Vibration of structures with non-linear damping

Abstract

The work reported here is directed towards the problem of measuring and modeling non-linear damping in steel space frame civil engineering structures. In order to gain a better understanding of the damping mechanism in such structures, tests were performed on a full scale bolted lattice structure and the results of section A show that the joint' damping can be represented approximately in the form: FD =C (1 +e IXIn) where n=1. Other situations. where this form of non-linear damping occurs is in the case of fluid flow past a solid body. In offshore structures the hydro-dynamic force due to drag effects are found to be proportional to velocity squared. For non linear material damping, n, takes a value of 6. In section B. various methods of solution to the non-linear dynamical system under random excitation were studied and it was found that the 'Equivalent Non- Linear Differential Equationl, (ENL) method yields a better measure of the response of the non-linear system to white noise excitation than other approximate methods. Analytical expressions are derived for the mean-square response, probability density function and level crossing rates. With the modified IENLI method (MENL) it is shown how one can extract the non-linear damping and excitation power spectral density. A good correlation is obtained between experimental and theoretical results