A Study on Vibration of Tapered Non-Homogeneous Rectangular Plate with Structural Parameters
More details
Hide details
Department of Mathematics, Statistics and Physics, Punjab Agricultural University, Ludhiana, Punjab, India
Department of Mathematics, Dr. Akhilesh Das Gupta Institute of Technology and Management, New Delhi, India
Department of Mathematics, D.A.V. College Sadhaura, Yamunanagar, Haryana, India
Online publication date: 2018-11-21
Publication date: 2018-11-01
International Journal of Applied Mechanics and Engineering 2018;23(4):873-884
Effects of structural parameters on the vibration of a tapered non-homogeneous rectangular plate with different combinations of boundary conditions are discussed. Tapering in the plate is assumed to be sinusoidal in the x-direction. Here, temperature variation and non-homogeneity in the plate material are also considered sinusoidal in the x-direction. The Rayleigh-Ritz method is used to calculate the frequency parameter for the first two modes of vibration for different values of the structural parameters, i.e. the taper parameter, thermal gradient, aspect ratio and non-homogeneity constant. Results are obtained for three boundary conditions, i.e. clamped boundary (C-C-C-C), simply supported boundary (SS-SS-SS-SS) and clamped-simply supported boundary (CSS-C-SS). Numerical values of the frequency parameter are given in a compact tabular form.
Leissa A.W. (1969): Vibration of Plates. – Washington, D.C.: NASA.
Sobotka Z. (1978): Free vibration of visco-elastic orthotropic rectangular plates. – Acta Technica (CSAV), vol.6, pp.678-705.
Tomar J.S. and Gupta A.K. (1983): Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness. – Journal of Sound and Vibration, vol.90, No.3, pp.325-331.
Tomar J.S., Gupta D.C. and Jain N.C. (1984): Free vibrations of an isotropic non-homogeneous infinite plate of parabolically varying thickness. – Indian Journal of Pure and Applied Mathematics, vol.15, No.2, pp.211-220.
Cheung Y.K. and Zhou D. (1999): The free vibrations of tapered rectangular plates using a new set of beam functions with the Rayliegh-Ritz method. – Journal of Sound and Vibration, vol.223, No.5, pp.703-722.
Lal R. (2003): Transverse vibrations of orthotropic non-uniform rectangular plates with continuously varying density. – Indian Journal of Pure and Applied Mathematics, vol.34, No.4, pp.587-606.
Li W.L. (2004): Vibration analysis of the rectangular plate with general elastic boundary supports. – Journal of Sound and Vibration, vol.273, No.3, pp.619-635.
Gupta A.K., Kumar M., Kumar S. and Khanna A. (2011): Thermal effect on vibration of parallelogram plate of bidirection linearly varying thickness. – Applied Mathematics, vol.1, No.2, pp.33-38.
Gupta A.K. and Sharma P. (2013): Thermal analysis on frequencies of non-homogeneous trapezoidal plate of variable thickness and density. – Acta Tecnica, vol.58, No.2, pp.189-205.
Khanna A. and Singhal A. (2015): A study on free vibration of visco-elastic tapered plate with clamped ends. – Romanian Journal of Acoustics and Vibration, vol.12, No.1, pp.43-48.
Chakraverty S. (2009): Vibration of Plates. – Florida: Taylor and Francis.
Gupta A.K., Agarwal N. and Kaur H. (2011): Transverse vibration of non-homogeneous orthotropic visco-elastic circular plate of varying parabolic thickness. – Mathematical Methods in the Applied Sciences, vol.34, pp.2065-2076.
Khanna A. and Singhal A. (2013): An analytical approach on thermally induced vibrations of non-homogeneous tapered plate. – Journal of Mathematics, vol. 2013, Article ID 721868, 6 pages.
Khanna A. and Kaur N. (2016): Effect of thermal gradient on vibration of non-uniform visco-elastic rectangular plate. – Journal of the Institution of Engineers (India): Series C, vol.97, No.2, pp.141-148.
Khanna A. and Kaur N. (2016): Effect of structural parameters on vibration of non-homogeneous visco-elastic rectangular plate. – Journal of Vibration Engineering and Technologies, vol.4, No.5, pp.459-466.
Khanna A. and Singhal A. (2016): Effect of bi-directional temperature variation on vibration of rectangular plate with bi-parabolic thickness variation. – Journal of Low Frequency Noise, Vibration and Active Control, vol.35, No.2, pp.139-151.
Singhal A. (2016): V ibrational Behavior of Visco-Elastic Tapered Rectangular Plate. – Ph.D. Thesis, M.M.D.U.- Mullana, India.
Khanna A. and Kaur N. (2014): A study on vibration of tapered rectangular plate under non-uniform temperature field. – Mechanika, vol.20, No.4, pp.376-381.
Journals System - logo
Scroll to top