Abstract
The present paper deals with the influence of large amplitudes on inextensional and extensional vibration of slender uniform elastic beams, when the boundaries are constrained to undergo a time-dependent displacement. Employing a fixed inertial co-ordinate system and a Lagrangian description of motion, the governing equations are formulated using energy principles, assuming the motion to be extensional. The solutions are attempted by a regular perturbation technique with finite transform method and a Galerkin's method extended to the present problem using Mindlin's transformations. The stability of periodic solutions are discussed by transforming the variational equation to the standard form of Hills' and Mathieus' equations, for the inextensional and extensional cases, respectively.
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