Vibration of Nonhomogeneous Square Plate with Circular Variation in Density

Sharma, Amit

doi:10.1007/978-981-13-1642-5_23

Cited by 9 publications

(22 citation statements)

References 9 publications

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“…Vibrational freuquency of rectangle plate [17,18] comprises the nonhomogeneity, and the Poisson's ratio effect has been investigated under the temperature field. The Rayleigh-Ritz technique has been employed to investigate the frequency modes of a skew plate [19,20] made of nonhomogeneous material with temperature effect.…”

Section: Introductionmentioning

confidence: 99%

Temperature effect on frequencies of a tapered triangular plate

Khodiya¹,

Sharma²

2021

J. Appl. Math. Comput. Mech.

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The two dimensional temperature effect on the vibration is computed for the first time for a clamped triangular plate with two dimensional thickness. In the study we focused on isosceles, right-angled and scalene triangles only. The first three modes of vibration are computed on different variations of plate parameters using the Rayleigh-Ritz method. The objective of the study is to reduce the frequency of the plates. A comparative study of the frequencies with other available results well presents the objective of the study.

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Section: Introductionmentioning

confidence: 99%

Temperature effect on frequencies of a tapered triangular plate

Khodiya¹,

Sharma²

2021

J. Appl. Math. Comput. Mech.

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“…Singh and Sexena [6] applied Rayleigh Ritz method to study the transverse vibrations of tapered skew plates with different combinations of boundary conditions and obtained first three modes of frequency and mode shapes. Sharma et al [7,8] studied the natural vibration of tapered (exponential and circular variation in thickness) square plate with non homogeneity (variation in density and Poisson's ratio) under temperature variation (bi linear and bi parabolic). An effect of circular variation in thickness on vibrational frequencies of parallelogram plate has been studied by Sharma [9] and obtained first two modes of vibrations for different combinations of plate parameters on clamped edges.…”

Section: Introductionmentioning

confidence: 99%

Natural vibration of tapered rectangular plate with exponential variation in non homogeneity

Sharma¹,

Mani²,

Bhardwaj³

2019

J. vibroeng.

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In this paper, authors studied the natural vibration of tapered non homogeneous rectangular plate on clamped edges. For tapering in plate, authors considered circular variation in thickness and for non-homogeneity (in plate's material) Poisson's ratio varies exponentially. Bilinear temperature (linear along both the axes) variation on the plate is being viewed. Rayleigh Ritz method is used to solve differential equation of motion. All the results are presented with the help of tables and graphs. A comparison of results is also given to support the present study.

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“…They compared the results obtained by MMA and HPM with the exact solution to show the effectiveness of the method. The study of free vibration of a square plate was presented by Sharma et al (2016. They showed the effect of circular variation in density and Poisson's ratio on vibrational frequency in two papers.…”

Section: Introductionmentioning

confidence: 99%

Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson’s ratio

Sharma¹

2019

Journal of Theoretical and Applied Mechanics

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The frequency for the first two modes of vibration of a nonhomogeneous tapered rectangular plate is calculated under a bi linear (i.e., linear along both the axes) temperature field. For consideration of the nonhomogeneous material, the author assumed circular variation in Poisson's ratio. Tapering in the plate is assumed to be linear in one direction. The results are calculated for different values of plate parameters and presented with the help of graphs. Comparison of the results is also given, to support the results of the present study.

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Vibration of Nonhomogeneous Square Plate with Circular Variation in Density

Cited by 9 publications

References 9 publications

Temperature effect on frequencies of a tapered triangular plate

Temperature effect on frequencies of a tapered triangular plate

Natural vibration of tapered rectangular plate with exponential variation in non homogeneity

Vibration frequencies of a rectangular plate with linear variation in thickness and circular variation in Poisson’s ratio

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