Dynamic analysis of non-homogenous varying thickness rectangular plates resting on Pasternak and Winkler foundations

Abstract

Modern day technological advancement has resulted in manufacturing industries intensify the use and application of thin plates in their productions thereby, resulting in increased research awareness in the study of dynamic behavior of thin plates. This research analyzes the free vibration dynamic behavior of thin rectangular plates resting on elastic Winkler and Pasternak foundations using two-dimensional differential transformation method. The reliability of the obtained analytical solutions are validated with results presented in cited literature and confirmed very precise. However, the analytical solutions obtained are used to investigate the influence of elastic foundations, homogeneity and thickness variation on the dynamic behavior of the plates under clamped and condition. From the results obtained, it is realized that increase in non-homogenous material results in corresponding increase in natural frequency of the plates. Also, increase in Winkler, Pasternak and combine Winkler and Pasternak foundations stiffness leads to increase in natural frequency of the plates. Increase in thickness results to natural frequency increases. The findings will serve as benchmark for further study of plate vibration research.

Investigation of the Dynamic Behaviour of Non-Uniform Thickness Circular Plates Resting on Winkler and Pasternak Foundations

“…Galerkin method of weighted residual determined the natural frequency in dimensionless form. However, the accuracy of the analytical solutions obtained are compared with results as reported in the literature [25] and confirm in good harmony along the entire values under different boundary conditions and presented in Table 1 and 2. Since the dimensionless value of the natural frequency Ω is obtained in the analysis, the results are valid for all thickness to radius ratio.…”

“…Meanwhile, the HPM also suffers the setback of finding the embedded parameter and initial approximation of the governing equation that satisfies the given conditions. Nonetheless, several researches on a free vibration of circular plates using different methods have been presented in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, the reliability and flexibility of the Galerkin method of weighted residual [26] have made it more effective than any other semi-numerical method.…”

On Caputo–Fabrizio Fractional Integral Inequalities of Hermite–Hadamard Type for Modified h -Convex Functions

“…Many researchers in the last three decades are studying fractional calculus [8][9][10][11][12]. Some researchers deduced that it is essential to define new fractional derivatives with different singular or nonsingular kernels in order to provide more sufficient area to model more real-world problems in different fields of science and engineering [13][14][15][16][17][18][19].…”

Comparative Study of Some Fixed-Point Methods in the Generation of Julia and Mandelbrot Sets

“…e Latin word fractal (means fractured, divided, or broken) is commonly used for an image having the property of selfsimilarity in complex graphics [1]. Fractals have many applications in social sciences and engineering.…”