A New Analytical Approach for Free Vibration of Membrane from Wave Standpoint
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.
[1] L. Meirovitch, Principles and techniques of vibration, Prentice-Hall
International, 1997.
[2] J. D. Achenbach, wave propagation in elastic solids, North-Holland
Publishing Company, 1973.
[3] B.R. Mace, Wave reflection and transmission in beams, Journal of
Sound and Vibration 97 (1984) 237-246.
[4] 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.
[5] 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.
[6] 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.
[7] C. Mei, "The Analysis and Control of Longitudinal Vibrations from
Wave Viewpoint", ASME Journal of Vibration and Acoustics, Vol. 124,
pp. 645-649, 2002.
[8] 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.
[1] L. Meirovitch, Principles and techniques of vibration, Prentice-Hall
International, 1997.
[2] J. D. Achenbach, wave propagation in elastic solids, North-Holland
Publishing Company, 1973.
[3] B.R. Mace, Wave reflection and transmission in beams, Journal of
Sound and Vibration 97 (1984) 237-246.
[4] 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.
[5] 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.
[6] 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.
[7] C. Mei, "The Analysis and Control of Longitudinal Vibrations from
Wave Viewpoint", ASME Journal of Vibration and Acoustics, Vol. 124,
pp. 645-649, 2002.
[8] 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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:55368", author = "Mansour Nikkhah-Bahrami and Masih Loghmani and Mostafa Pooyanfar", title = "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.", keywords = "Rectangular and circular membranes, propagation
matrix, reflection matrix, vibration analysis.", volume = "2", number = "5", pages = "661-4", }