Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson’s ratio

• Autorzy: Sharma Amit

Identyfikatory

DOI

10.15632/jtam-pl/109707

• Języki publikacji: EN

Abstrakty

EN

The frequency for the first two modes of vibration of a nonhomogeneous tapered rectangular plate is calculated under a bi linear (i.e., linear along both the axes) temperature field. For consideration of the nonhomogeneous material, the author assumed circular variation in Poisson’s ratio. Tapering in the plate is assumed to be linear in one direction. The results are calculated for different values of plate parameters and presented with the help of graphs. Comparison of the results is also given, to support the results of the present study.

Słowa kluczowe

EN

rectangular plate; circular variation; linear variation; Poisson’s ratio

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2019
• Tom: Vol. 57 nr 3
• Strony: 605--615
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Sharma Amit

• Amity University Haryana, Department of Mathematics, Gurugram, India

Bibliografia

• 1. Ansari A.H., Gupta U.S., 2003, Transverse vibration of polar orthotropic parabolically tapered circular plate, Indian Journal of Pure and Applied Mathematics, 34, 6, 819-830
• 2. Amabili M., Carra S., 2012, Experiments and simulations for large-amplitude vibrations of rectangular plates carrying concentrated masses, Journal of Sound and Vibration, 331, 155-166
• 3. Bayat M., Pakar I., Bayat M., 2011, Analytical study on the vibration frequencies of tapered beams, Latin American Journal of Solids and Structures, 8, 149-162
• 4. Chen L.Q., Peng L., Zhan A.Q., 2017, Transverse vibration of viscoelastic Timoshenko beam columns, Journal of Vibration and Control, 23, 10, 1572-1584
• 5. Dozio L., 2011, On the use of the trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates, Thin-Walled Structures, 49, 129-144
• 6. Hota S.S., Padhi P., 2007, Vibration of plates with arbitrary shapes of cutouts, Journal of Sound and Vibration, 302, 1030-1036
• 7. Joshi P.V., Jain N.K., Ramtekkar G.D., 2014, Analytical modeling and vibration analysis of internally cracked rectangular plates, Journal of Sound and Vibration, 333, 5851-5864
• 8. Khanna A., Kaur N., 2014, A study on vibration of tapered rectangular plate under non uniform temperature field, Mechanics, 20, 4, 376-381
• 9. Kumar A., Lather N., Bhardwaj R., Mani N., Sharma A., 2018, Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate, Vibroengineering Procedia, 21, 14-19
• 10. Kumar Y., Lal R., 2012, Vibrations of nonhomogeneous orthotropic rectangular plates with bilinear thickness variation resting on Winkler foundation, Meccanica, 47, 893-915
• 11. Lal R., Kumar Y., Gupta U.S., 2010, Transverse vibrations of nonhomogeneous rectangular plates of uniform thickness using boundary characteristic orthogonal polynomials, International Journal of Applied Mathematics and Mechanics, 6, 14, 93-109
• 12. Lam K.Y., Hung K.C., Chow S.T., 1989, Vibration analysis of plates with cutouts by the modified Rayleigh-Ritz method, Applied Acoustics, 28, 49-60
• 13. Liew K.M., Xiang Y., Kitipornchai S., 1995, Research on thick plate vibration: A literature survey, Journal of Sound and Vibration, 180, 163-176
• 14. Sharma A., Sharma A.K., Raghav A.K., Kumar V., 2016, Vibrational study of square plate with thermal effect and circular variation in density, Romanian Journal of Acoustics and Vibration, 13, 146-152
• 15. Sharma A., Kumar V., Raghav A.K., 2017, Vibrational frequency of circular tapered square plate, Romanian Journal of Acoustics and Vibration, 14, 21-27
• 16. Sharma A., Mani N., Bhardwaj R., 2019, Natural vibration of tapered rectangular plate with exponential variation in non homogeneity, Journal of Vibroengineering, 21, 187-197
• 17. Sharma S., Lal R., Singh N., 2017, Effect of non-homogeneity on asymmetric vibrations of non-uniform circular plates, Journal of Vibration and Control, 23, 10, 1635-1644
• 18. Soni S., Jain N.K., Joshi P.V., 2018, Vibration analysis of partially cracked plate submerged in fluid, Journal of Sound and Vibration, 412, 28-57

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).