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.
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- 1.Easley J.G., Nonlinear deformation of elastic beams, rings, and strings, Appl. Mech. Reviews, 16, 677–680, 1963Google Scholar