Modeling of nonlocal Caputo–Fabrizio integral models in a nanoscale resonator

Abstract

In the present work, the nonlocal integral constitutive laws for application to nano-beams, are investigated in a general setting. Evidence of boundary effects are enlightened by theoretical analysis and numerical computations. The proposed compensation procedures efficiently analyzes the thermoelastic interaction in a nanoscale resonator in the context of two-temperature three-phase lag model of thermoelasticity involving Caputo Fabrizio (CF) derivative where both the ends of the nanoscale beam is clamped. Employing the Laplace transform as a tool, the solutions for conductive temperature, thermodynamic temperature, stress and deflection have been determined. The corresponding solutions in the space-time domain is obtained by incorporating the numerical inversion of the Laplace transform using Riemann-sum approximation technique. According to the graphical representations corresponding to the numerical results, effectiveness of the recently proposed theory is demonstrated due to the presence of nonlocal CF order and the nonsingular kernel.