Random vibration analysis of a non-linear system with dry friction damping by the short-time gaussian cell mapping method

Abstract

Some vibration attenuation devices make use of material non-linearity and dry friction damping mechanisms. Such devices are often exposed to a random vibration environment. It is important for engineers to be able to calculate the random vibration response of a system involving these devices, and thereby to predict the fatigue life of the device and the reliability of the system. However, the analytical study of random vibration problems of such a system is usually difficult. This paper extends the previously developed generalized cell maping method based upon the short-time Gaussian approximation (GCM/STGA) to systems with dry friction damping. In the paper, the non-linear moment equations of the state variables of a general non-linear system with dry friction damping are derived for the construction of the one-step short-time Gaussian transition probability matrix of the GCM/STGA method. Transient and steady state solutions of some numerical examples are presented. Excellent agreement is found between the results of the present method and the available exact solutions or simulation data. This study indicates that the GCM/STGA method is well suited to random vibration studies of complex systems with dry friction damping, and offers an attractive tool for random vibration analysis of these systems.