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

Abstract

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.

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

“…2. Frequency modes for rectangular plate are less in case of circular variation in nonhomogeneity (present study) in comparison of sinusoidal variation in nonhomogeneity (Kaur et al, 2018) as shown in Table 2. 3.…”

“…Comparison of frequency parameter λ for the present study and obtained by Sharma (2018) corresponding to thermal gradient α for fixed skew angle θ = 30°and aspect ratio a/b = 1.5. Kaur et al (2018) corresponding to nonhomogeneity parameter m for fixed aspect ratio a/b = 1.5. Kaur et al (2018) β 1 = β 2 = 0.0, 0.2 and nonhomogeneity parameter m, that is m = 0.2 and 0.4 on CCCC condition.…”

“…Kaur et al (2018) corresponding to nonhomogeneity parameter m for fixed aspect ratio a/b = 1.5. Kaur et al (2018) β 1 = β 2 = 0.0, 0.2 and nonhomogeneity parameter m, that is m = 0.2 and 0.4 on CCCC condition.…”

“…Table 2 shows the comparison of frequency modes of the rectangular plate (by taking skew angle θ = 0°in the present study) and obtained by Kaur et al (2018) corresponding to nonhomogeneity parameter m for fixed aspect ratio a/b = 1.5, tapering parameters β 1 = β 2 = 0.0, and thermal gradient α = 0.0 for CCCC and CSCS edge conditions. Here, also the frequency modes are very less in comparison of frequency modes reported in the study given by Kaur et al (2018) for both edge conditions.…”

“…Khanna and Singhal (2013) analyzed the effect of bilinear thickness and temperature variations on vibrational frequency of a nonhomogeneous rectangular plate using the Rayleigh-Ritz method, and first two modes of vibrations are calculated on different variation of plate parameters. An analysis of frequency parameter on a tapered rectangular plate with one dimensional sinusoidal variation in thickness, density, and temperature is presented by Kaur et al (2018), on CCCC, CSCS, and SSSS edge conditions, using the classical plate theory. Time period of frequency parameter of a nonuniform rectangular plate with variation in density, Poisson's ratio, and temperature is examined by Kumar et al (2018) by applying the Rayleigh-Ritz method.…”