BENDING, VIBRATION AND BUCKLING OF LAMINATED COMPOSITE PLATES USING A SIMPLE FOUR VARIABLE PLATE THEORY
Keywords:SHEAR DEFORMATION, BENDING, BUCKLING, VIBRATION, CROSS-PLY LAMINATES, TRIGONOMETRIC THEORY, LAMINATED PLATES
AbstractIN THE PRESENT STUDY, A SIMPLE TRIGONOMETRIC SHEAR DEFORMATION THEORY IS APPLIED FOR THE BENDING, BUCKLING AND FREE VIBRATION OF CROSS-PLY LAMINATED COMPOSITE PLATES. THE THEORY INVOLVES FOUR UNKNOWN VARIABLES WHICH ARE FIVE IN FIRST ORDER SHEAR DEFORMATION THEORY OR ANY OTHER HIGHER ORDER THEORIES. THE IN-PLANE DISPLACEMENT FIELD USES SINUSOIDAL FUNCTION IN TERMS OF THICKNESS CO-ORDINATE TO INCLUDE THE SHEAR DEFORMATION EFFECT. THE TRANSVERSE DISPLACEMENT INCLUDES BENDING AND SHEAR COMPONENTS. THE PRESENT THEORY SATISFIES THE ZERO SHEAR STRESS CONDITIONS AT TOP AND BOTTOM SURFACES OF PLATES WITHOUT USING SHEAR CORRECTION FACTOR. EQUATIONS OF MOTION ASSOCIATED WITH THE PRESENT THEORY ARE OBTAINED USING THE DYNAMIC VERSION OF VIRTUAL WORK PRINCIPLE. A CLOSED FORM SOLUTION IS OBTAINED USING DOUBLE TRIGONOMETRIC SERIES SUGGESTED BY NAVIER. THE DISPLACEMENTS, STRESSES, CRITICAL BUCKLING LOADS AND NATURAL FREQUENCIES OBTAINED USING PRESENT THEORY ARE COMPARED WITH PREVIOUSLY PUBLISHED RESULTS AND FOUND TO AGREE WELL WITH THOSE.
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