On Nonlinear Dynamics of Planar Shear Indeformable Beams

Abstract

The planar forced oscillations of shear indeformabie beams with either movable or immovable supports are studied through a unified approach. An exact nonlinear beam model is referred to and a consistent procedure up to order three nonlinearities is followed. By eliminating the longitudinal displacement component through a constraint condition and assuming one mode, the problem is reduced to one nonlinear differential equation. A perturbational solution in the neighborhood of the resonant frequency is determined and the stability of the steady-state solutions is studied. The dependence of the phenomenon on the geometrical and mechanical characteristics of the system is put into light and the frequency-response curves for different boundary conditions are furnished.