Generalized thermoelastic diffusive waves in heat conducting materials

• Published in: Journal of sound and vibration Vol. 301; no. 3; pp. 979 - 993
• Main Author: Sharma, J.N.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 03.04.2007; Elsevier
• Subjects: Analytical and numerical techniques; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wave equation; Conducting material; Thermoelastic wave; Geophysics; Temperature effect; Solutes; Wave damping; Metal; Longitudinal wave; Elastic wave; Low frequency; Modeling; Mass transfer; Phase velocity; Transverse wave; Diffusion process; Characteristic equation; Electrical conductor; Copper; Heat transfer
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2006.11.001

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.