Application of translational edge restraint for vibration analysis of free edge Kirchhoff’s plate including rigid-body modes

• Autorzy: Verma Y. , Datta N.
• Języki publikacji: EN

Abstrakty

EN

A comprehensive theoretical study of closed-form rigid-body modes of a free-free and translationally edge-restrained Euler-Bernoulli beam is presented. Accurate vibrational analysis of a free-free-free-free plate is not possible without the inclusion of degenerate rigid-body beamwise admissible functions. The trivial solution(s) of the beam frequency equation produce(s) a non-trivial modeshape, which satisfies the boundary conditions, has zero curvature, and is orthogonal to the other modeshapes. These frequency parameters are “trivial”, i.e. they lead to zero natural frequency, since their modeshapes have no curvature. Mathematicallygenerated orthogonal free-free (classical) beam-wise rigid-body modeshapes, and those generated from non-classical edged beams, have been both separately used as admissible functions in the Rayleigh-Ritz method (RRM) to generate the plate natural frequencies of a free-freefree-free rectangular uniform isotropic Kirchhoff’s plate. With respect to the increasing elastic support, the trifurcation and bifurcation of plate frequencies from the trivial to the flexural frequencies, is investigated. The completely free plate modeshapes are also presented. Also, combination of present closed-form rigid-body modes with polynomial functions, trigonometric functions is also demonstrated.

Słowa kluczowe

EN

free edge plate; translational restraint; frequency parameter; rigid body modes; waveform coefficients

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2018
• Tom: Vol. 66, iss. 1
• Strony: 21--60
• Opis fizyczny: Bibliogr. 27 poz., rys., tab., wykr.

Twórcy

autor

Verma Y.

• Indian Institute of Technology Kharagpur, India

autor

Datta N.

• Indian Institute of Technology Kharagpur, India

Bibliografia

• 1. Bardell N.S., Free vibration analysis of a flat plate using the hierarchical finite element method, Journal of Sound and Vibration, 51(2): 263–289, 1991.
• 2. Bassily S.F., Dickinson S.M., On the use of beam functions for problems of plates involving free edges, Journal of Applied Mechanics, 42(4): 858–864, 1975.
• 3. Bhat R.B., Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method, Journal of Sound and Vibration, 102(4): 493–499, 1985.
• 4. Budiansky B., Hu P.C., The Lagrangian multiplier method of finding upper and lower limits to critical stresses of clamped plates, NASA Technical Report, NTIS Issue Number 199609, 1946.
• 5. Chen C.P., Huang C.H., Chen Y.Y., Vibration analysis and measurement for piezoceramic rectangular plates in resonance, Journal of Sound and Vibration, 326(1–2): 251–262, 2009.
• 6. De Rosa M.A., Lippiello M., Natural vibration frequencies of tapered beams engineering, Engineering Transactions, 57(1):45–66, 2009.
• 7. Dickinson S.M., Blasio A.D., On the use of orthogonal polynomials in the RayleighRitz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates, Journal of Sound and Vibration, 108(1): 51–62, 1986.
• 8. Dozio L., On the use of the Trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates, Thin-Walled Structures, 49: 129–144, 2011.
• 9. Eatock Taylor R., Ohkusu M., Green functions for hydroelastic analysis of vibrating free–free beams and plates, Applied Ocean Research, 22(5): 295–314, 2000.
• 10. Hurlebaus S., Gaul L., An exact series solution for calculating the eigenfrequencies of orthotropic plates with completely free boundary, Journal of Sound and Vibration, 244(5): 747–759, 2001.
• 11. Katsikadelis J.T., Armenakas A.E., A new boundary equation solution to the plate problem, ASME Journal of Applied Mechanics, 56(2): 364–374, 1989.
• 12. Leissa A.W., The free vibration of rectangular plates, Journal of Sound and Vibration, 31(3): 257–293, 1973.
• 13. Li W.L., Comparison of Fourier sine and cosine series expansions for beams with arbitrary boundary conditions, Journal of Sound and Vibration, 255(1), 185–194, 2002.
• 14. Li W.L., Vibration analysis of rectangular plates with general elastic boundary supports, Journal of Sound and Vibration, 273(3): 619–635, 2004.
• 15. Ma C.C., Huang C.H., Experimental whole-field interferometry for transverse vibration of plates, Journal of Sound and Vibration, 271(3–5): 493–506, 2004.
• 16. Mizusawa T., Natural frequencies of rectangular plates with free edges, Journal of Sound and Vibration, 105(3): 451–459, 1986.
• 17. Monterrubio L.E., IIanko S., Proof of convergence for a set of admissible functions for the Rayleigh-Ritz analysis of beams and plates and shells of rectangular planform, Computers and Structures, 147(C): 236–243, 2015.
• 18. Mukhopadhyay M., Structural dynamics: vibrations & systems, Ane Books India, 2008.
• 19. Rao C.K., Mirza S., A note on vibrations of generally restrained beams, Journal of Sound and Vibration, 130(3): 453-465, 1989.
• 20. Rao L.B., Rao C.K., Vibrations of circular plate supported on a rigid concentric ring with transnational restraint boundary, Engineering Transactions, 64(3): 259–269, 2016.
• 21. Saha K.N., Kar R.C., Datta P.K., Free vibration analysis of rectangular Mindlin plates with elastic restraints uniformly distributed along the edges, Journal of Sound and Vibration, 192(4): 885–904, 1996.
• 22. Saha K.N., Misra D., Pohit G., Ghosal S., Large amplitude free vibration study of square plates under different boundary conditions through a static analysis, Journal of Vibration and Control, 10(7): 1009–1028, 2004.
• 23. Szilard R., Theories and applications of plate analysis: classical numerical and engineering method, John Wiley & Sons, 2004.
• 24. Tang Y., Numerical evaluation of uniform beam modes, Journal of Engineering Mechanics, 129(12): 1475–1477, 2003.
• 25. Warburton G.B., Edney S.L., Vibrations of rectangular plates with elastically restrained edges, Journal of Sound and Vibration, 95(4): 537–552, 1984.
• 26. Xiang Y., Liew K.M., Kitipornchai S., Vibration analysis of rectangular Mindlin plates resting on elastic edge supports, Journal of Sound and Vibration, 204(1): 1–16, 1997.
• 27. Zhou D., Natural frequencies of elastically restrained rectangular plates using a set of static beam functions in the Rayleigh-Ritz method, Computers and Structures, 57(4): 731– 735, 1995.

Uwagi

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