Abstract
In this joint CECS/UFABC and EPUSP research project, we intend to study the effects of geometric nonlinearities on vibrations of rotating machines support structures. Dynamic characteristics of structures depend on their stiffness and mass. With those, we determine their natural frequencies and modes of free vibrations. Nevertheless, the initial stiffness of a structure, computed in its unloaded state, is affected by the applied forces, the so-called geometric stiffness. Compressive forces usually reduce the stiffness and the frequencies and may lead to buckling, for zero frequencies. In the other hand, tractions loads tend to increase stiffness and frequencies, a phenomenon resorted upon by the so-called tensostructures. A class of structures of economic-strategic importance are bases of machines, excited by vibrations induced by the supported equipment. These vibrations may affect the structures but, in general, may generate damage to the suspended equipment and the quality of the production. They may also render inadequate human working conditions. Almost all industrial branches are subjected to this problem, including highly sensitive ones such as the petrol energy, Eolic energy and atomic energy areas. Although machine support structures are, as a rule, very bulky, and thus little affected by geometric stiffness considerations, the tendency of modern structural engineering is towards slender members, due to more efficient materials and more powerful analysis tools. In this research Project, we study these effects via theoretical, numerical and experimental methods. Both laboratory essays and Finite Element models will be developed. A first model is a metal beam under pretension supporting a rotational machine. We suppose the original design have provided for natural frequencies away from the excitation frequency. Nevertheless, the presence of large axial compressive force will reduce the beam stiffness and natural frequencies leading to unexpected potentially dangerous resonance states. A second model is a simple portal frame, formed by two vertical columns and a horizontal beam. Geometric nonlinearity is introduced by considering shortening due to bending. We calibrate the model in such a way to have 2:1 internal resonance between the second mode (the first symmetric mode) and the first mode (the sway mode). Further, we impose external resonance between the machine rotation speed and the second mode frequency. We intend to demonstrate that energy pumped into the system via the second mode leads it to saturation and surplus energy being passed to the first mode, which will experience large amplitude oscillations, potentially dangerous not predicted in linear theory not considering the geometric stiffness effect. (AU)