The model of a non-smooth oscillator with hysteresis and impacts will be proposed in order to perform an overall optimization of an innovative Shock Absorber (SA) by means of numerical and experimental investigations. The starting point for the research is an existing multi-purpose device proposed and patented in recent years by Lacarbonara and Carboni, which is characterized by hysteretic restoring forces provided by assemblies of shape memory alloys and steel wire ropes. The hysteretic behavior exhibited by the device is due to the concurrency of inter-wire friction, phase transformations of the shape memory alloy and geometrically induced nonlinearities. In order to develop a Shock Absorber with optimized performances, several configurations will be considered and compared taking into account the influence of soft and hard impacts on the device dynamic response. The improved Shock Absorber will be finally tested to control the nonlinear vibrations of a 2DOF system composed by a main structure to be protected and by the Shock Absorber itself.
The expected results will lead to an advance of the knowledge on different topics: these cover both basic problems related to the modeling of non-smooth systems and more technological issues related to the design and experimental validation of improved devices for shock absorption and vibration mitigation. Furthermore, on the level of the understanding of the dissipative features of this type of device, the project will produce innovative phenomenological models for shape memory alloys. The project will finally provide a refinement of innovative and traditional techniques for the analysis of highly nonlinear and non-smooth systems and for an optimized dynamical response identification.
The present project will deal with a topic which is new in the field, since it proposes an innovative Shock Absorber with optimized performances that exploits SMA in the form of wire ropes. The possibility to achieve a definite goal is facilitated by the fact that the starting point of the work is a well-developed device which has been already tested and patented. For this reason the research group will be immediately operative.
The project will lead to an advance of the knowledge, at the technological and theoretical level, on three main topics: 1) design and experimental validation of improved devices for shock absorption, 2) phenomenological modeling and parameter identification, 3) analytical/numerical analysis of the dynamics of non-smooth systems.
1) Design and experimental validation of improved devices for shock absorption.
Starting from an existing basis, the research will lead to the modeling and development of a new SA based on a specific configuration not tested so far. The novelty will consist of various aspects: the modelling of the interplay between impacts and damping mechanisms, the evaluation and the comparison of different arrangements of the PSG and SSG, as well as the identification of the best operating mode for the operation as Shock Absorber and the corresponding experimental analyses.
2) Phenomenological modeling and parameter identification.
The models proposed so far for the devices [16] are based on the Ivhsin-Pence model used in an isothermal setting. This project will use a full thermomechanical model in order to evaluate, for the first time, the entity and the corresponding relevance in the device performances of the temperature variations arising due to the thermomechanical coupling.
Exhaustive experimental campaigns will be performed for the model validation and for the identification of model parameters which best fit the behavior of the system. The parameters will be identified minimizing the difference between the experimental measurements and the numerically-obtained responses. According to the highly nonlinear and discontinuous nature of the faced problem heuristic methods will be adopted as for example the Particle Swarm Optimization and the Differential Evolutionary Algorithm. The identification will be performed in the time domain reproducing the whole acquired time histories.
3) Non-smooth dynamics.
The effect of impulsive loads coupled with the effect of impacts is completely unexplored both for the SDOF as well as the 2DOF systems. The nonlinear dynamic behavior of different types of 2DOF systems with impacts, geometrical nonlinearity and thermomechanical SMA will be studied in a large range of conditions, for the first time. To this end various models the forcing excitation will be considered. The contact mechanics will be described with two different modelling approaches. The first one is based on the smoothing of the relationship between force and displacement. In particular, cubic or higher order terms will be activated from a threshold displacement but preserving the continuity of the stiffness at the transition point. This model will comprise also the possibility to variate the level of damping as function of the displacement. The second approach will take into account the real discontinuous nature of the problem and will be also used for the validation of the smoothing approach. The dynamical study of systems involving impacts, as the SA proposed here, poses several challenges also from a numerical point of view. To tackle these problems novel refined analytical/numerical tools dedicated to non-smooth nonlinearities will be developed and computationally efficient techniques based on path following procedures will be designed for these kind of non-smooth dynamical systems.