Numerical Computing of Frequencies for Rectangular and Square Plates with Transcendental Thickness Variation
Neetu Singh1, Vipin Saxena2 

1Neetu Singh, Department of Mathematics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.
2Vipin Saxsena, Department of Computer Science, Babasaheb Bhimrao Ambedkar University, Lucknow, India.

Manuscript received on 15 March 2019 | Revised Manuscript received on 21 March 2019 | Manuscript published on 30 July 2019 | PP: 4017-4030 | Volume-8 Issue-2, July 2019 | Retrieval Number: B3197078219/19©BEIESP | DOI: 10.35940/ijrte.B3197.078219
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Abstract: The frequencies of the thin plate play an important role for the design of the engineering machines, naval structure, etc. Tremendous amount of the literature on the study of vibrations of rectangular and square plate are available with various kinds of the thickness variations. From the study it is observed that transcendental thickness variation has not been studied by the researchers which satisfy the boundary conditions. Therefore, the present work is the attempt in this direction. A well-known Rayleigh-Ritz method has been used for computation of the first three frequencies alongwith mode shapes and by varying the boundary conditions at the side of the plate. The convergence of the computed results has been presented through table and comparison has also been made with the existing result.
Index Terms: Rayleigh-Ritz Method, Frequencies, Mode Shape, Convergence and Comparison, Plates.

Scope of the Article:
Cloud Computing