FREE-VIBRATION OF A CLASS OF HOMOGENEOUS ISOTROPIC SOLIDS

A Ritz approach, with simple polynomials as trial functions, is used t o obtain the natural frequencies of vibration of a class of solids. Ea ch solid is modeled by means of a segment which is described in terms of Cartesian coordinates and is bounded by the yz, zx, and xy orthogon al coordinate planes as well as by a fourth curved surface, which is d efined by a polynomial expression in the coordinates x, y, and z. By e xploiting symmetry, a number of three-dimensional solids previously co nsidered in the open literature are treated including a sphere, a cyli nder and a parallelepiped The versatility of the approach is then demo nstrated by considering several solids of greater geometric complexity including an ellipsoid, an elliptical cylinder, and a cone.