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Khanna, Anupam
- Effect of Varying Poisson Ratio on Thermally Induced Vibrations of Non-homogeneous Rectangular Plate
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Authors
Affiliations
1 Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, Haryana, IN
2 Department of Mathematics, ManavBharti University, Solan (H.P.), IN
1 Department of Mathematics, Maharishi Markandeshwar University, Mullana, Ambala, Haryana, IN
2 Department of Mathematics, ManavBharti University, Solan (H.P.), IN
Source
Indian Journal of Science and Technology, Vol 5, No 9 (2012), Pagination: 3263-3267Abstract
A mathematical model will help the engineers in science and technology applications. In this paper, authors studied a temperature-thickness coupling problem of a non-homogeneous rectangular plate in which temperature varies bilinearly&thickness varies linearly in x-direction. Due to non-homogeneity, it is considered that poisson ratio varies exponentially in x direction. Ray-Leigh Ritz method has been adopted to calculate the time period for fixed two modes of vibration for different values of aspect ratio, thermal gradient and taper constants. All results are shown in graphs.Keywords
Vibration, Thermal Gradient, Taper Constant, Aspect Ratio, Time PeriodFull Text
References
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- Gupta Dharam V, Khanna Anupam and Gupta Arun (2009) Free Vibration of clamped visco elastic rectangular plate having bi-direction exponentially thickness variation. J. Theoretical &Appl. Mech., Warsaw. 2, 457-471.
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- Kumar and Sanjay (2003) Effect of thermal gradient on some vibration problems of orthotropic visco elastic plates of variable thickness. Ph.D. Thesis, C.C.S. Univ., Meerut, U.P., India.
- Khanna and Anupam (2005) Some vibration problems of visco-elastic plate of variable thickness in two directions. Ph.D. Thesis, C.C.S. Univ., Meerut, U.P. India.
- LalRoshan and Dhanpati (2009) Effect of non homogeneity on vibration of orthotropic rectangular plates of varying thickness resting on pasternak foundation. J. Vibration & Acoustics, ASME. 131,1-9.
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- Leissa AW (1987) Recent studies in plate vibration 1981-1985. Part II, complicating effects. The Shock & Vibration Digest.19, 10-24.
- Singh B and Saxena V (1996) Transverse vibration of rectangular plate with bidirectional thickness variation. J. Sound & Vibration. 198, 51-65.
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- Effect of Sinusoidal Thickness Variation on Vibrations of Non-homogeneous Parallelogram Plate with Bi-linearly Temperature Variations
Abstract Views :421 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, M. M. Engineering College, M. M. University, Mullana, Haryana, IN
1 Department of Mathematics, M. M. Engineering College, M. M. University, Mullana, Haryana, IN
Source
Indian Journal of Science and Technology, Vol 6, No 9 (2013), Pagination: 5228-5234Abstract
The present study is the computational prediction about the effect of sinusoidal varying thickness on the vibrations of non-homogeneous parallelogram plate. Consideration of the plate's material is visco-elastic with clamped boundary. It is assumed that the temperature varies bi-linearly while the density of the plate's material varies linearly in one direction due to non-homogeneity. The general equation of motion and consecutive equations are solved by using the Rayleigh-Ritz method. To study the vibrational behavior of parallelogram plate, natural frequency for both the modes of vibration is calculated for different values of parameters and shown in the graphs. All the calculations are carried out for duralumin.Keywords
Vibration, Taper Constant, Sinusoidal, Thickness Variation, Non-homogeneity, Frequency, Thermal GradientFull Text
References
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- Chakarverty S, and Petyt M (1997). Natural frequencies for free vibration of non-homogeneous elliptic and circular plate using two dimensional orthogonal polynomials, Applied Mathematical Modelling, vol 21(7), 399–417.
- Gupta A K, and Khanna A (2007). Vibration of visco-elastic rectangular plate with linearly varying thickness vibration in both directions, Journal of Sound and Vibration, vol 301, No 3–5, 450–457.
- Gupta A K, and Khanna A(2010). Thermal effect on vibrations of parallelogram plate of linearly varying thickness, Advanced Studies of Theoretical Physics, vol 4, No.17, 817–826.
- Gupta A K, Kumar A et al. (2010). Vibration of visco-elastic parallelogram plate with parabolic thickness varia-tion, Applied Mathematics, vol 1, 128–136.
- Gupta A K, and Kumar M (2011). Thermal effect of vibration of a parallelogram plate of bi-direction linearly varying thickness, Applied Mathematics, vol 2, 33–38.
- Gupta A K, and Kaur H (2008). 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(4), 449–458.
- Anupam K, and Sharma A K (2011). Thermally induced vibration of non-homogeneous visco-elastic plate of variable thickness, Advances in Physics, Theories and Application, vol 1, 1–5.
- Khanna A, Kaur N et al. (2012). Effect of varying poisson ratio on thermally induced vibration of non-homogeneous rectangular plate, Indian Journal of Science and Technology, vol 5(9), 3263–3276.
- Khanna A, and Sharma N (2012). Vibrational analysis of non-homogeneous tapered square plates with bi-parabolic temperature variations, International Journal of Mathematical Sciences and Applications, vol 6, No.VI, 327–334.
- Lal R, and Dhanpati (2009). Effect of non-homogeneity on the vibration of orthotropic rectangular plates of varying thickness resting on a Pasternak foundation, Journal of Vibration and Acoustics: ASME, vol 131(1), 1–9.
- Leissa A W (1969). Vibration of plates, NASA SP, Scientific and Technical Information Division, National Aeronautics and Space Administration, vol 160.
- Leissa A W (1987). Recent studies in plate vibration 1981–1985, Part-II complicating effect, The Shock and Vibration Digest, vol 19, 10–24.
- Li W L (2004). Vibration analysis of rectangular plate with general elastic boundary support, Journal of Sound and Vibration, vol 273(3), 619–635.
- Tomar J S, and Gupta A K (1983). Thermal effect on frequencies of an orthotropic rectangular plate of linearly varying thickness, Journal of Sound and Vibration, vol 90(3), 325–331.