19. Linear free vibration analysis of rectangular Mindlin plates using coupled displacement field method

Rajesh Korabathina1, Meera Saheb Koppanati2

Jawaharlal Nehru Technological University, Kakinada, 533003, India

1Corresponding author

E-mail: 1k.rajeshmtechmba@gmail.com, 2meera.aec@gmail.com

(Received 27 January 2016; accepted 27 February 2016)

Abstract. Many of the structural members like aircrafts, automobiles and any machine elements are made of simple structures, they may be beams or columns (one dimensional), plates (two dimensional) and shells (three dimensional) structures. These structural components are generally subjected to dynamic loadings in their working life. Very often these components may have to perform in severe dynamic environment where in the maximum damage results from the resonant vibration. Maximum amplitude of the vibration must be in the limit for the safety of the structure. Hence vibration analysis has become very important in designing a structure to know in advance its response and to take necessary steps to control the structural vibrations and its amplitudes. In the current investigation, a simple and efficient coupled displacement field method is developed to study the free vibration behavior of the moderately thick rectangular plates. A single term trigonometric admissible displacement field is assumed for one of the variables (in both ,  directions). Making use of the coupling equation, the spatial variation for the lateral displacement field is derived in terms of the total rotations. The linear fundamental frequency parameters for the all edges simply supported moderately thick rectangular plates are derived and the numerical results obtained from the present formulation are in very good agreement with those obtained from the existing literature.

Keywords: linear free vibrations, coupled displacement filed method, rectangular Mindlin plates.

References

[1]        Cheung Y. K., Zhou D. Vibrations of moderately thick rectangular plates in terms of a set of static Timoshenko beam functions. Journal of Computers and Structures, Vol. 78, 2000, p. 757‑768.

[2]        Dawe D. J., Roufaeil O. L. Rayleigh-Ritz vibration analysis of Mindlin plates. Journal of Sound and Vibration, Vol. 69, Issue 3, 1980, p. 345‑359.

[3]        Eftekhari S. A., Jafari A. A. High accuracy mixed finite Element-Ritz formulation for free vibration analysis of plates with general boundary conditions. Applied Mathematics and Computation, Vol. 219, 2012, p. 1312‑1344.

[4]        Ferreira A. J. M. Free Vibration analysis of Timoshenko beams and Mindlin plates by radial basis functions. International Journal of Computational Methods, Vol. 2, Issue 1, 2005, p. 15‑31.

[5]        Han J. B., Liew K. M. Static analysis of Mindlin plates: the differential quadrature element method (DQEM). Journal of Computer Methods in Applied Mechanics and Engineering, Vol. 177, 1999, p. 51‑75.

[6]        Kanaka Raju K., et al. Effect of geometric non-linearity on the free flexural vibrations of moderately thick rectangular plates. Journal of Computers and Structures, Vol. 9, 1978, p. 441‑444.

[7]        Lee J. M., Kim K. C. Vibration analysis of rectangular isotropic plates using Mindlin plate characteristic functions. Journal of Sound and Vibration, Vol. 187, Issue 5, 1995, p. 865‑877.

[8]        Ma Y. Q., Ang K. K. Free vibration of Mindlin plates based on the relative displacement plate element. Finite Elements in Analysis and Design, Vol. 42, 2006, p. 1021‑1028.

[9]        Roufaeil O. L., Dawe D. J. Vibration analysis of rectangular Mindlin plates by the finite strip method. Journal of Computers and Structures, Vol. 12, 1980, p. 833‑842.

[10]     Sadrnejad S. A., et al. Vibration equations of thick rectangular plates using Mindlin plate theory. Journal of Computer Science, Vol. 5, Issue 11, 2009, p. 838‑842.

[11]     Sakiyama T., Matsuda H. Free vibration of rectangular Mindlin plate with mixed boundary conditions. Journal of Sound and Vibration, Vol. 113, Issue 1, 1987, p. 208‑214.

[12]     Xiang Y., et al. DSC-element method for free vibration analysis of rectangular Mindlin plates. International Journal of Mechanical Sciences, Vol. 52, 2010, p. 548‑560.

[13]     Yufeng Xing, Bo Liu Characteristic equations and closed-form solutions for free vibrations of rectangular Mindlin plates. Acta Mechanica Solida Sinica (China), Vol. 22, Issue 2, 2009, p. 125‑136.

[14]     Zhou D. Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method. International Journal of Solids and Structures, Vol. 38, 2001, p. 5565‑5580.