The paper present the so-called "an extended averaged equation approach" to the investigation of nonlinear vibration problems. The numerical results in analysing the vibration systems with weak, middle and strong non-linearity show the advantages of the method. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 24, 2002, No3 (133 - 141) EXTENSION OF METHOD OF MOMENT EQUATION TO NONLINEAR DETERMINISTIC VIBRATIONS NGUYEN DONG ANH 1 AND NINH QUANG HAI 2 1 2 Institute of Mechanics, Hanoi Vietnam Hanoi Architectural University, Vietnam ABSTRACT. The paper present the so-called "an extended averaged equation approach" to the investigation of nonlinear vibration problems. The numerical results in analysing the vibration systems with weak, middle and strong non-linearity show the advantages of the method. Keywords. Extended averaged equation, moment equation (ME) method, nonlinear vibration l. Introduction In recent decades, a great number of achievements in nonlinear oscillation field has been obtained. There are several documents specializing in approximate techniques for solving deterministic and / or random vibration problems, for instance, see [1-6] and see [7-9], respectively. Many outstanding analysis methods as well as numerical methods are established. As results, significant characteristics of nonlinear systems subject to deterministic or random excitations are discovered. These properties have been effectively applied to many engineering fields, such as problems of vibration for machines, traffic means, civil-engineering etc . However, there still exist many problems that need to be investigated, namely, there is a number of gaps between weakly nonlinear systems and strongly nonlinear ones, between deterministic systems and stochastic ones. Some well-known methods which can be applied to stochastic systems (for instant, the F-P-K equation method, the Gaussian closure method . ) normally cannot be used for deterministic ones and vice verse (for example, the harmonic balance method, . ) due to the fact that many principal concepts in stochastic vibrations do not make sense in deterministic fields. Furthermore, it is obviously that some outstanding methods such as: the method of small parameter, the averaging .
