THICKNESS EXPANSIONS FOR HIGHER-ORDER EFFECTS IN VIBRATING CYLINDRICAL-SHELLS

In the spirit of Mindlin and others who have used series expansions to express transverse dependences in thin bodies, the present work uses Ritz expansions in a variational formulation for cylindrical shell vib rations. By expanding displacements in spatial coordinates, integral e xpressions for strain and kinetic energy are converted to quadratic su ms involving time-dependent generalized coordinates. Hamilton's princi ple provides ordinary differential equations for these coordinates. Th is view-point yields physical insight into the mechanisms of energy st orage and avoids the geometrically thin assumption inherent to many fo rmulations. A set of Legendre polynomials multiplied by a radial facto r represent the radial dependences of displacement components, while c ircumferential variations are represented by sinusoidal functions. Exc ellent agreement in natural frequencies is found between this approach and analytical solutions over the entire range of shell thicknesses, including the limiting case of a solid cylinder. Comparisons to severa l thin shell theories are given, leading to conclusions about the rang e of validity of these theories.