Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam struc...
International audience
Quaternion-based finite-element computation of nonlinear modes and frequency responses of geometrically exact beam struc...
In this paper, a novel method for computing the nonlinear dynamics of highly flexible slender structures in three dimensions (3D) is proposed. It is the extension to 3D of a previous work restricted to inplane (2D) deformations. It is based on the geometrically exact beam model, which is discretized with a finite-element method and solved entirely ...
Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically-oriented cantilever beam is investigated. The extreme nonlinear vibrations are modeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a ...
Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
International audience
Extreme nonlinear dynamics of cantilever beams: effect of gravity and slenderness on the nonlinear modes
In this paper, the effect of gravity on the nonlinear extreme amplitude vibrations of a slender, vertically oriented cantilever beam is investigated. The extreme nonlinear vibrations aremodeled using a finite element discretization of the geometrically exact beam model solved in the frequency domain through a combination of harmonic balance and a c...
Finite element computation of nonlinear modes and frequency response of geometrically exact beam structures
An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the cross-s...
Finite element computation of nonlinear modes and frequency response of geometrically exact beam structures
International audience
Nonsmooth Modal Analysis of a Varying Cross-Sectional Area Bar in Unilateral Contact
Nonsmooth modes of vibration allow for identification of resonant behaviours and attendant vibratory frequencies in structures prone to unilateral contact conditions on the boundary. The prominent approach for finding nonsmooth modes of vibration entails finding continua of periodic solutions to the system in question. In this paper, nonsmooth mode...
Finite element computation of nonlinear modes and frequency response of geometrically exact beam structures
An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the crossse...
Nonlinear dynamics of coupled oscillators in 1:2 internal resonance: effects of the non-resonant quadratic terms and rec...
This article considers the nonlinear dynamics of coupled oscillators featuring strong coupling in 1:2 internal resonance. In forced oscillations, this particular interaction is the source of energy exchange, leading to a particular shape of the response curves, as well as quasi-periodic responses and a saturation phenomenon. These main features are...
