Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

Kumar, Ashok; Lather, Neeraj; Bhardwaj, Reeta; Mani, Naveen; Sharma, Amit

doi:10.21595/vp.2018.20367

Cited by 6 publications

(1 citation statement)

References 14 publications

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“…The natural vibration of non-uniform skew (parallelogram) plate with circular variation in thickness at different edge conditions was studied in [10] and [11]. [9] and [12] employed Rayleigh Ritz approach at various plate parameters to assess isotropic and orthotropic rectangular plate vibrational modes of frequency. From the above literature done, it is observed that negligible amount of work has been reported for orthotropic material with circular profile.…”

Section: Introductionmentioning

confidence: 99%

Thermal Vibration of Nonhomogeneous Orthotropic Tapered Skew Plate

Lather,

Sharma,

Yadav

2024

Preprint

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In this article, an analysis is carried out on nonhomogeneous skew (orthotropic) plate with circular profile in thickness. One dimensional circular variation in density parameter along with bi-linear temperature profile is considered. The technique of Rayleigh-Ritz is implemented to solve the resultant frequency equation. Along with this, the convergence study of frequency modes on orthotropic skew plate, rectangle plate, square plate were conducted for different boundary conditions. The major conclusion made from the current research that the circular variation in thickness parameter reduces the variation in time period as compared to linear, exponential and parabolic variation in thickness.

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Section: Introductionmentioning

confidence: 99%

Thermal Vibration of Nonhomogeneous Orthotropic Tapered Skew Plate

Lather,

Sharma,

Yadav

2024

Preprint

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Time period of transverse vibration of skew plate with parabolic temperature variation

Bhardwaj

Mani

Sharma

2020

Journal of Vibration and Control

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Time period of natural transverse vibration of a nonhomogeneous skew (parallelogram) plate with variable thickness and temperature field has been investigated on clamped CCCC and combination of clamped and simply supported CSCS edge conditions. The thickness variation on the plate is assumed to be linear in two dimensions, and the temperature variation on the plate is considered to be parabolic in two dimensions. For nonhomogeneity, authors considered circular variation in density. The Rayleigh–Ritz technique is applied to solve the differential equation of motion. A comparative analysis of frequency modes of the present study with the available published result is also given to support the present findings. The convergence study of obtained results is also presented with the help of figures.

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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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Effect of linear variation in density and circular variation in Poisson’s ratio on time period of vibration of rectangular plate

Cited by 6 publications

References 14 publications

Thermal Vibration of Nonhomogeneous Orthotropic Tapered Skew Plate

Thermal Vibration of Nonhomogeneous Orthotropic Tapered Skew Plate

Time period of transverse vibration of skew plate with parabolic temperature variation

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

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