On size-dependent generalized thermoelasticity of nanobeams

Abstract

In this article, a size-dependent generalized thermoelasticity model is established to appraise the small-scale effect on thermoelastic vibrations of Euler-Bernoulli nanobeams. Small-scale effect on the structure and heat conduction is captured by exploiting nonlocal strain gradient theory (NSGT) and nonclassical heat conduction model of Guyer and Krumhansl (GK model). NSGT enables the model to account for both nonlocal and strain gradient effects on structure, and GK formulation empowers the model to incorporate both nonlocal and lagging effect into heat conduction equation. The normalized forms of size-dependent equations of motion and heat conduction are provided by introducing some dimensionless parameters. This system of normalized differential equations is then solved with the aid of the Laplace transform to determine thermoelastic responses of nanobeams. Through various examples, a complete parametric study is conducted to clarify the pivotal role of nonclassical scale parameters in thermoelastic behavior of nanobeams. Comparing the results extracted based on various relative magnitudes of nonlocal and strain gradient length scale parameters implies that NSGT is capable of expounding both hardening and softening phenomenon in nanoscale structures. The outcomes also reveal that GK model anticipates less energy dissipation.

KEYWORDS:

• Small-scale effect
• Euler–Bernoulli nanobeam
• nonlocal strain gradient theory
• Guyer-Krumhansl model
• thermoelastic coupling
• analytical solution

Disclosure statement

No potential conflict of interest was reported by the author(s).