Fractional Order Thermoelastic Wave Assessment in a Nanoscale Beam Using the Eigenvalue Technique

• Published in: Strength of materials Vol. 51; no. 3; pp. 427 - 438
• Main Authors: Abbas, I., Alzahrani, F., Abdalla, A. N., Berto, F.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-05-2019; Springer; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Chemistry and Materials Science; Classical Mechanics; Computer simulation; Conduction heating; Conductive heat transfer; Differential equations; Displays (Marketing); Eigenvalues; Exact solutions; Laplace transforms; Lateral displacement; Materials Science; Matrix algebra; Matrix methods; Methods; Numerical analysis; Silicon; Solid Mechanics; Thermal conductivity; Transformations (mathematics); Laplace transforms; nanoscale beam; eigenvalues approach; fractional order
• ISSN: 0039-2316; 1573-9325
• DOI: 10.1007/s11223-019-00089-2

This paper presents an analytical approach associated with Laplace transforms and a sequential concept over time to obtain the increment of temperature in nanoscale beam with fractional order heat conduction clamped from both ends. The governing equations are written in the forms of differential equations of matrix-vector in the domain of the Laplace transforms and are then solved by the eigenvalue technique. The analytical solutions are obtained for the increment of temperature, displacement, lateral deflection, and stresses in the Laplace domain. Numerical simulations are provided for silicon-like nanoscale beam material, with graphical display of calculated results. The physical implications of distributions of physical variables considered in this article are discussed.