Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Varying Thickness and Density

Gupta, Arun Kumar; Sharma, Pragati

doi:10.5923/j.ajcam.20120206.05

Cited by 2 publications

(1 citation statement)

References 18 publications

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“…Gupta and Sharma [23] observed the effect of linear thermal gradient on vibrations of trapezoidal plates whose thickness varies parabolically. Gupta and Sharma [24] study the thermally induced vibration of non-homogeneous trapezoidal plate with varying thickness and density.…”

Section: Introductionmentioning

confidence: 99%

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

Kavita¹,

Kumar²,

Sharma³

2016

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The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homogeneous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young's modulus and mass density is the main cause for the occurrence of non-homogeneity in plate's material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.

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Section: Introductionmentioning

confidence: 99%

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

Kavita¹,

Kumar²,

Sharma³

2016

Self Cite

View full text Add to dashboard Cite

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Vibration study of non-homogeneous trapezoidal plates of variable thickness under thermal gradient

Gupta¹,

Sharma²

2014

Journal of Vibration and Control

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The aim of the present work is to study the free transverse vibrations of non-homogeneous trapezoidal plates of linear thickness variation in the x-direction under thermal gradient effect. The non-homogeneity of the plate is assumed to arise due to parabolic density variation in the y-direction. A two term deflection function has been taken for clamped-simply supported–clamped-simply supported boundary conditions. The Rayleigh-Ritz method is used to obtain a frequency equation for the first two modes of vibration. The effect of non-homogeneity constant, aspect ratios, taper constant and thermal gradient on the frequencies of non-homogeneous trapezoidal plate has been illustrated for the first two modes of vibration. Results are presented in graphical form. Confirmation of results in special cases with authors published one has also been presented.

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Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Varying Thickness and Density

Cited by 2 publications

References 18 publications

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

Vibration study of non-homogeneous trapezoidal plates of variable thickness under thermal gradient

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