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A New Analytical Approach for Free Vibration of Membrane from Wave Standpoint
Abstract:In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062618Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1763
 L. Meirovitch, Principles and techniques of vibration, Prentice-Hall International, 1997.
 J. D. Achenbach, wave propagation in elastic solids, North-Holland Publishing Company, 1973.
 B.R. Mace, Wave reflection and transmission in beams, Journal of Sound and Vibration 97 (1984) 237-246.
 C.A. Tan, B. Kang, Wave reflection and transmission in an axially strained, rotating Timoshenko shaft, Journal of Sound and Vibration 213 (3) (1998) 483-510.
 N.R. Harland, B.R. Mace, R.W. Jones, Wave propagation, reflection and transmission in tunable fluid-filled beams, Journal of Sound and Vibration 241 (5) (2001) 735-754.
 C. Mei, B.R. Mace, Wave reflection and transmission in Timoshenko beams and wave analysis of Timoshenko beam structures, ASME Journal of Vibration and Acoustics 127 (4) (2005) 382-394.
 C. Mei, "The Analysis and Control of Longitudinal Vibrations from Wave Viewpoint", ASME Journal of Vibration and Acoustics, Vol. 124, pp. 645-649, 2002.
 C. Mei, Y. Karpenko, S. Moody and D. Allen, Analytical Approach to Free and Forced Vibrations of Axially Loaded Cracked Timoshenko Beams, Journal of Sound and Vibration, Vol. 291, pp. 1041-1060, 2006.