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Vibration of circular plate with multiple eccentric circular perforations by the Rayleigh-Ritz method

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Abstract

The free vibration of a circular plate with multiple perforations is analyzed by using the Rayleigh-Ritz method. Admissible functions are assumed to be separable functions of radial and tangential coordinates. Trigonometric functions are assumed in the circumferential direction. The radial shape functions are the boundary characteristic orthogonal polynomials generated following the Gram-Schmidt recurrence scheme. The assumed functions are used to estimate the kinetic and the potential energies of the plate depending on the number and the position of the perforations. The eigenvalues, representing the dimensionless natural frequencies, are compared with the results obtained using Bessel functions, where the exact solution is available. Moreover, the eigenvectors, which are the unknown coefficients of the Rayleigh-Ritz method, are used to present the mode shapes of the plate. To validate the analytical results of the plates with multiple perforations, experimental investigations are also performed. Two unique case studies that are not addressed in the existing literature are considered. The results of the Rayleigh-Ritz method are found to be in good agreement with those from the experiments. Although the method presented can be employed in the vibration analysis of plates with different boundary conditions and shapes of the perforations, circular perforations that are free on the edges are studied in this paper. The results are presented in terms of dimensionless frequencies and mode shapes.

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Authors and Affiliations

  1. CONCAVE Research Center, Mechanical and Industrial Engineering Department, Concordia University, Montreal, QC, Canada

    Khodabakhsh Saeedi, Rama B. Bhat & Ion Stiharu

  2. Parker Filtration Canada, Laval, QC, Canada

    Alfin Leo

Authors
  1. Khodabakhsh Saeedi
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  2. Alfin Leo
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  3. Rama B. Bhat
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  4. Ion Stiharu
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Correspondence to Khodabakhsh Saeedi.

Additional information

Recommended by Associate Editor Cheolung Cheong.

Khodabakhsh Saeedi is a Ph.D student in the Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Canada. He received his M.Sc. in Applied Mechanics from Sharif University of Technology, Tehran, Iran. His research interests include, vehicle dynamics, vibration of structures, and composite materials.

Alfin Leo is a Mechanical Engineer with a Doctoral degree in Microsystems Engineering for high temperature applications from Concordia University, Montreal, Canada. He is currently involved in R&D activities in the railroad division of Parker filtration Canada and in developing filtration systems for locomotive engines. Along with his publications he has filed a Patent in the area of locomotive exhaust filtration system. His specialization includes vibrations, high temperature microsystems, engine intake and exhaust filtration systems for rail road applications, fluid power systems and automation.

Rama Bhat is a Professor of Mechanical and Industrial Engineering at Concordia University, Montreal, Canada. He completed his Ph.D in Mechanical Engineering from IIT Madras, India, in 1972. Dr. Bhat’s research area covers mechanical vibrations, vehicle dynamics, structural acoustics, rotor dynamics, and dynamics of micro-electro-mechanical systems. He served as the president of Canadian Society for Mechanical Engineering in 2004–2006. He has been awarded the prestigious NASA Award for Technical Innovation for his contribution in developing “PROSSS—Programming Structured Synthesis System”. Dr. Bhat proposed the use of Boundary Characteristic Orthogonal Polynomials for use in the Rayleigh-Ritz method in 1985.

Ion Stiharu received Dipl. Eng. and Ph.D degrees from the Polytechnic University of Bucharest, Bucharest, Romania, in 1979 and 1989, respectively. He is currently a Professor and the Director of the CONCAVE Research Centre with the Department of Mechanical and Industrial Engineering, Concordia University, Montreal, QC, Canada, where he founded the micro-systems research back in 1990s. His research covers mainly micro-system technologies and MEMS. He has more than 350 publications along with few patents on the applications of MEMS to his credit Dr. Stiharu is a Fellow of the Canadian Society of Mechanical Engineers and the American Society of Mechanical Engineers ASME International. He has been part of many conference organizing committees and has been the organizer of a number of lecture series in MEMS and NEMS.

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Saeedi, K., Leo, A., Bhat, R.B. et al. Vibration of circular plate with multiple eccentric circular perforations by the Rayleigh-Ritz method. J Mech Sci Technol 26, 1439–1448 (2012). https://doi.org/10.1007/s12206-012-0325-7

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  • DOI: https://doi.org/10.1007/s12206-012-0325-7

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