Abstract
This paper deals with steady-state response of a continuous system with nonlinear boundary conditions which are motion-limiting constraint. An analytical method of approximate solution for the continuous system with unsymmetrical collision characteristics in which the beam end collides with a stop once in one period of its vibration is presented. Some numerical results of the approximate solution are shown. Contrary to the case of continuous system with symmetrical collision characteristics, the resonance curves of nonlinear response of approximate solution are shown as discontinuous line. Some numerical results of a continuous system with no hysteresis damping are compared with those of a continuous system with hysteresis damping and a single-degree-of-freedom system.
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References
Watanabe, T., ‘Forced vibration of continuous system with nonlinear boundary conditions’, ASME Journal of Mechanical Design 100, 1978, 487‐491.
Moon, F. C. and Shaw, S. W., ‘Chaotic vibrations of a beam with non-linear boundary conditions’, International Journal of Non-Linear Mechanics 18(6), 1983, 465‐477.
Shaw, S. W., ‘Forced vibrations of a beam with one-sided amplitude constraint: Theory and experiment’, Journal of Sound and Vibration 99(2), 1985, 199‐212.
Lin, C. W., ‘Seismic evaluation of systems and components’, ASME Journal of Pressure Vessel Technology 113, 1991, 273‐283.
Worner, J. D., ‘Determination of ultimate aseismic strength of equipment and piping’, ASME, Seismic Engineering-1989 Design, Analysis, Testing, and Qualification Method PVP-182, 1989, 155‐158.
Aoki, S. and Watanabe, T., ‘Forced vibration of continuous system with unsymmetrical hysteresis loop characteristics’, in Proceedings of Asia-Pacific Vibration Conference’ 93, Vol. 4, Japan Society of Mechanical Engineers, 1993, pp. 1680‐1685.
Watanabe, T. and Shibata, H., ‘On nonlinear vibration of a beam-response of a beam with a gap at one end’, Report of the Institute of Industrial Science, The University of Tokyo 36(1), 1991, 1‐25.
Watanabe, T, Shibata, H., and Maezawa, S., ‘Steady impact vibration of a body having hysteresis collision characteristics’, Bulletin of the Japan Society of Mechanical Engineers 22(167), 1979, 655‐660.
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Aoki, S., Watanabe, T. Forced Vibration of Continuous System with Unsymmetrical Collision Characteristics. Nonlinear Dynamics 17, 141–157 (1998). https://doi.org/10.1023/A:1008207721738
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DOI: https://doi.org/10.1023/A:1008207721738