Effect of nonlinear constitutive equation on vibrations of beams

Abstract

This paper is concerned with the analytical investigation of static and dynamic nonlinear behaviors of beams with different boundary conditions. While geometric type of nonlinearities on beams have been investigated extensively, material type nonlinearities have received very little attention. Therefore, material nonlinearities of the Ramberg-Osgood type are considered in this analysis. The use of Self-Generating functions for nonlinear beam problems is demonstrated for this type of nonlinearity. Transverse shear and rotatory inertia effects have been included in the formulation to study moderately thick beams. For all the cases investigated here nonlinear frequency ratios are calculated at various amplitudes of vibration and geometric parameters of beams. Numerical results indicate that the Ramberg-Osgood type nonlinearity produces softening-type responses. The study is limited to materials which are nonlinearly elastic and the effect of geometric nonlinearity is not considered in this paper.