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Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing.… (More)

- G. KERSCHEN, J. C. GOLINVAL
- 2001

Proper orthogonal decomposition is a statistical pattern analysis technique for "nding the dominant structures, called the proper orthogonal modes, in an ensemble of spatially distributed data. While the proper orthogonal modes are obtained through a statistical formulation, they can be physically interpreted in the "eld of structural dynamics. The purpose… (More)

- G. Kerschen
- 2006

This paper focuses on the relation between the vibration modes of mechanical systems and the modes computed through a blind source separation technique called independent component analysis (ICA). For free and random vibrations of weakly damped systems, a one-to-one relationship between the vibration modes and the ICA modes is demonstrated using the concept… (More)

- Gaetan Kerschen, Young Sup Lee, Alexander F. Vakakis, D. Michael McFarland, Lawrence A. Bergman
- SIAM Journal of Applied Mathematics
- 2005

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal analysis is limited to structures showing a linear behaviour. In non-linear structural dynamics, it is well known that mode shapes are no longer useful for… (More)

- G. Kerschen
- 2002

The present study focuses on the model reduction of non-linear systems. The proper orthogonal decomposition is exploited to compute eigenmodes from time series of displacement. These eigenmodes, called the proper orthogonal modes, are optimal with respect to energy content and are used to build a low-dimensional model of the non-linear system. For this… (More)

- G. KERSCHEN
- 2001

The identi"cation of the dynamic characteristics of linear systems is now widely used and interest in non-linear systems has increased. The objective of this paper is to demonstrate the performance of the restoring force surface method as far as the identi"cation of non-linear systems is concerned. The vibrations of a clamped beam are investigated for two… (More)

- G Habib, T Detroux, R Viguié, G Kerschen, Giuseppe Habib
- 2016

This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring… (More)

- Gaetan Kerschen, Vincent Lenaerts, Stefano Marchesiello, Alessandro Fasana
- 2001

The present paper aims to compare two techniques for identification of nonlinear dynamical systems. The Conditioned Reverse Path method, which is a frequency domain technique, is considered together with the Restoring Force Surface method, a time domain technique. Both methods are applied for experimental identification of wire rope isolators and the… (More)

Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts… (More)