Effect of memory dependent derivative and variable thermal conductivity in cantilever nano-Beam with forced transverse vibrations

Abstract

This research work studies the effect of variable thermal conductivity on transversely isotropic thermoelastic (TIT) homogeneous nonlocal clamped-free beam. The beam undergoes forced vibrations due to two types of heat sources i.e. exponential time-varying and time-harmonic load. The mathematical model has been formed for a 2-D problem using a heat equation with two temperature (2T) involving memory-dependent derivatives (MDD) and Euler Bernoulli beam theory (EBBT). Laplace transforms are used to solve the problem. The dimensionless expressions for a thermal moment, axial stress, lateral deflection, and temperature change are calculated for these two types of forced vibrations. MATLAB software is used for programming and numerical data for cobalt nanobeam has been considered. The influence of variable thermal conductivity and kernel function of MDD has been depicted graphically on the physical quantities such as temperature change, lateral deflection, axial stress thermal moment, for the forced vibrations. Specific cases have also been mentioned.

Keywords

• Nano-beam
• Variable thermal Conductivity
• Memory dependent derivative
• Two temperature
• Nonlocal