More MDOF systems: Forced vibration and response analysis

2014 ◽  
pp. 287-332

2011 ◽  
Vol 199-200 ◽  
pp. 835-838
Author(s):  
Xu Bin Lu ◽  
Zhong Rong Lv ◽  
Ji Ke Liu

The composite element method is utilized to discretise a stepped Euler-Bernoulli beam with a crack. The local stiffness reduction due to the crack is introduced by using a simplified crack model. The finite element equation for the forced vibration analysis is obtained using the composite element method (CEM). The forced vibration response of the cracked stepped beam is numerically calculated using Newmark integration method. Numerical results indicate that the position and depth of a crack affects the low and high natural frequencies and modes of a cantilever beam, respectively. And the position of the crack has significant effects on the dynamic responses of the beam.



2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jian Duan ◽  
Zhi-xin Yan ◽  
Rui-jian Guo ◽  
Zhi-hua Ren

Based on certain assumptions, the dynamic mechanical model for frame supporting structure of slope is established, the dynamic equilibrium governing equation for vertical beam under forced vibration is derived, and hence its analytical solutions to harmonic forced vibration are obtained. What is more, the finite difference format and corresponding calculation procedure for vertical beam under forced vibration are given and programmed by using MATLAB language. In the case studies, comparative analyses have been performed to the response of vertical beam under horizontal harmonic forced vibration by using different calculating methods and with anchoring system damping effect neglected or considered. As a result, the feasibility, correctness, and characteristics of different methods can be revealed and the horizontal forced vibration law of vertical beam can be unveiled as well.







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