Oyibo, G. A. | Engineering Papers

NASA NTRS1985

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. The classical linear plate theory and Hamilton's principle are employed. The equations of motion of the plate are particularly simple in the chosen affine space, permitting a free-vibration study of the entire spectrum of composite materials with polar orthotropy. Approximate but very accurate standing-wave-type mode shapes are used 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. It is also discovered that, contrary to the trends observed for rectangular geometry and orthotropy by Oyibo (1981), Brunelle (1982), and Brunelle and Oyibo (1983), the affine-space frequency increases with increasing generalized Poisson's ratio.

Oyibo, G. A.↗

NASA NTRS1983

Generic buckling curves for specially orthotropic rectangular plates

Using a double affine transformation, the classical buckling equation for specially orthotropic plates and the corresponding virtual work theorem are presented in a particularly simple fashion. These dual representations are characterized by a single material constant, called the generalized rigidity ratio, whose range is predicted to be the closed interval from 0 to 1 (if this prediction is correct then the numerical results using a ratio greater than 1 in the specially orthotropic plate literature are incorrect); when natural boundary conditions are considered a generalized Poisson's ratio is introduced. Thus the buckling results are valid for any specially orthotropic material; hence the curves presented in the text are generic rather than specific. The solution trends are twofold; the buckling coefficients decrease with decreasing generalized rigidity ratio and, when applicable, they decrease with increasing generalized Poisson's ratio. Since the isotropic plate is one limiting case of the above analysis, it is also true that isotropic buckling coefficients decrease with increasing Poission's ratio.

Brunnelle, E. J.↗