Eigenfrequencies and eigenmodes of beam structures on an elastic foundation

Abstract

A method for determining the eigenfrequencies of continuous structures containing beams in plane bending-shearing vibration is presented. Each beam member may rest on a general Winkler-type elastic foundation (including the Pasternak foundation as a special case) and may carry a large static axial load calling for use of a second order theory. The method could preferably be implemented in the Wittrick-Williams bisection algorithm. A numerical verification is given for a repetitive structure where an alternative solution is available through the use of exact difference equations. Practical applications to a rail/pad/sleeper system on its ballast and roadbed are foreseen. © 1991.