On the application of viscoelastic orthotropic double-nanoplates systems as nanoscale mass-sensors via the generalized Hooke’s law for viscoelastic materials and Eringen’s nonlocal elasticity theory

Abstract

Reviewing the literature reveals that in all previous research works related to the damped vibration analysis of nanoplates, the material damping of nanoplates has been represented by Kelvin-Voigt model without any reasonable justification. The Kelvin-Voigt model has no instantaneous elasticity in creep and also shows unrealistic behavior in relaxation. Due to these drawbacks, the Kelvin-Voigt model fails to capture time domain characteristics of viscoelastic solid materials correctly. On the other hand, the Zener model can predict both creep and relaxation functions of a viscoelastic solid material well in the time domain.The generalized Hooke’s law for viscoelastic materials (GHLVMs) bridges the differential form of linear viscoelasticity and the integral form of linear viscoelasticity. In the present study based on the combination of GHLVMs and the nonlocal elasticity theory, a general 2-D theory of nonlocal viscoelasticity is obtained. A nanoscale mass-sensor is proposed based on the damped frequency analysis of a viscoelastic orthotropic double-nanoplates system (VODNS). The material damping of the nanoplates is represented by the Zener model. It has been assumed that the nanoplates obey the Kirchhoff-Love plate hypotheses. Detailed parametric study is presented.