Transient response of a thin cylinder with local material inhomogeneity

Abstract

Analyzed is transient response of a thin cylinder with a local material inhomogeneity to a pulse of short duration. The Galerkin method is utilized to solve the inhomogeneous dynamic equations with the eigenfunctions of the homogeneous cylinder serving as trial functions. Also treated is response of the limiting cases of a disk and of a ring with the same local inhomogeneity. All limiting cases yield to analysis when modulus E is approximated by segments of constant E along the radius for the disk and circumference for the ring. Transfer matrices relating variables at the two ends of a segment combine to satisfy continuity of variables at interfaces of segments. Curvature and axial dependence make the cylinder unique in response properties that neither disk nor ring possess.

Transient waves in a thin sphere enclosing an acoustic medium from a moving planar pressure discontinuity

“…h is circumferential coordinate, (R, h) are ring mean radius and thickness, (q, E, m) are mass density, modulus and Poisson ratio, t is time, p w (h;t) is the externally applied pressure, j is Mindlin's shear constant (Mindlin, 1951), v is shear deformation factor derived in El-Raheb (2005), and p f is acoustic pressure of the internal fluid. The constitutive relations are…”