SIZE-DEPENDENT VIBRATIONS OF POST-BUCKLED FUNCTIONALLY GRADED MINDLIN MICROPLATES

Abstract

IN THIS PAPER, THE FREE VIBRATION BEHAVIOR OF POST-BUCKLED FUNCTIONALLY GRADED (FG) MINDLIN MICROPLATES ARE DESCRIBED BASED ON THE MODIFIED COUPLE STRESS THEORY (MCST). THIS THEORY ENABLES THE CONSIDERATION OF THE SIZE-EFFECT THROUGH INTRODUCING MATERIAL LENGTH SCALE PARAMETERS. THE FG MICROPLATES MADE OF A MIXTURE OF METAL AND CERAMIC ARE CONSIDERED WHOSE VOLUME FRACTION OF COMPONENTS IS EXPRESSED BY A POWER LAW FUNCTION. BY MEANS OF HAMILTON’S PRINCIPLE, THE NONLINEAR GOVERNING EQUATIONS AND ASSOCIATED BOUNDARY CONDITIONS ARE DERIVED FOR FG MICROPLATES IN THE POSTBUCKLING DOMAIN. THE GOVERNING EQUATIONS AND BOUNDARY CONDITIONS ARE THEN DISCRETIZED BY USING THE GENERALIZED DIFFERENTIAL QUADRATURE (GDQ) METHOD BEFORE SOLVING NUMERICALLY BY THE PSEUDO-ARCLENGTH CONTINUATION TECHNIQUE. IN THE SOLUTION PROCEDURE, THE POSTBUCKLING PROBLEM OF MICROPLATES IS INVESTIGATED FIRST. AFTERWARDS, THE FREE VIBRATIONS OF MICROPLATES AROUND THE BUCKLED CONFIGURATION IS DISCUSSED. THE EFFECTS OF DIMENSIONLESS LENGTH SCALE PARAMETER, MATERIAL GRADIENT INDEX AND ASPECT RATIO ON THE ON THE POSTBUCKLING PATH AND FREQUENCY OF FG MICROPLATES SUBJECT TO ARBITRARY EDGE SUPPORTS ARE THOROUGHLY DISCUSSED.