (Partial Differential Equations)
Some complex system can be studied as SDOF systems,either exactly or under some simplifying assumption 1.SDOF rigid body assemblages. Principle of Virtual Displacements the D'Alembert Principle 2.Simple structural systems.(in an approximate manner) Assume a fixed pattern of displacement,whose amplitude(the single degree of freedom)varies with time. 目 土本2程季院
Some complex system can be studied as SDOF systems, either exactly or under some simplifying assumption 1. SDOF rigid body assemblages. Principle of Virtual Displacements the D’Alembert Principle 2. Simple structural systems. (in an approximate manner) Assume a fixed pattern of displacement, whose amplitude (the single degree of freedom) varies with time
Generalized SDOF System can be treated as SDOF Many different,more complex systems can be studied as SDOF systems,either exactly or under some simplifying assumption. Case 1:Assemblage of rigid bodies The analysis provides exact results for an assemblage of rigid bodies supported such that it can deflect in only one shape Case 2:System with distributed mass and stiffness. Only approximate results for systems with distributed m and k Depends on the assumed deflected shape 闺 土本程李悦
Generalized SDOF • System can be treated as SDOF • Many different, more complex systems can be studied as SDOF systems, either exactly or under some simplifying assumption. Case 1: Assemblage of rigid bodies • The analysis provides exact results for an assemblage of rigid bodies supported such that it can deflect in only one shape Case 2: System with distributed mass and stiffness. • Only approximate results for systems with distributed m and k • Depends on the assumed deflected shape