Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

• Published in: Waves in random and complex media Vol. 29; no. 4; pp. 595 - 613
• Main Authors: Bachher, Mitali, Sarkar, Nantu
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.10.2019; Taylor & Francis Ltd
• Subjects: Algorithms; Eigenvalues; Heat sources; Inversions; Laplace transforms; Nonlocal elasticity; Time dependence; Voids; Wave propagation
• ISSN: 1745-5030; 1745-5049
• DOI: 10.1080/17455030.2018.1457230

A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen's nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above theory is then applied to study transient wave propagation in an infinite thermoelastic materials with voids due to a time-dependent continuous heat sources distributed in a plane area. Laplace transform and eigenvalue approach techniques are used to obtain the closed form solution in the transform domain. Numerical inversions of the studied physical variables are carried out by Zakian algorithm in the space-time domain. Numerical results are plotted graphically in some cases and the results obtained are analyzed. Some comparisons for different cases are also noted.