ANALYTICAL SOLUTION FOR NONLINEAR DYNAMIC BEHAVIOR OF VISCOELASTIC NANO-PLATES MODELED BY CONSISTENT COUPLE STRESS THEORY

Abstract

THIS PAPER ANALYSES THE NON-STATIONARY FREE VIBRATION AND NONLINEAR DYNAMICS OF THE VISCOELASTIC NANO-PLATES. FOR THIS PURPOSE, A SIZE-DEPENDENT THEORY DEVELOPED IN THE FRAMEWORK OF THE CONSISTENT COUPLE STRESS THEORY FOR VISCOELASTIC MATERIALS. THE MODIFIED COUPLE STRESS THEORY THAT WAS PREVIOUSLY PRESENTED USED SOME CONSIDERATION, WHICH MAKES ITS USE DOUBTFUL. THIS PAPER USED THE RECENT FINDING FOR THESE PROBLEM AND DEVELOPED IT TO ANALYZE THE NONLINEAR DYNAMICS OF NANO-PLATES WITH NONLINEAR VISCOELASTICITY. THE MATERIAL IS SUPPOSED TO FOLLOW THE LEADERMAN INTEGRAL NONLINEAR CONSTITUTIVE RELATION. IN ORDER TO CAPTURE THE GEOMETRICAL NONLINEARITY THE VON–KARMAN STRAIN DISPLACEMENT RELATION IS USED. THE VISCOUS PARTS OF THE SIZE-INDEPENDENT AND SIZE-DEPENDENT STRESS TENSORS ARE CALCULATED IN THE FRAMEWORK OF THE LEADERMAN INTEGRAL AND THE RESULTANT VIRTUAL WORK ARE OBTAINED. THE GOVERNING EQUATIONS OF MOTION ARE DERIVED USING THE HAMILTON PRINCIPLE IN THE FORM OF THE NONLINEAR SECOND ORDER INTEGRO-PARTIAL DIFFERENTIAL WITH COUPLED TERMS. THESE COUPLED SIZE-DEPENDENT VISCOELASTIC EQUATIONS ARE SOLVED WITH USING THE HARMONIC BALANCE METHOD AFTER SIMPLIFYING BY THE GALERKIN TECHNIQUE. THE SHORT-TIME FOURIER TRANSFORM IS PERFORMED TO EXAMINE THE SYSTEM FREE VIBRATION. IN ADDITION, FREQUENCY AND FORCE RESPONSES OF THE NANOSYSTEM SUBJECTED TO DISTRIBUTE HARMONIC LOAD ARE OBTAINED. THE OBTAINED RESULTS SHOW THAT THE VISCOELASTIC MODEL VIBRATION IS NON-STATIONARY UNLIKE ELASTIC MODEL. MOREOVER, THE DAMPING MECHANISM OF THE VISCOELASTICITY IS AN AMPLITUDE DEPENDENT AND THE CONTRIBUTION OF VISCOELASTIC DAMPING TERMS AT HIGHER FORCING BECOMES NOTICEABLE