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.
Nielsen, J. C. O. (1991). Eigenfrequencies and eigenmodes of beam structures on an elastic foundation. Journal of Sound and Vibration, 145(3), 479–487. https://doi.org/10.1016/0022-460X(91)90115-Z