Vibration Properties of Curved Thin-Walled Beams

A simple procedure is proposed to evaluate the out-of-plane vibration frequencies for a class of horizontally curved beams. The two governing differential equations are first partly uncoupled by means of a linear transformation. When the remaining coupling terms cannot be neglected, a two-degree-of-freedom solution is obtained by taking advantage of the similarity between the two uncoupled mode shapes. The method yields an exact solution only for simply suported curved beams. For other support conditions the solution is approximate. The method is illustrated by a numerical example: a fixed-fixed curved highway with open cross-section.