Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales

Investigating dynamic free vibration response of isotropic thin rectangular plate resting on two-parameter elastic foundation is of interest in the field of geotechnics, structure, highway, railway and mechanical engineering. This study employs analytical approach to the investigation of free vibration analysis of isotropic rectangular plate submerged in fluid and resting on combined elastic foundations under different support conditions. The nonlinear partial differential equation of the system is transformed into nonlinear ordinary differential equation using the Galerkin method of separation. The resulting ordinary differential equation is solved using Adomian decomposition method (ADM). The reliability of the solutions obtained is validated with numerical and existing results as reported in the literature. Also, the bending moment and stress are analysed. The analytical solutions are used for the investigation of dynamic behaviour of plates in fluid, effect of aspect ratio, effect of elastic foundation parameters on natural frequency and effect of bending moment and stress on the mode of the vibrating plate. From the results, it is observed that the increase in elastic foundation parameter increases the natural frequency. Increasing the aspect ratio increases the natural frequency. Increasing the combined elastic foundation parameters increases the natural frequency. Natural frequency of plates reduces when submerged in fluid with the mode shapes not significantly affected. The node and antinodes of the mode shapes are affected by moment and stress. It is expected that the present study will add to the existing knowledge in the field of vibration of plates.

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Application of Adomian decomposition method to free vibration analysis of thin isotropic rectangular plates submerged in fluid

Sobamowo

Salawu

Yinusa

2020

J Egypt Math Soc

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New technique for the approximation of the zeros of nonlinear scientific models

Ali

Aslam

Huang

2020

International Journal of Nonlinear Sciences and Numerical Simulation

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Most of the problems in mathematical and engineering sciences can be studied in the context of nonlinear equations. In this paper, we develop a new family of iterative methods for the approximation of the zeros of mathematical models whose governing equations are nonlinear in nature. The proposed methods are based on decomposition technique due to Daftardar-Gejji and Jaffri [1]. The new family gives several iterative schemes as special cases. The convergence analysis of proposed methods is also presented. In order to determine the performance of newly developed methods, numerical as well as graphical analysis of four complex mathematical models from diverse fields of science and engineering are considered. We also consider some complex polynomials to visualize the roots through polynomiography in the context of proposed methods.

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Oscillation Criteria for Second-Order Nonlinear Dynamic Equations on Time Scales

Abstract: The main goal of this article is to study the oscillation criteria of the second-order neutral differential equations on time scales. We give several theorems and related examples to illustrate the applicability of these theorems. Our results extend some recent work in the literature.

Cited by 2 publications

References 20 publications

Application of Adomian decomposition method to free vibration analysis of thin isotropic rectangular plates submerged in fluid

Application of Adomian decomposition method to free vibration analysis of thin isotropic rectangular plates submerged in fluid

New technique for the approximation of the zeros of nonlinear scientific models

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