Study of thermal gradient effect on vibrations of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations

Gupta, AK; Johri, Tripti; Vats, R. P.

doi:10.1007/s11012-009-9258-3

Cited by 26 publications

(5 citation statements)

References 13 publications

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“…Gupta et al (2007) carried out work out to investigate the thermal effect on vibration of nonhomogeneous orthotropic rectangular plate having bidirectional parabolically varying thickness. Gupta et al (2010) calculated the thermal gradient effect on vibration of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variation.…”

Section: Introductionmentioning

confidence: 99%

Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness

Gupta¹,

Sharma²

2010

Journal of Vibration and Control

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In this paper, the thermal effect on vibration of orthotropic trapezoidal plate of linearly varying thickness is studied. The Rayleigh Ritz method is used to evaluate the fundamental frequencies. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. Frequency corresponding to the first two modes of vibration is calculated for the trapezoidal plate having clamped-simply supported-clamped-simply supported (C-S-C-S) edges for different values of thermal gradient, taper constant and aspect ratio. The proposed method is applied to solve orthotropic trapezoidal plate of variable thickness with C-S-C-S boundary conditions. Results are shown by figures for different values of thermal gradient, taper constant and aspect ratio for first two modes of vibrations.

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Section: Introductionmentioning

confidence: 99%

Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness

Gupta¹,

Sharma²

2010

Journal of Vibration and Control

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“…all the four degree of freedoms of the nodes to the side faces of the plates are constrained. Using (13) in (10) …”

Section: Solution and Frequency Equationsmentioning

confidence: 99%

“…Krishnan and Deshpande [11] have studied the free vibration analysis of the trapezoidal plates. Gupta et al [12][13][14][15] have worked on the vibration analysis of visco-elastic rectangular plates of variable thickness and studied the thermal gradient effect and non-homogeneity effect on the free vibrations of the plate. Huang, Hsu and Lin [16] studied the experimental and numerical investigations for the free vibration of cantilever trapezoidal plates.…”

Section: Introductionmentioning

confidence: 99%

Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness

Gupta¹,

Sharma²

2010

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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.

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“…Akiyama and Kuroda (1997) discussed the fundamental frequencies of rectangular plates with linearly varying thickness. Civalek (2009) discussed the fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method, and Gupta et al (2010a) studied the thermal gradient effect on vibration of a nonhomogeneous orthotropic rectangular plate having bi-direction linearly thickness variation. Gupta et al (2010b) did the vibration analysis of visco-elastic rectangular plate with thickness varying linearly in one direction and parabolically in the other direction.…”

Section: Introductionmentioning

confidence: 99%

Forced vibrations of non-homogeneous rectangular plate of linearly varying thickness

Gupta¹,

Saini²,

Singh³

et al. 2012

Journal of Vibration and Control

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An analysis is presented of the forced vibrations of non-homogeneous rectangular plate of variable thickness on the basis of classical plate theory. The non-homogeneity of the plate material is assumed to arise due to the variation in density which is assumed to vary linearly. The thickness of the plate also varies linearly. Approximate formulae are proposed for estimating the maximum deflection of a rectangular plate subject to a uniformly distributed harmonic lateral load. Maximum deflection for the different values of the fundamental frequency of vibration is computed for a simply supported-free-simply supported-free plate for various values of taper constant, non-homogeneity constant and aspect ratios. Results are presented in graphical form.

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Study of thermal gradient effect on vibrations of a non-homogeneous orthotropic rectangular plate having bi-direction linearly thickness variations

Cited by 26 publications

References 13 publications

Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness

Thermally induced vibration of orthotropic trapezoidal plate of linearly varying thickness

Study the Thermal Gradient Effect on Frequencies of a Trapezoidal Plate of Linearly Varying Thickness

Forced vibrations of non-homogeneous rectangular plate of linearly varying thickness

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