Natural frequencies of clamped cylindrical shells.

Abstract

E = modulus of elasticity p = mass density v = Poisson's ratio a = mean radius of shell L = length of shell h = thickness of shell x, 4> = axial and circumferential coordinates of shell t = time co = circular frequency m = number of circumferential waves around shell u, v, w = displacements of a point on the middle surface of the shell (axial, tangential, and radial, respectively) p = number of axial nodal circles not including the ends