THERMO-MECHANICAL VIBRATION ANALYSIS OF ANNULAR AND CIRCULAR GRAPHENE SHEET EMBEDDED IN AN ELASTIC MEDIUM

Abstract

IN THIS STUDY, THE VIBRATION BEHAVIOR OF ANNULAR AND CIRCUAR GRA-PHENE SHEET COUPLED WITH TEMPERATURE CHANGE AND UNDER IN-PLANE PRE-STRESSED IS STUDIED. BY USING THE NONLOCAL ELASTICITY THEORY THE GOVERNING EQUATION IS DERIVED FOR SINGLE-LAYERED GRAPHENE SHEETS (SLGS). THE CLOSED-FORM SOLUTION FOR FREQUENCY VIBRATION OF CIRCULAR GRAPHENE SHEETS HAS BEEN OBTAINED AND NONLOCAL PARAMETER, IN-PLANE PRE-STRESSED, THE PARAMETERS OF ELASTIC MEDIUM AND TEMPERATURE CHANGE APPEARS INTO ARGUMENTS OF BESSEL FUNCTIONS. THE RESULTS ARE SUBSEQUENTLY COMPARED WITH VALID RESULT REPORTED IN THE LITERATURE AND THE MOLECULAR DYNAMICS RESULTS. THE EFFECTS OF THE SMALL SCALE, PRE-STRESSED, MODE NUMBER, TEMPERATURE CHANGE, ELASTIC MEDIUM AND BOUNDARY CONDITIONS ON NATURAL FREQUENCIES ARE INVESTIGATED. THE NON-DIMENSIONAL FREQUENCY DECREASES AT HIGH TEMPERATURE CASE WITH INCREASING THE TEMPERATURE CHANGE FOR ALL BOUNDARY CONDITIONS. THE EFFECT OF TEMPERATURE CHANGE ON THE FREQUENCY VIBRATION BECOMES THE OPPOSITE AT HIGH TEMPERATURE CASE IN COMPRESSION WITH THE LOW TEMPERATURE CASE. THE PRESENT RE-SEARCH WORK THUS REVEALS THAT THE NONLOCAL PARAMETER, BOUNDARY CONDITIONS AND TEMPERATURE CHANGE HAVE SIGNIFICANT EFFECTS ON VIBRATION RESPONSE OF THE CIRCULAR NANOPLATES. THE PRESENT RESULTS CAN BE USED FOR THE DESIGN OF THE NEXT GENERATION OF NANODEVICES THAT MAKE USE OF THE THERMAL VIBRATION PROPERTIES OF THE GRAPHENE.