A THREE‐DIMENSIONAL ANALYSIS OF THE SPHEROIDAL AND TOROIDAL ELASTIC VIBRATIONS OF THICK‐WALLED SPHERICAL BODIES OF REVOLUTION

摘要: This paper addresses the spheroidal (i.e. coupled bending-stretching) and toroidal torsional or equivoluminal) elastic vibrations of thick-walled, spherical bodies revolution by means three-dimensional theory elasticity in curvilinear (spherical) co-ordinates. Stationary values dynamical energies body are obtained Ritz method using a complete set algebraic-trigonometric polynomials to approximate radial, meridional, circumferential displacements. Extensive convergence studies non-dimensional frequencies presented for modes thin-walled revolution. Results include all possible 3-D modes, i.e. radial stretching, combined bending-stretching, pure torsion, shear deformable flexure through wall thickness (including thickness-shear, thickness-stretch, thickness-twist). It is shown that assumed displacement yield strictly upper-bound exact solutions title problem, as sufficient number terms retained. Since effects transverse rotary inertia inherent present formulation, an examination made variation with thickness, h/R ranging from (h/R=0⋅05) thick-walled (h/R=0⋅5) bodies. The findings confirm increases increasing mode number, whereas decreases number. work offers some accurate reference data problem which refined drawn thin thick shell theories sophisticated finite element techniques may be compared. © 1997 John Wiley & Sons, Ltd.