Accurate analytical type solutions for free vibration frequencies and mode shapes of multi-span bridge decks: the span-by-span approach

Utilizing the superposition method an accurate analytical type solution is obtained for the free vibration frequencies and mode shapes of multi-span bridge decks. In this approach to the problem, a separate solution is obtained for the lateral displacement of each individual span. Simple support is provided at the outer extremities of the deck. Conditions of plate continuity and zero lateral displacement are enforced at inter-span support locations. Edges running parallel to the long centre line of the bridge are free. Eigenvalues and mode shapes are presented for a typical bridge deck of three spans, though it is shown that decks of any number of spans may be analysed. Advantages of this approach over an earlier one in which the entire deck was considered as a single plate with intermediate line supports, are discussed. The mathematical procedure developed constitutes one part of an overall study of bridge dynamics. Extension of the analysis to handle orthotropic bridge decks is easily accomplished.