Stability analysis of a simply supported uniform flexible rod with large deflections is considered. Assumed the relationship normal stress-strain is weakly nonlinear. Free vibration of the simply supported uniform beam is considered the material of the beam does not obey to Hooke’s law. This axial force induced by the deflection of a beam is the source of the static nonlinearity in the problem. In this case the axial force is not active force but reaction occurs due to free vibrations. “Restrained” free transverse vibration of the one-span uniform beam with both immovable supports are considered. The peculiarity of this type of problems: despite the initial linear relations and the classical assumptions, the obtained solutions satisfy the superposition principle only partially thus, the combination of axial and transversal loads leads to nonlinear results. This chapter deals with some simplest nonlinear problems of the statics, stability, and vibrations of deformable systems.Ĭompressed rods with lateral loading.
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