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Nonlinear vibration of multi-walled carbon nanotubes with initial curvature resting on elastic foundations in a nonlinear thermo-magnetic environment

Sobamowo Gbeminiyi, Akanum James, Adeleye Olurotimi, Akingbade Samuel, Yinusa Ahmed

Engineering Transactions

2021

Vol. 69, iss. 2

87--165

The present work focuses on nonlinear dynamics models of multi-walled carbon nanotubes with initial curvature resting on Winkler-Pasternak elastic foundations in a nonlinear thermomagnetic environment using nonlocal elasticity theory. The derived systems of nonlinear vibration models are solved with the aid of the Galerkin decomposition and the homotopy perturbation method. Effects of temperature, magnetic field, multi-layer, and other thermomechanical parameters on the dynamic responses of the slightly curved multi-walled carbon nanotubes are investigated and discussed. As the temperature increases, the frequency ratio decreases as the linear natural frequency of the system increases. The results reveal that the frequency ratios decrease as the number of nanotube walls, temperature, spring constants, magnetic field strength, and the ratio of the radius of curvature to the length of the slightly curved nanotubes increase. These trends are the same for all the boundary conditions considered. However, clamped-simple and clamped-clamped supported multi-walled nanotube have the highest and lowest frequency ratio, respectively. Also, from the parametric studies to control nonlinear vibration of the carbon nanotubes, it is shown that quadruple-walled carbon nanotubes can be taken as pure linear vibration even at any value of linear Winkler and Pasternak constants. Therefore, this can be used for the restraining of the chaos vibration in the objective structure. These research findings will assist the designers and manufacturers in developing multi-walled carbon nanotubes for various structural, electrical, mechanical, and biological applications, especially in the areas of designing nanoelectronics, nanodevices, nanomechanical systems, nanobiological devices, and nanocomposites, and particularly when they are subjected to thermal loads, magnetic fields and elastic foundations.

Analysis of heat transfer between an inert gas and a porous structure with ultralow thermal conductivity using the Sumudu transform method

Sobamowo Gbeminiyi

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 3

79--87

The relatively new integral transform called the Sumudu transform method can be used to solve partial differential equations with variable coefficients and as well as intricate problems in engineering and applied mathematics without resorting to a new frequency domain. Unlike the other integral transforms, the Sumudu transform has scale and unit-preserving properties. However, the method is still not widely known or used for solving differential equations especially in the area of applied mathematics and engineering. As a means of demonstrating the potency of the method, the paper applied the Sumudu transform to present analytical solutions of a one-dimensional problem of heat transfer between an inert gas and an ultralow thermal conductivity porous medium. The developed analytical solutions are used to investigate the heat propagation in the porous medium. Depending on the initial temperature, it is established from the study that there are snapshots of the heat wave propagating and a sharp heat front propagation through the medium during its heating or cooling. This sharp front is difficult to detect and quantify by numerical methods. Hence, exact analytical solutions are presented in this study. As it is demonstrated in this study, it is hoped that the Sumudu transform method will be applied to other various complex engineering problems.