结构动力学课件—dyanmics-of-structures-ch8知识资料18页PPT
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If it is assumed that damping stresses are developed in proportion to the strain velocity, a uniaxial stressstrain relation of the form Using this equation, the basic relations may be expressed as follows:
The potential energy
kinetic energy
CHAPTER 8. GENERALIZED SDOF SYSTEMS
Generalized SDOF:
CHAPTER 8. GENERALIZED SDOF SYSTEMS
84 SELECTION OF THE RAYLEIGH VIBRATION SHAPE
CHAPTER 8. GENERALIZED SDOF SYSTEMS
谢谢！
CHAPTER 8. GENERABiblioteka IZED SDOF SYSTEMS
Example E82.
CHAPTER 8. GENERALIZED SDOF SYSTEMS
82 GENERALIZED PROPERTIES: DISTRIBUTED FLEXIBILITY
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
Example E83.
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
It is of interest to note that the condition of zero generalized stiffness represents a neutral stability or critical buckling condition in the system.
Example E84. Fig. 86
Error: about 20% Exact one
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 lower sketch. The resulting deflected shape is:
CHAPTER 8. GENERALIZED SDOF SYSTEMS
83 VIBRATION ANALYSIS BY RAYLEIGH'S METHOD
SDOF:
Consider the freevibration motion of the undamped springmass system. With an appropriate choice of time origin, the displacement can be expressed
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
The potential energy
kinetic energy
CHAPTER 8. GENERALIZED SDOF SYSTEMS
Generalized SDOF:
CHAPTER 8. GENERALIZED SDOF SYSTEMS
84 SELECTION OF THE RAYLEIGH VIBRATION SHAPE
CHAPTER 8. GENERALIZED SDOF SYSTEMS
谢谢！
CHAPTER 8. GENERABiblioteka IZED SDOF SYSTEMS
Example E82.
CHAPTER 8. GENERALIZED SDOF SYSTEMS
82 GENERALIZED PROPERTIES: DISTRIBUTED FLEXIBILITY
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
Example E83.
CHAPTER 8. GENERALIZED SDOF SYSTEMS
CHAPTER 8. GENERALIZED SDOF SYSTEMS
It is of interest to note that the condition of zero generalized stiffness represents a neutral stability or critical buckling condition in the system.
Example E84. Fig. 86
Error: about 20% Exact one
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 lower sketch. The resulting deflected shape is:
CHAPTER 8. GENERALIZED SDOF SYSTEMS
83 VIBRATION ANALYSIS BY RAYLEIGH'S METHOD
SDOF:
Consider the freevibration motion of the undamped springmass system. With an appropriate choice of time origin, the displacement can be expressed
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