Abstract
In this study, two-dimensional circular thickness effects on time period of skew plate made with nonhomogeneous material properties are computed in variable temperature environment. Clamped C , simply supported S , and free-edge F conditions are the various combinations considered in this work. One-dimensional circular density and two-dimensional parabolic temperature variation on the plate are considered due to the nonhomogeneous nature of the material and variable temperature environment. Rayleigh–Ritz method is used to compute the time period for the first two modes of vibration. A convergence study of frequency modes of skew plate on various edge conditions has also been performed. The present work has been compared with the frequency modes of parallelogram and rectangle plate on various edge conditions. The objective of the study is to present a numerical data of time period as well as to show how one can control the frequencies of plate by taking an appropriate variation in plate parameters.
Highlights
(ii) e rate of decrement in time period K in case of tapering π2 is more in comparison to the rate of decrement in time period K in case of tapering π1 on all edge conditions
(iii) e time period K is higher on SCSC edge condition and lower on CCCS edge condition
In order to validate the findings of the present study as well as to present the objective of the study, a comparison of frequency modes obtained in the present study was done with the following: (i) Frequency modes of parallelogram plate obtained in [11] on CCCC and CSCS edge condition corresponding to tapering parameters π1, π2 and aspect ratio (a/b)
Summary
A large number of structures/equipments are made up of plates, and this fact has prompted the researchers to do a detailed study of vibrational frequencies of plates. Ritz method has been applied in [10] to investigate vibrational behavior (first three modes) of nonhomogeneous, nonuniform circular plates on clamped, supported, and free edges and presented the various plate parameters impact on frequencies. Effect of circular variation in density on time period of parallelogram plate having two-dimensional thickness and temperature on CCCC and CSCS edge condition has been computed in [11] using Rayleigh–Ritz method, where C and S stand for clamped and supported edge conditions, respectively. Generalized layer-wise (LW) along with generalized differential quadrature (GDQ) method has been used in [15] to analyze anisotropic double curved shells with an arbitrary shape In this current study, the authors focused to show the impact of two-dimensional circular thickness on the time period of nonhomogeneous parallelogram plate on various boundary conditions under variable temperature field. In order to authenticate the findings and to present the objectives, a comparative analysis of frequency modes of parallelogram and rectangle plate with the available published results is presented in tabular form
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