Axially Symmetric Vibrations of a Finite, Isotropic Cylinder

Abstract

Vibrations corresponding to the different propagation constants for the same frequency parameter have been superimposed to satisfy the boundary conditions approximately at the flat surfaces of the cylinder for the frequency-parameter range where the Pocchammer-Chree frequency equation yields two real and one imaginary root. Taking the Poisson's ratio as 0.31, the thickness/diameter ratios (in the range of 1.0328–5.5630) for which resonance will occur at any particular frequency parameter have been calculated and shown graphically. The corresponding vibration patterns have been drawn for three particular cases for ka = 4.0 and the residual stresses calculated as a test for the validity of the approximation.