On thermoelastic damping in axisymmetric vibrations of circular nanoplates: incorporation of size effect into structural and thermal areas

Abstract

The paper at hand intends to evaluate thermoelastic damping (TED) in circular plates by incorporating nonlocal effect within the constitutive and heat conduction frameworks. To attain this purpose, nonclassical coupled thermoelastic equations are established on the basis of nonlocal elasticity theory and Guyer–Krumhansl (GK) heat conduction model. By considering symmetric time–harmonic vibrations, the size-dependent thermoelastic frequency equation is derived. By solving this nonclassical eigenvalue problem, real and imaginary parts of damped natural frequency are separated. According to the definition of TED in the framework of complex frequency approach, a closed-form expression characterizing TED in circular nanoplates is introduced. With the aim of surveying the nonlocal effect on TED, a comparison study is performed between the size-dependent outcomes and those extracted by way of classical continuum mechanics and heat conduction theories for simply supported and clamped circular nanoplates. When the dimensions of nanoplate become smaller, an obvious discrepancy between classical and nonclassical results is observed, which is irrefutable evidence of size effect on mechanical behavior of nanostructures.