An iterative procedure for computing periodic solutions of nonlinear vibrating beams is presented. The nonlinear partial differential equation is replaced by a coupled system of equations. The contraction mapping principle is then applied to generate a method of successive approximations. The coupled equations are then approximated by discrete equations that are solved by matrix-theoretic techniques and numerical quadrature procedures. Some numerical examples are provided to illustrate the method.
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Nonlinear Forced Vibrations of Beams
Department of Mathematics and Statistics, Louisiana Tech University, Ruston, La. 71272
Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019
Countryman, M., and Kannan, R. (March 1, 1985). "Nonlinear Forced Vibrations of Beams." ASME. J. Appl. Mech. March 1985; 52(1): 163–166. https://doi.org/10.1115/1.3168988
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