Abstract
An analysis is presented for the three‐dimensional vibration problem of determining the natural frequencies and the mode shapes of axisymmetrical solid bodies, with meridionally varying profiles, expressed as an arbitrary function. For this purpose, the body is transformed into a circular cylinder with unit axial length and unit radius, by a transformation of variables. With the displacements of the transformed cylinder assumed in the forms of algebraic polynomials, the dynamical energies of the cylinder are evaluated, and the frequency equation is derived by the Ritz method. This method is applied to barrel or hourglass‐type bodies and frustums of cone, under two combinations of boundary conditions at the ends, and the natural frequencies and the mode shapes are calculated, numerically giving the results.
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