The Earthquake Engineering Online Archive

An Approximate Theory for the Vibrations of Hollow, Elastic Rods

McNiven, Hugh D.; Shah, Arvind H.; Sackman, Jerome L.

UCB/SESM-1965/13, Dept. of Civil Engineering, University of California, Berkeley, 1965, 48 pages (500/C23/65/13)

A system of approximate, one-dimensional equations is derived for axially symmetric motions of hollow, elastic rods of circular cross section. The theory is valid for a range of wall thicknesses from the very thin to thick walls, and takes into account the coupling between the longitudinal, radial, and axial shear modes. The theory is based on expansion of the displacements in a series of orthogonal polynomials in the radial coordinate, retaining only the earliest terms representing the longitudinal, radial, and axial shear deformations.

Available online: http://nisee.berkeley.edu/documents/SEMM/SEMM-65-13.pdf (912 KB)