VIBRATIONS OF CIRCULAR ORTHOTROPIC PLATES IN AFFINE SPACE

The vibration of an initially compressed plate having a circular geometry and orthotropy is examined in an affine space. Classical linear plate theory and the Hamilton's principle are employed. The plate's equations of motion are particularly simple in the chosen affine space, permitting a free vibration study of the entire composite materials having polar orthotropy. Approximate, but very accurate, standing-wave-type mode shapes are utilized in solving the essentially double eigenvalue problem to determine the effects of midplane forces on the vibration frequencies of the plate. The results indicate that the affine space frequency increases with increasing stiffness ratio but decreases with increasing midplane compression.