Effects of changing the height of take-off in long jump

Abstract

The nonlinear dynamics of Shape Memory Alloys (SMA) oscillators with pseudoelastic behaviour has been studied extensively in the last years by using different constitutive models for the restoring force. The response of SMA devices is rather complex and is characterized by several aspects that, usually, are not taken into account within a single model. For this reason, the constitutive models that are typically used to study the nonlinear dynamics are often of a rather simplified nature that neglects one or more aspects.This works investigates the extent to which the choice of a more or less refined constitutive model can affect the evaluation of the nonlinear dynamic behaviour of a SMA oscillator. In order to compare different constitutive models, a comprehensive thermomechanical modelling framework capable to simulate different constitutive assumptions is proposed first. Then, numerical simulations are carried out to compare the different dynamical responses. The obtained results show that, for single trajectories with specific features, different models can give similar dynamical information, although with the exception of different transient behaviour. However, when the overall scenario of local dynamics is investigated by computing frequency-response curves, it becomes evident that the simplified models, and in particular those with polynomial restoring force, fail to capture main aspects such as the location of the jumps and the order of magnitude of response peaks. Moreover, they generally lead to significant errors in the estimation of the dissipated energy, which is crucial for the quantification of the structural damping. The results of this work should then be helpful to guide the choice of SMA models to be used in nonlinear dynamic applications.