A definition and a constructive methodology for normal nodes of motion are developed for a class of vibratory systems the dynamics of which are governed by non-linear partial differential equations. The definition for normal modes is given in terms of the dynamics on two-dimensional invariant ...
This paper presents two methods for numerical calculation of nonlinear normal modes (NNMs) in multi-degree-of-freedom, conservative, nonlinear structural dynamics models. The approaches used are briefly described as follows.Method 1: Starting with small amplitude initial conditions determined by a selec...
ZHANG X H.Geodesics non-linear normal modes ofconservative vibratory systems and decompositionmethod.Journal of Sound and Vibration. 2004Zhang, X.: Geodesics, nonlinear normal modes of conservative vibratory systems and decomposition method. J. Sound Vib. 282 , 971–989 (2005)...
Nonlinear normal modesHarmonic balanceModel order reductionNon-intrusive methodDimensionality reduction in mechanical vibratory systems poses challenges for distributed structures including geometric nonlinearities, mainly because of the lack of invariance of the linear subspaces. A reduction method based on ...
In this paper, two factors that affect the behaviors of the non-linear normal modes (NNMs) of conservative vibratory systems are investigated. The first factor is the base points (which are equivalent to Taylor series expanding points) of the non-linear normal modes and the second one is ...
A method for producing accurate reduced order models of non-linear vibratory systems is presented based on the invariant manifold description of non-linear normal modes (NNM). This approach makes use of polar co-ordinates to obtain equations which govern the geometry of the invariant manifold. ...