A memory response in the vibration of a microscale beam induced by laser pulse

Abstract

In the application of pulsed laser heating, such as the laser hardening of metallic surfaces, the conduction limited process is the dominant mechanism during the laser-workpiece interaction. As a consequence, time unsteady analysis of this problem becomes necessary. The present study examines the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale beam resonator. Due to the shortcomings of power law distributions in fractional derivatives, the usage of some other forms of derivatives with some other kernel functions is proposed. With this motivation, the heat transport equation is defined in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer. Finite sinusoidal Fourier and Laplace transform techniques are then employed to determine the lateral vibration of the beam and the temperature increment within the medium. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are drawn. An excellent predictive capability is demonstrated due to the presence of the energy absorption depth, memory dependent derivative, and delay time.

Keywords:

• Finite Fourier transform
• Laplace Transform
• microscale beam
• memory dependent derivative
• Non-Gaussian laser pulse
• three-phase-lag thermoelastic model

Acknowledgments

We express our sincere thanks to the reviewers for their valuable suggestions for the improvement of the article.