The forced vibrations of a curved-in-plane nonprismatic beam with a variable cross section and any curvature, generated by a load moving at a variable velocity are analyzed. Approximation with Chebyshev series and a generalized eigentransformation were used to solve the system of the partial differential equations describing the considered problem. The derived equations in their final form enable one to determine displacement and rotation functions for any beam. In order to verify the derived formulas the eigenproblem solution (used in the eigentransformation method) was compared with the one obtained by the finite element method.
Meissner, M., & Ruta, P. (2012). Out-of-plane vibrations of curved nonprismatic beam under a moving load. Journal of Civil Engineering and Management, 18(6), 773-782. https://doi.org/10.3846/13923730.2012.720937
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