MS8.4 -Dynamic Stability, Multistability and Buckling-induced Smart Applications

Engineering applications have conventionally aimed to avoid phenomena related to mechanical instabilities or buckling, as they can bring undesired nonlinear effects or even failure. In recent years however the research in this field has experienced an inversion of direction making use of such phenomena to improve the performance of solids and structures. In this context, the adoption of pre-compressed slender beam elements is one of the most common solutions. A typical application is the development of quasi-zero stiffness (QZS) vibration isolators, that bring a high static stiffness and an extremely low dynamic stiffness. As a general rule, the QZS characteristics can be obtained by coupling a negative stiffness effect with a positive one. When considering beam elements, the application of a compressive axial force can lead to a mechanical instability and to a negative stiffness region in the force-displacement characteristics. This paper studies the dynamical behaviour of such elements by comparing experimental measurements with a mathematical model. To this end, a 3D-printed V-shaped structure is considered, comprising two pre-compressed beam elements and a controllable pre-load. The regulation of the pre-load allows the V-structure to undergo tensile or compressive forces, thus altering its characteristics. In particular, the restoring force of the system can show regions of negative or quasi-zero stiffness when compressive forces are applied. The system is excited with an electromagnetic shaker considering different pre-loads, and the nonlinear dynamic behaviour is estimated from the measured responses using nonlinear identification techniques. A comparison between experimental measurements and model predictions is eventually carried out to strengthen the understanding of the observed dynamical phenomena.

Recent decades have witnessed a new interest in the field of structural stability due to the use of multistable systems in several applications such as vibration control, energy harvesting, deployable and collapsible structures, micro- and nanocomponents and the development of metamaterials, among others. In many of these structures multistable behavior is attained by coupling bistable elements. The most basic example of bistable structure is the Von Mises truss, which presents two stable equilibrium configurations. In this work, the multistable be-havior of a sequence of Von Mises trusses connected through a flexible element is studied. This system has several stable and unstable equilibrium configurations resulting from the nonlinear coupling, which significantly influences its non-linear oscillations and dynamic stability. To obtain the equilibrium paths, the nonlinear equilibrium equations are derived in nondimensional form and solved by using the Newton-Raphson method and continuation techniques. Hamilton's principle is then employed to obtain the equations of motion around an equilibrium configuration. They are numerically integrated to obtain bifurcation diagrams and basins of attraction, which clarify the effect of load and system parameters on the nonlin-ear oscillations and instabilities of the coupled trusses, in particular the geometric nonlinear-ity and connection stiffness. This may help in the development of new engineering applica-tions where multistability is desired.

With the increasing demand for energy consumption in recent years, several areas of science have been looking to produce clean and renewable energy. In this context, several devices are used, such as converting mechanical movement of sea waves, portal frame systems, and so on Nowadays, with the energy demand consumption, the development and analysis of mathematical models to predict and obtain energy harvesting is increasing every day. By the other hand, devices that have been gaining prominence are those that have the Shape Memory Alloy Effect (SMA) because the SMA materials have a memory feature and can return to their original shape without heating. Therefore, in this paper, we explore the dynamic behavior using bifurcation diagrams, Lyapunov exponents, basis and attraction and entropy of a magnetic structure acting on a mass coupled to spring with the SMA behavior driven by a DC motor with limited power supply. The changes observed in the scan of the analyzed parameters of the adopted mathematical model, showed an influence on the average output power because of its coupling to the magnetic mass displacement. This dynamic analysis supported control designs that suppress chaotic behavior, and thus determine a constant energy production process. Determining the non-linear dynamic behavior of the system for energy collection makes it possible to establish parameters that allow the maximum collection of average power and to establish analyzes such as control design for suppression of chaos. Therefore, the aim of this work was also applied two control techniques: the Optimal Linear Feedback (OLFC) control due to its high computational efficiency and SDRE (State Dependent Riccati Equation) both to suppress the chaotic behavior and thus maintain the energy production in a periodic orbit. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.