Abstract

The present work is concerned with the propagation of magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic finitely conducting elastic medium permeated by a uniform magnetic field. The problem has been formulated under the purview of Green and Naghdi theory of thermoelasticity of type-III (GN-III). Interactions among elastic, thermal and magnetic fields have been taken into account. A dispersion relation is derived to investigate the nature of waves propagating in the medium. Perturbation technique has been employed to obtain the solution of the dispersion relation, when the magneto-thermoelastic coupling parameter is small. This enables to identify three different types of waves. Phase velocity, specific loss and penetration depth have been discussed. Using derived analytical expressions, numerical results have been computed for the variation of several physical quantities of interest. The impact of the magnetic field has been studied. Computational results have been presented graphically for all the three cases GN-I, GN-II, GN-III. A comparative study has been performed for these three cases. The study reveals that in the case of GN-II theory, coupled magneto-thermoelastic waves are unattenuated and non-dispersive in contrast to the cases of GN-I and GN-III theories.

摘要

目前的工作涉及指定频率的磁热弹性平面波在均匀磁场渗透的均匀各向同性有限导电弹性介质中的传播。该问题是在 Green 和 Naghdi III 型热弹性理论 (GN-III) 的范围内制定的。已经考虑了弹性、热和磁场之间的相互作用。导出色散关系以研究波在介质中传播的性质。当磁热弹性耦合参数较小时，已经采用微扰技术来获得色散关系的解。这使得能够识别三种不同类型的波。已经讨论了相速度、比损耗和穿透深度。使用派生的分析表达式，已经计算了几个感兴趣的物理量的变化的数值结果。已经研究了磁场的影响。GN-I、GN-II、GN-III这三种情况的计算结果已经以图形方式呈现。对这三种情况进行了比较研究。研究表明，在 GN-II 理论的情况下，与 GN-I 和 GN-III 理论的情况相比，耦合磁热弹性波是未衰减和非色散的。