Application of the generalized Hooke's law for viscoelastic materials (GHVMs) in nonlocal free damped vibration analysis of viscoelastic orthotropic nanoplates

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.Recently a refined 3-D theory of linear viscoelasticity termed the generalized Hooke's law for viscoelastic materials (GHVMs), is developed by Rajabi and Hosseini-Hashemi [1]. In that theory new 3-D linear viscoelastic constitutive equations are derived which bridge the differential form of linear viscoelasticity and the integral form of linear viscoelasticity.In the present paper vibration characteristics of simply supported orthotropic nanoplates are studied using the nonlocal Kirchhoff-Love plate theory in conjunction with GHVMs. Using GHVMs the material damping of the nanoplates is represented by other rheological models namely the Maxwell model and the standard linear solid model for illustration purposes. Results have revealed that for the same physical and geometrical properties and also for the same contents of damping, the characteristic of various rheological models differ considerably from each other. This indicates that for correct and accurate modeling of 2-D and 3-D viscoelasticity problems in nanoscale it is crucial to perform the material characterization experimentally or by MD simulation.