Reflection of plane wave at free boundary of micro-polar nonlocal semiconductor medium

Abstract

This work presents the reflection phenomena of thermo-elastic waves in nonlocal micro-polar semi-conducting solid. The thermo-elasticity theory of factional-order time derivative three phase lag thermo-elastic model is applied to study the thermal effect on the waves. Governing equations of the problem are decomposed by using the Helmholtz decomposition. Two frequency dispersion relations corresponding to couple longitudinal and transverse waves are obtained. It is observed that three coupled longitudinal and two coupled transverse waves are propagating through the elastic solid. Relations for amplitude ratios, Energy flux balance are obtained analytically. All the results obtained mathematically are represented graphically for the selected material. The silicon crystal has been selected for computational purpose to check the variation of amplitude ratios against incident angle. The dependence of reflection coefficients upon nonlocal and fractional order parameters is been represented graphically.

Keywords:

• Fractional order time derivative
• nonlocal theory
• nanostructure
• micro-polar theory
• reflection
• semiconductor

Disclosure statement

The authors declare that they have no conflict of interest.