Effects of thermal stress, magnetic field and rotation on the dispersion of elastic waves in an inhomogeneous five-layered plate with alternating components.

Rahmatullah Ibrahim Nuruddeen,Qazi Muhammad Zaigham Zia,Rab Nawaz

doi:10.1177/0036850420940469

Rahmatullah Ibrahim Nuruddeen, Qazi Muhammad Zaigham Zia + Show 1 more

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https://doi.org/10.1177/0036850420940469

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Abstract

This study explores the effects of the thermal stress, rotation, and magnetic fields on the propagation of surface waves in a symmetric five-layered inhomogeneous elastic plate. The harmonic wave solution was adopted to reduce the given partial differential equations to their corresponding ordinary differential equations, which were later solved using a classical method. The Mathematica software was also employed for the numerical simulations. The dispersion relations associated with both the symmetric and antisymmetric modes have been determined and analyzed with regard to the aforementioned external effects and rotation. The variations in thermal stress positively affect the wave propagation in the plate even for relatively smaller values of the temperature variation. Also, the same trend is observed in the case of the magnetic field, but for higher values. Finally, for the rotation, it was found that the angular velocity must reach at least 104 before a significant change is observed; which in fact differs from the situations of half-plane reflection and single-layered.

Highlights

Propagation of elastic waves in various structures has been extensively examined in the past decades due to its frequent occurrence in nature and encounters in different phenomena of science and engineering applications
The effect of magnetic field forces on the propagation of waves in elastic bodies was studied in Chadwick[5] and Kaliski and Petykiewicz,[6] while the thermal stress effects on the propagation of waves in an initially stressed anisotropic plate and double-layered nano-plates were presented by Selim[7] and Wang et al.,[8] respectively
The influence of an initial stress on the vibration of conducting medium amidst gravitational field forces was analysed by El-Naggar et al.[12] and initially stressed multilayered piezoelectric composite bodies were examined in Qian et al.,[13] while the propagation of surface elastic waves under thermal relaxation and voids presence was studied by Abo-Dahab et al.[14]

Summary

Introduction

Propagation of elastic waves in various structures has been extensively examined in the past decades due to its frequent occurrence in nature and encounters in different phenomena of science and engineering applications. The influence of an initial stress on the vibration of conducting medium amidst gravitational field forces was analysed by El-Naggar et al.[12] and initially stressed multilayered piezoelectric composite bodies were examined in Qian et al.,[13] while the propagation of surface elastic waves under thermal relaxation and voids presence was studied by Abo-Dahab et al.[14] In addition, several investigations of the wave propagation in bodies and elastic media comprise the presence of viscous damping by Leissa and Qatu[15] and the presence of material and structural discontinuities.[16,17] the propagation and dispersion of waves in multilayered and composite structures were examined in the literature.[18,19] Such structures include sandwich plates, layered laminates, composite rods, photovoltaic panels and beams to mention a few. The acceleration on the right-hand side of equation (3) in a rotating frame of reference with angular velocity O takes the following form:

The rotational acceleration

Conclusion