Non linear dynamics of structures: passive suppression of vibrations, energy harvesting and periodic systems

• Grant number: 25/18381-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: November 01, 2025
• End date: October 31, 2027
• Field of knowledge: Engineering - Civil Engineering - Structural Engineering
• Principal Investigator: Carlos Eduardo Nigro Mazzilli
• Grantee: Vitor Schwenck Franco Maciel
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/00770-0 - Nonlinear dynamics applied to engineering problems, AP.TEM

Abstract

The present research project belongs to the thematic project entitled "Applications of nonlinear dynamics in engineering". Therefore, the focus will be on the application of analyses and concepts of nonlinear dynamical systems with focus on practical engineering applications. In accordance with the documentation related to the present Post Doctorate grant, two subprojects on the topic will be supervised by the candidate, namely P1.2 and P1.4.The main objective of the first subproject is to design and assess the performance of suppression devices aiming to mitigate oscillations of tubular structures subjected to fluid-structure interactions, with and without energy harvesting, both from the theoretical and experimental standpoints. It is worth mentioning that the same concepts and analysis tools are utilized in the study of vibration mitigation and energy harvesting, and both topics can be considered as two sides of the same coin. More specifically, the harvested energy may originate from the mitigation of undesirable oscillations in a given structural system, usually denominated by main structure in the literature on the topic. For the main structure, the consideration of articulated towers is highlighted, which are typical systems in Offshore engineering and are subject to dynamical phenomena of different natures such as, for example, parametric excitation, induced by waves, and vortex-induced vibrations, induced by currents. The suppressors to be considered are variants of the one known as rotative nonlinear vibration absorber (NVA). Besides the classical rotative NVA composed by a mass connected to the extremity of a rigid rod which is, in turn, hinged to the main structure by means of a rotational damper, the case in which the rod is extensible and contains piezoelectric materials will also be considered, allowing for energy harvesting. Firstly, mathematical models for the problems under consideration will be derived, which will be investigated using tools such as stability analyses, attractors identification and the construction of bifurcation diagrams and of the basins of attraction. Additionally, experiments will be conducted with physical models both immersed in water, as well as emersed, and the theoretical results will be compared to experimental ones. As for the second subproject, the main objective is to analyse the conditions of admissibility for the occurrence of asynchronous modes in structural systems of different typologies, including periodic structures, to explore their potential for the purposes of vibration mitigation and energy harvesting. Asynchronous modes are localized modes which, depending on the structural system, can arise due to a judicious design of its parameters. Inducing these modes is interesting from the standpoint of vibration control, given that part of the structure is spared from oscillations which are resonant with asynchronous modes. In addition, it is also interesting from the standpoint of energy harvesting, given that localized modes increase the energy density in a given part of the main structure. This can lead to more economic solutions since the number or length of the energy harvesting elements may be consequently reduced. For the structures to be considered in this investigation, mathematical models will be derived using variational principles, leading to partial differential equations, for systems modeled as being continuous, or ordinary ones, for discrete systems. These models will be subsequently studied using tools such as perturbation methods, stability analyses, Poincaré maps, bifurcation diagrams and basins of attraction. Lastly, it is mentioned that experiments will be carried out using physical models whose parameters will be calibrated such as to allow for the existence of asynchronous modes to be excited upon forced scenarios.