In this paper, the transition probability density functions between response velocity and response displacement in nonlinear vibration systems which have the restoring force characteristic of a cubic equation are governed by the Fokker-Planck Equation. The experimental probability density functions are compared with analytical results. The analytical model of the cubic equation as Duffing Equation is proposed by the restoring force characteristic of the nonlinear vibration system with gaps in the experiments. However, a slight difference for the frequency range of the transfer function was shown by simulation results. Then, it is considered using transition probability density functions in the response characteristic. For stationary random input waves, the probability density function between the response displacement and the response velocity are easily estimated by the Fokker-Planck Equation and the Duffing Equation. The slight difference of the transfer function of the response acceleration is evaluated by the scattering of the restoring force characteristic estimated by the probability density function and self-natural frequency curve. The R.M.S. value and the transfer function of the experimental results are compared with the analytical results. It is thought that the estimation of the probability density function of the response has validity. It is thought that the evaluation of the nonlinear vibration characteristics by the probability density function is valid.
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ASME/JSME 2004 Pressure Vessels and Piping Conference
July 25–29, 2004
San Diego, California, USA
Conference Sponsors:
- Pressure Vessels and Piping Division
ISBN:
0-7918-4681-4
PROCEEDINGS PAPER
Study on Nonlinear Vibration Characteristic Evaluation of Nonlinear Vibration System With Gaps by Transition Probability Density Function Available to Purchase
Masanori Shintani,
Masanori Shintani
University of Fukui, Fukui-shi, Fukui, Japan
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Hiroyuki Ikuta,
Hiroyuki Ikuta
University of Fukui, Fukui-shi, Fukui, Japan
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Hajime Takada
Hajime Takada
Yokohama National University, Yokohama, Kanagawa, Japan
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Masanori Shintani
University of Fukui, Fukui-shi, Fukui, Japan
Hiroyuki Ikuta
University of Fukui, Fukui-shi, Fukui, Japan
Hajime Takada
Yokohama National University, Yokohama, Kanagawa, Japan
Paper No:
PVP2004-2949, pp. 165-172; 8 pages
Published Online:
August 12, 2008
Citation
Shintani, M, Ikuta, H, & Takada, H. "Study on Nonlinear Vibration Characteristic Evaluation of Nonlinear Vibration System With Gaps by Transition Probability Density Function." Proceedings of the ASME/JSME 2004 Pressure Vessels and Piping Conference. Seismic Engineering, Volume 2. San Diego, California, USA. July 25–29, 2004. pp. 165-172. ASME. https://doi.org/10.1115/PVP2004-2949
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