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Quasi-Green’s function approach to fundamental frequency analysis of elastically supported thin circular and annular plates with elastic constraints

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Free vibration analysis of homogeneous and isotropic thin circular and annular plates with discrete elements such as elastic ring supports is considered. The general form of quasi- -Green’s function for thin circular and annular plates is obtained. The nonlinear characteristic equations are defined for thin circular and annular plates with different boundary conditions and different combinations of the core and support radius. The continuity conditions at the ring supports are omitted based on the properties of Green’s function. The fundamental frequency of axisymmetric vibration has been calculated using the Newton-Raphson method and calculation software. The obtained results are compared with selected results presented in literature. The exact frequencies of vibration presented in a non-dimensional form can serve as benchmark values for researchers to validate their numerical methods when applied for uniform thin circular and annular plate problems.
Rocznik
Strony
87--101
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
  • Bialystok University of Technology, Faculty of Management, Kleosin, Poland
Bibliografia
  • 1. Azimi S., 1988, Free vibration of circular plates with elastic or rigid interior support, Journal of Sound and Vibration, 120, 37-53
  • 2. Bodine R.Y., 1967, Vibration of a circular plate supported by a concentric ring of arbitrary radius, Journal of the Acoustical Society of America, 41, 1551
  • 3. Ding Z., 1994, Free vibration of arbitrarily shaped plates with concentric ring elastic and rigid supports, Computers and Structures, 50, 685-692
  • 4. Jaroszewicz J., Zoryj L., 2005, Methods of Free Axisymmetric Vibration Analysis of Circular Plates Using by Influence Functions, Bialystok University of Technology, Poland
  • 5. Kukla S., Szewczyk M., 2004, The Green’s functions for vibration problems of circular plates with elastic ring supports, Scientific Research of the Institute of Mathematics and Computer Science, 4, 1, 79-86
  • 6. Kukla S., Szewczyk M., 2005, Application of Green’s function method in frequency analysis of axisymmetric vibration of annular plates with elastic ring supports, Scientific Research of the Institute of Mathematics and Computer Science, 3, 1, 67-72
  • 7. Kukla S., Szewczyk M., 2007, Frequency analysis of annular plates with elastic concentric supports by Green’s function method, Journal of Sound and Vibration, 300, 387-393
  • 8. Kunukkasseril V.X., Swamidas A.S.J., 1974, Vibration of continuous circular plates, International Journal of Solids and Structures, 10, 603-619
  • 9. Laura P.A.A., Gutierrez R.H., Vera S.A., Vega D.A., 1999, Transverse vibrations of circular plate with a free edge and a concentric circular support, Journal of Sound and Vibration, 223, 5, 843-845
  • 10. Liu C.F., Chen G.T., 1995, A simple finite element analysis of axisymmetric vibration of annular and circular plates, International Journal of Mechanical Sciences, 37, 8, 861-871
  • 11. McLachlan N.W., 1955, Bessel Functions for Engineers, Clarendon Press, Oxford
  • 12. Rao L.B., Rao C.K., 2014a, Frequencies of circular plate with concentric ring and elastic edge support, Frontiers on Mechanical Engineering, 9, 2, 168-176
  • 13. Rao L.B., Rao C.K., 2014b, Frequency analysis of annular plates with inner and outer edges elastically restrained and resting on Winkler foundation, International Journal of Mechanical Sciences, 81, 184-194
  • 14. Singh A.V., Mirza S., 1976, Free axisymmetric vibration of a circular plate elastically supported along two concentric circles, Journal of Sound and Vibration, 48, 425-429
  • 15. Vega D.A., Vera S.A., Laura P.A.A., Gutierrez R.H., Pronsato M.E., 1999, Transverse vibrations of an annular circular plate with free edges and an intermediate concentric circular support, Journal of Sound and Vibration, 223, 493-496
  • 16. Vega D.A., Laura P.A.A., Vera S.A., 2000, Vibrations of an annular isotropic plate with one edge clamped or simply supported and an intermediate concentric circular supports, Journal of Sound and Vibration, 233, 1, 171-174
  • 17. Wang C.M., Thevendran V., 1993, Vibration analysis of annular plates with concentric supports using a variant of Rayleigh-Ritz method, Journal of Sound and Vibration, 163, 137-149
  • 18. Wang C.Y., 2001, On the fundamental frequency of a circular plate supported on a ring, Journal of Sound and Vibration, 243, 5, 945-946
  • 19. Wang C.Y., Wang C.M., 2003, Fundamental frequencies of circular plates with internal elastic ring support, Journal of Sound and Vibration, 263, 1071-1078
  • 20. Wang C.Y., 2006, Fundamental frequencies of annular plates with movable edges, Journal of Sound and Vibration, 290, 524-528
  • 21. Wang C.Y., 2014, The vibration modes of concentrically supported free circular plates, Journal of Sound and Vibration, 333, 835-847
  • 22. Żur K.K., 2015, Green’s function in frequency analysis of circular thin plates of variable thickness, Journal of Theoretical and Applied Mechanics, 53, 4, 873-884
  • 23. Żur K.K., 2016a, Green’s function approach to frequency analysis of thin circular plates, Bulletin of the Polish Academy of Sciences – Technical Sciences, 64, 1, 181-188
  • 24. Zur K.K., 2016b, Green’s function for frequency analysis of thin annular plates with nonlinear variable thickness, Applied Mathematical Modelling, 40, 5-6, 3601-3619
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-627b169b-df53-4230-84ca-090f3e230b64
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