Free vibration frequencies of a circular thin plate with variable parameters
DOI:
https://doi.org/10.21638/spbu01.2020.314Abstract
Transverse vibrations of an inhomogeneous circular thin plate are studied in the paper. Nondimensional equations based on Kirchhoff-Love hypotheses describing nonaxisymmetric vibrations of inhomogeneous plate are derived. Using the perturbation method, asymptotic formulas are obtained for the free vibration frequencies of a plate, whose thickness and Young’s modulus linearly depend on the radial coordinate. The influence of the plate edge conditions on the frequencies and the behavior of frequencies for a plate with the fixed mass are analyzed. For the lower free vibration frequencies the results of asymptotic and finite elements analyses are compared.
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References
Литература
1. Leissa A.W. Vibration of plates. Washington: US Government Printing Office, 1969.
2. Singh B., Chakraverty S. Use of characteristic orthogonal polynomials in two dimensions for transverse vibration of elliptic and circular plates with variable thickness // J. Sound Vibrat. 1994. Vol. 173. Iss. 3. P. 289–299. https://doi.org/10.1006/jsvi.1994.1231
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References
1. Leissa A.W., Vibration of plates (US Government Printing Office, Washington, 1969).
2. Singh B., Chakraverty S., “Use of characteristic orthogonal polynomials in two dimensions for transverse vibration of elliptic and circular plates with variable thickness”, J. Sound Vibrat. 173(3), 289–299 (1994). https://doi.org/10.1006/jsvi.1994.1231
3. Singh B., Saxena V., “Transverse vibration of a circular plate with unidirectional quadratic thickness variation”, Int. J. Mech. Sci. 38(4), 423–430 (1996). https://doi.org/10.1016/0020-7403(95)00061-5
4. Singh B., Hassan S.M., “Transverse vibrations of a circular plate with arbitrary thickness variation”, Int. J. Mech. Sci. 40(11), 1089–1104 (1998).
5. Wang X., Yang J., Xiao J., “On free vibration analysis of circular annular plates with non-uniform thickness by the differential quadrature method”, J. Sound Vibration 184, 547–551 (1995).
6. Prasad C., Jain R.K., Soni S.R., “Axisymmetric vibrations of circular plates of linearly varying thickness”, ZAMP 23, 941–948 (1972).
7. Eisenberger M., Jabareen M., “Axisymmetric vibrations of circular and annular plates with variable thickness”, International Journal of Structural Stability and Dynamics 1(2), 195–206 (2001). https://doi.org/10.1142/S0219455401000196
8. Salmane A., Lakis A.A., “Natural frequencies of transverse vibrations of non-uniform circular and annular plates”, J. Sound Vibration 220, 225–249 (1999).
9. Singh B., Saxena V., “Axisymmetric vibration of a circular plate with exponential thickness variation”, J. Sound Vibration 196, 35–42 (1996).
10. Smirnov A. L., “Free vibrations of annular circular and elliptic plates”, COMPDYN Proceedings 2, 3547–3555 (2019).
11. Smirnov A., Lebedev A., “Free vibrations of perforated thin plates”, The International Conference on Numerical Analysis and Applied Mathematics 1648, 300009 (AIP Conference Proceeding, 2014). https://doi.org/10.1063/1.4912551
12. Anikina T.A., Vatulyan A.O., Uglich P. S., “On the calculation of variable stiffness for a circular plate”, Computational Technologies 17(6), 26–35 (2012). (In Russian)
13. Bauer S.M., Filippov S.B., Smirnov A. L., Tovstik P.E., Vaillancourt R., Asymptotic methods in mechanics of solids (Birkh¨auser, Basel, 2015).
14. Laura P.A.A., Sonzogni V., Romanelli E., “Effect of Poisson’s ratio on the fundamental frequency of transverse vibration and buckling load of circular plates with variable profile”, Appl. Acoustics 47, 263–273 (1996). https://doi.org/10.1016/0003-682X(95)00053-C
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Published
2020-09-04
How to Cite
Vasiliev, G. P., & Smirnov, A. L. (2020). Free vibration frequencies of a circular thin plate with variable parameters. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7(3), 518–526. https://doi.org/10.21638/spbu01.2020.314
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
