AM  Vol.1 No.5 , November 2010
Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness
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.

Cite this paper
nullA. Gupta and P. Sharma, "Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness," Applied Mathematics, Vol. 1 No. 5, 2010, pp. 357-365. doi: 10.4236/am.2010.15047.
References
[1]   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.

[2]   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.

[3]   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.

[4]   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.

[5]   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.

[6]   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.

[7]   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.

[8]   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.

[9]   H. T. Saliba, “Free Vibration Analysis of Simply Supported Symmetrical Trapezoidal Plates,” Journal of Sound Vibration, Vol. 110, No. 1, 1986, pp. 87-97.

[10]   H. T. Saliba, “Transverse Free Vibration of Fully Clamped Symmetrical Trapezoidal Plates,” Journal of Sound Vibration, Vol. 126, No. 2, 1988, pp. 237-247.

[11]   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.

[12]   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.

[13]   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.

[14]   A. K. Gupta, T. Johri and R. P. Vats, “Thermal Effect on Vibration of Non Homogeneous Orthotropic Rectangular Plate Having Bi-Directional Parabolic Ally Varying Thickness,” Proceedings of International Conference on Engineering & Computer Science, San Francisco, 2007, pp. 784-787.

[15]   A. K. Gupta and A. Khanna, “Vibration of Visco-Elastic Rectangular Plate with Linearly Thickness Variations in both Directions,” Journal of Sound Vibration, Vol. 301, No. 3-5, 2007, pp. 450-457.

[16]   C.-H. Huang, C.-H. Hsu and Y.-K. Lin, “Experimental and Numerical Investigations for the Free Vibration of Cantilever Trapezoidal Plates,” Journal of the Chinese Institute of Engineers, Vol. 29, No. 5, 2006, pp. 863-872.

[17]   J. S. Tomar and A. K. Gupta, “Effect of Thermal Gradient on Frequencies of an Orthotropic Rectangular Plate Whose Thickness Varies in Two Directions,” Journal of Sound Vibration, Vol. 98, No. 2, 1985, pp. 257-262.

[18]   J. S. Tomar and A. K. Gupta, “Thermal Effect on Frequencies of an Orthotropic Rectangular Plate of Linearly Varying Thickness,” Journal of Sound Vibration, Vol. 90, No. 3, 1983, pp. 325-331.

[19]   N. J. Hoff, “High Temperature Effect in Air Craft Structures,” Pergamon Press, New York, 1958.

 
 
Top