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Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness
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Applied Mathematics·Volume 01 (2010)·Pages 357–365·Published 30 November 2010·DOI10.4236/am.2010.15047
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Abstract
In this paper, effect of thermal gradient on vibration of trapezoidal plate of varying thickness is studied. Thermal effect and thickness variation is taken as linearly in x-direction. Rayleigh Ritz technique is used to calculate the fundamental frequencies. The frequencies corresponding to the first two modes of vibrations are obtained for a trapezoidal plate for different values of taper constant, thermal gradient and aspect ratio. Results are presented in graphical form.
KeywordsFrequenciesTrapezoidal PlateLinearly ThicknessThermal Gradient
- K. M. Liew and K. Y. Lam, “Vibrational Response of Symmetrically Laminated Trapezoidal Composite Plates with Point Constraints,” International Journal of Solids and Structures, Vol. 29, No. 24, 1992, pp. 1535-1547.
- I. Chopra and Durvasula, “Vibration of Simply Supported Trapezoidal Plates I. Symmetric Trapezoids,” Journal of Sound Vibration, Vol. 19, No. 4, 1971, pp. 379-392.
- Y. Narita, K. Maruyama and M. Sonoda, “Transverse Vibration of Clamped Trapezoidal Plates Having Rectangular Orthotropy,” Journal of Sound Vibration, Vol. 77, 1981, pp. 345-356.
- K. M. Liew and M. K. Lim, “Transverse Vibration of Trapezoidal Plates of Variable Thickness: Symmetric Trapezoids,” Journal of Sound Vibration, Vol. 165, No. 1, 1993, pp. 45-67.
- M. S. Qatu, N. A. Jaber and A. W. Leissa, “Natural Frequencies for Completely Free Trapezoidal Plates,” Journal of Sound Vibration, Vol. 167, No. 1, 1993, pp. 183- 191.
- M. S. Qatu, “Vibrations of Laminated Composite Completely Free Triangular and Trapezoidal Plates,” International Journal of Mechanical Sciences, Vol. 36, No. 9, 1994, pp. 797-809.
- D. V. Bambill, P. A. A. Laura and R. E. Rossi, “Transverse Vibrations of Rectangular, Trapezoidal and Triangular Orthotropic, Cantilever Plates,” Journal of Sound Vibration, Vol. 210, No. 2, 1998, pp. 286-290.
- C. C. Chen, S. Kitipornchai, C. W. Lim and K. M. Liew, “Free Vibration of Cantilevered Symmetrically Laminated Thick Trapezoidal Plates,” International Journal of Mechanical Sciences, Vol. 41, No. 6, 1999, pp. 685-702.
- H. T. Saliba, “Free Vibration Analysis of Simply Supported Symmetrical Trapezoidal Plates,” Journal of Sound Vibration, Vol. 110, No. 1, 1986, pp. 87-97.
- H. T. Saliba, “Transverse Free Vibration of Fully Clamped Symmetrical Trapezoidal Plates,” Journal of Sound Vibration, Vol. 126, No. 2, 1988, pp. 237-247.
- A. Krishnan and J. V. Deshpande, “A Study on Free Vibration of Trapezoidal Plates,” Journal of Sound Vibration, Vol. 146, No. 2, 1991, pp. 507-515.
- A. K. Gupta and H. Kaur, “Study of the Effect of Thermal Gradient on Free Vibration of Clamped Visco-Elastic Rectangular Plates with Linearly Thickness Variation in both Directions,” Meccanica, Vol. 43, No. 3, 2008, pp. 449-458.
- A. K. Gupta, T. Johri and R. P. Vats, “Study of Thermal Gradient Effect on Vibrations of a Non-Homogeneous Orthotropic Rectangular Plate Having Bi-Direction Linearly Thickness Variations,” Meccanica, Vol. 45, No. 3, 2010, pp. 393-400.