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1、CHAPTER 8.GENERALIZED SDOF SYSTEMS8.1 GENERALIZED PROPERTIES:ASSEMBLAGES OF RIGID BODIESExample E81.CHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMSIt is of interest to note that the condition of zero generalized stiffness represents a neutral st
2、ability or critical buckling condition in the system.CHAPTER 8.GENERALIZED SDOF SYSTEMSExample E82.CHAPTER 8.GENERALIZED SDOF SYSTEMS82 GENERALIZED PROPERTIES:DISTRIBUTED FLEXIBILITYCHAPTER 8.GENERALIZED SDOF SYSTEMSIf it is assumed that damping stresses are developed in proportion to the strain vel
3、ocity,a uniaxial stressstrain relation of the formUsing this equation,the basic relations may be expressed as follows:CHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMSExample E83.CHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMS
4、83 VIBRATION ANALYSIS BY RAYLEIGHS METHODConsider the freevibration motion of the undamped springmass system.With an appropriate choice of time origin,the displacement can be expressedThe potential energykinetic energySDOF:CHAPTER 8.GENERALIZED SDOF SYSTEMSGeneralized SDOF:CHAPTER 8.GENERALIZED SDOF
5、 SYSTEMS84 SELECTION OF THE RAYLEIGH VIBRATION SHAPEExample E84.Fig.86Exact oneError:about 20%CHAPTER 8.GENERALIZED SDOF SYSTEMSCHAPTER 8.GENERALIZED SDOF SYSTEMSExample 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 lower sketch.The resulting deflected shape is:CHAPTER 8.GENERALIZED SDOF SYSTEMS