Modeling and Simulation of Higher Order Couplings of a Guided Nonlinear Elastic Beam

Nowadays, with the increasing demand for an exploitative productivity the speed of machines is also increased respectively. The effect of inertia forces, in case of operation at high speed, will become significantly because it causes the change of the stiffness, may result to unstable situations and change the natural frequencies of the system. In a previous study, the nonlinear modeling of the elastic beam with coupling between axial, bending, and transverse deformations was presented. From this point of view geometric stiffening effects on the deformation of the elastic beam considering high-order coupling terms at high angular velocities are investigated in this paper and compared to other modeling approaches [1, 2]. The goal of this contribution is to develop a suitable and easy to use modeling approach of higher order.