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Models and experiments with nonlinear dynamic systems


The aim of this paper is to provide an overview of recent theoretical and experimental investigations carried out in the laboratory on different academic and industrial mechanical systems in order to illustrate non linear phenomena that occur mainly in systems with localized nonlinearities and/or with time-varying parameters. Many mechanical systems can be considered as linear structures with localized nonlinear components modeled with either rheological or restoring force approaches. It is shown that the modified Dahl model selected is a reasonably efficient restoring force method for modeling nonlinear mechanical component such as suspension mountings, belt-tensioner and passive actuator. It is simply described by a first order differential equation coupled to the reduced equations of motion of the linear structure. Time-varying parameters may be due to parametric excitation, which provide lateral-axial couplings and a motion governed by linear Mathieu equations. In the presence of a nonlinear term, the limiting curves of the instability chart, evaluated by using a perturbation method, depend on the forward or backward forcing frequency sweeps: jump and hysteresis phenomena are observed. Different types of nonlinearities are illustrated using an academic autoparametric system, a pulley-belt system and resonant micro-gyroscope.
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hal-00936451 , version 1 (26-01-2014)


  • HAL Id : hal-00936451 , version 1


Régis Dufour. Models and experiments with nonlinear dynamic systems. DINAME - International Symposium on Dynamic Problem of Mechanics, Mar 2009, Angra Dos Reis, Brazil. ⟨hal-00936451⟩
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