Experimental evaluation of the effect of geometric nonlinearities on structural resonances

Abstract

In this research paper, we intend to study the effects of geometric nonlinearities on vibrations of rotating machinery 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 tensile structures. Classes 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 petrol, wind and atomic energy generation 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 paper, we study these effects via mathematical and experimental methods. Both laboratory essays and numerical models are developed. Our structure 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.