On Nonlinear Equations of a Beam
Nonlinear equations for beams are derived in the literature under various assumptions, [1–5]. The problem of major interest in regard to dynamic deflections has been the vibration of beams with ends restrained to remain a fixed distance apart, where the nonlinearity arises from the stretching of the middle line and leads to one nonlinear partial differential equation of the fourth order, . More complicated equations are studied in [2–5]. Nonlinearities there are of the geometric nature, and although dynamic deflections of beams are large strains remain small so that linear constitutive equations are valid.
KeywordsGalerkin Method Cantilever Beam Nonlinear Vibration Maxwell Model Elastic Beam
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- 1.Easley J.G., Nonlinear deformation of elastic beams, rings, and strings, Appl. Mech. Reviews, 16, 677–680, 1963Google Scholar