结构动力学课件—dyanmicsofstructures-ch8

1、,CHAPTER 8. GENERALIZED SDOF SYSTEMS,8.1 GENERALIZED PROPERTIES: ASSEMBLAGES OF RIGID BODIES,Example E81.,CHAPTER 8. GENERALIZED SDOF SYSTEMS,CHAPTER 8. GENERALIZED SDOF SYSTEMS,CHAPTER 8. GENERALIZED SDOF SYSTEMS,It is of interest to note that the condition of zero generalized stiffness represents

2、a neutral stability or critical buckling condition in the system.,CHAPTER 8. GENERALIZED SDOF SYSTEMS,Example E82.,CHAPTER 8. GENERALIZED SDOF SYSTEMS,82 GENERALIZED PROPERTIES: DISTRIBUTED FLEXIBILITY,CHAPTER 8. GENERALIZED SDOF SYSTEMS,If it is assumed that damping stresses are developed in propor

3、tion to the strain velocity, a uniaxial stressstrain relation of the form,Using this equation, the basic relations may be expressed as follows:,CHAPTER 8. GENERALIZED SDOF SYSTEMS,CHAPTER 8. GENERALIZED SDOF SYSTEMS,CHAPTER 8. GENERALIZED SDOF SYSTEMS,Example E83.,CHAPTER 8. GENERALIZED SDOF SYSTEMS

4、,CHAPTER 8. GENERALIZED SDOF SYSTEMS,83 VIBRATION ANALYSIS BY RAYLEIGHS METHOD,Consider the freevibration motion of the undamped springmass system. With an appropriate choice of time origin, the displacement can be expressed,The potential energy,kinetic energy,SDOF:,CHAPTER 8. GENERALIZED SDOF SYSTE

5、MS,Generalized SDOF:,CHAPTER 8. GENERALIZED SDOF SYSTEMS,84 SELECTION OF THE RAYLEIGH VIBRATION SHAPE,Example E84. Fig. 86,Exact one,Error: about 20%,CHAPTER 8. GENERALIZED SDOF SYSTEMS,CHAPTER 8. GENERALIZED SDOF SYSTEMS,Example E85.,For this study, the vibration shape has been taken to be that produced by a load applied to the end of the cantilever, as shown in the lo