Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness

Gupta, Arun Kumar; Kumar, Manoj; Kumar, Sanjay; Khanna, Anupam

doi:10.4236/am.2011.21004

Cited by 8 publications

(4 citation statements)

References 24 publications

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“…Li [7] analyzed the vibrations of a rectangular plate with general elastic boundary support. Gupta et al [8] analyzed the transverse vibrations of a non-homogeneous orthotropic visco-elastic circular plate of varying parabolic thickness. Gupta and Sharma [9] studied the thermal effect on the frequencies of a trapezoidal plate with varying thickness and density of the material.…”

Section: Introductionmentioning

confidence: 99%

A Study on Vibration of Tapered Non-Homogeneous Rectangular Plate with Structural Parameters

Kaur

Singhal²,

Khanna

2018

International Journal of Applied Mechanics and Engineering

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Effects of structural parameters on the vibration of a tapered non-homogeneous rectangular plate with different combinations of boundary conditions are discussed. Tapering in the plate is assumed to be sinusoidal in the x-direction. Here, temperature variation and non-homogeneity in the plate material are also considered sinusoidal in the x-direction. The Rayleigh-Ritz method is used to calculate the frequency parameter for the first two modes of vibration for different values of the structural parameters, i.e. the taper parameter, thermal gradient, aspect ratio and non-homogeneity constant. Results are obtained for three boundary conditions, i.e. clamped boundary (C-C-C-C), simply supported boundary (SS-SS-SS-SS) and clamped-simply supported boundary (CSS-C-SS). Numerical values of the frequency parameter are given in a compact tabular form.

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Section: Introductionmentioning

confidence: 99%

A Study on Vibration of Tapered Non-Homogeneous Rectangular Plate with Structural Parameters

Kaur

Singhal²,

Khanna

2018

International Journal of Applied Mechanics and Engineering

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“…Gupta (1983, 1985) studied the effect of thermal gradient on frequencies of orthotropic rectangular plate of variable thickness in one and two direction. Gupta et al (2010cGupta et al ( , 2011 studied the thermal effect on vibration of parallelogram plate of linearly varying thickness and bi-directional linearly varying thickness. Gupta et al (2010d) studied the vibration of visco-elastic parallelogram plate of linearly varying thickness.…”

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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“…The maximum kinetic energy, Tmax, and the maximum strain energy, V in the plate when it is executing transverse vibration mode shape W(ξ, η) in skew coordinates are [16]:…”

Section: Equation Of Transverse Motionmentioning

confidence: 99%

“…Park and Mongeau [15] used the vibration and radiation of visco elastically supported midline plates. Gupta et al [16] study the vibration of visco-elastic parallelogram plate of linearly varying thickness.…”

Section: Introductionmentioning

confidence: 99%

Vibration of Visco-Elastic Parallelogram Plate with Thickness Variation Linearly in one Direction and Parabolic in another Direction

Gupta¹,

Kumar²

2013

AJAMS

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The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies bi-directionally. It is assumed that the plate is clamped on all the four edges and that the thickness varies linearly in one direction and parabolically in another direction. Using the separation of variables method and Rayleigh-Ritz technique with a two-term deflection function, the governing differential equation has been solved for vibration of visco-elastic parallelogram plate. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection is made. Visco-elastic of the plate is taken of the "Kelvin Type". Time period and deflection function at different point for the first two modes of vibration are calculated for various values of taper constant, aspect ratio and skew angle and results are presented in tabular form. Alloy "Duralumin" is considered for all the material constants used in numerical calculations.

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Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness

Cited by 8 publications

References 24 publications

A Study on Vibration of Tapered Non-Homogeneous Rectangular Plate with Structural Parameters

A Study on Vibration of Tapered Non-Homogeneous Rectangular Plate with Structural Parameters

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

Vibration of Visco-Elastic Parallelogram Plate with Thickness Variation Linearly in one Direction and Parabolic in another Direction

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