ON THE NONLINEAR VIBRATION AND MODE SHAPES OF FG CYLINDRICAL SHELLS

Abstract

THE NONLINEAR VIBRATION AND NORMAL MODE SHAPES OF FG CYLINDRICAL SHELLS ARE INVESTIGATED USING AN EFFICIENT ANALYTICAL METHOD. THE EQUATIONS OF MOTION OF THE SHELL ARE BASED ON THE DONNELLÂS NONLINEAR SHALLOW SHELL, AND THE MATERIAL IS ASSUMED TO BE GRADUALLY CHANGED ACROSS THE THICKNESS ACCORDING TO THE SIMPLE POWER LAW. THE SOLUTION IS PROVIDED BY FIRST DISCRETIZING THE EQUATIONS OF MOTION USING THE MULTI-MODE GALERKINÂS METHOD. THE NONLINEAR NORMAL MODE OF THE SYSTEM IS THEN EXTRACTED USING THE INVARIANT MANIFOLD APPROACH AND EMPLOYED TO DECOUPLE THE DISCRETIZED EQUATIONS. THE HOMOTOPY ANALYSIS METHOD IS FINALLY USED TO DETERMINE THE NONLINEAR FREQUENCY. NUMERICAL RESULTS ARE PRESENTED FOR THE BACKBONE CURVES OF FG CYLINDRICAL SHELLS, NONLINEAR MODE SHAPES AND ALSO THE NONLINEAR INVARIANT MODAL SURFACES. THE VOLUME FRACTION INDEX AND THE GEOMETRIC PROPERTIES OF THE SHELL ARE FOUND TO BE EFFECTIVE ON THE TYPE OF NONLINEAR BEHAVIOR AND ALSO THE NONLINEAR MODE SHAPES OF THE SHELL. FOR THE NONLINEAR MODE SHAPES OF THINNER CYLINDERS, THE DISPLACEMENT VARIATION IN THE CIRCUMFERENTIAL DIRECTION IS FOUND TO CONSIDERABLY CHANGE WITH TIME.