Abstract
The present study represents a computational prediction for the effect of thermal gradient on the vibrations of non-homogeneous four sided clamped skew plate with variable thickness. Authors assumed that temperature varies bi-linearly, density of the plate’s material varies linearly in one direction due to non-homogeneity and thickness of plate varies exponentially in one direction. The general equation of motion and consecutive equations are solved by using the Rayleigh–Ritz method. Calculations are made for natural frequencies for first two modes of vibration of a parallelogram plate (a special type of skew plate) at the different combinations of parameters. Results are shown in graphs.
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Refrences
Leissa, A.W.: Vibration of plates. NASA SP-160 (1969)
Leissa, A.W.: Recent studies in plate vibration 1981–1985, part-II complicating effect. Shock Vib. Dig. 19, 10–24 (1987)
Chakraverty, S., Petyt, M.: Natural frequencies for free vibration of non-homogeneous elliptic and circular plate using two dimensional orthogonal polynomials. Appl. Math. Modell. 21, 399–417 (1997)
Singh, B., Sexena, V.: Transverse vibration of skew plates with variable thickness. J. Sound Vib. 206(1), 1–13 (1997)
Gupta, A.K., Khanna, A.: Vibration of visco-elastic rectangular plate with linearly varying thickness vibration in both directions. J. Sound Vib. 301(3–5), 450–457 (2007)
Lal, R., Dhanpati: Effect of non-homogeneity on the vibration of orthotropic rectangular plates of varying thickness resting on a Pasternak foundation J. Vib. Acoust. 131, 1–9 (2009)
Huang, C.S., Leissa, A.W.: Vibration analysis of rectangular plates with side cracks via the Ritz method. J. Sound Vib. 323(3–5), 974–988 (2009)
Alijani, F., Amabili, M.: Theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges. J. Sound Vib. 332, 3564–3588 (2013)
Wu, L.H., Lu, Y.: Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method. Int. J. Mech. Sci. 53, 494–504 (2011)
Quintana. M.V., Nallim L.G.: a general Ritz formulation for the free vibration analysis of thick trapezoidal and triangular laminated plates resting on elastic supports. Int. J. Mech. Sci. 69, 1–9
Quintana, M.V., Nallim, L.G.: A variational approach to free vibration analysis of shear deformable polygonal plates with variable thickness. Appl. Acoust. 71, 393–401 (2010)
Zhou, L., Zheng, W.X.: Vibration of skew plates by the MLS-Ritz method. Int. J. Mech. Sci. 50, 1133–1141 (2008)
Gupta, A.K., Kumar, M.: Thermal effect of vibration of a parallelogram plate of bi-direction linearly varying thickness. Appl. Math 2, 33–38 (2011)
Khanna, A., Arora, P.: Effect of sinusoidal thickness variation on vibrations of non-homogeneous parallelogram plate with bi-linearly temperature variations. Indian J. Sci. Technol. 6(9) (2013)
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Khanna, A., Arora, P. (2014). Theoretical Study on Vibration of Skew Plate Under Thermal Condition. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 259. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1768-8_16
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DOI: https://doi.org/10.1007/978-81-322-1768-8_16
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