Analytical, numerical, and experimental characterization of a piezoelectric-based actuation system for an active platform of the next-generation Superattenuators for Einstein Telescope

This thesis presents the activities performed by the Author from September 2024 to January 2025 at the European Gravitational Observatory (EGO) and INFN – Sezione di Pisa (Istituto Nazionale di Fisica Nucleare). The work focuses on the mechanical characterization and redesign of the actuators for the active platform of the Superattenuators (SAs) conceived for the next-generation gravitational-wave interferometer: the Einstein Telescope (ET). SAs are fundamental components of gravitational-wave interferometers, as they isolate the mirrors from seismic noise, enabling the optics to remain in a “free-fall-mass” condition relative to the ground. These systems are essential for ensuring the sensitivity and precision required for the detection of gravitational waves. The SA system consists of a large-scale mechatronic structure that operates through both active and passive mechanisms, allowing it to effectively mitigate a wide spectrum of local motion and seismic disturbances. The future SA design will benefit from the extensive expertise developed by the INFN Pisa group over 25 years of experience with Advanced Virgo (AdV): the predecessor of ET. For this reason the overall SA concept and its structure will be adopted also for ET but several upgrades and refinements are needed to meet the more stringent performance requirements for ET. These enhancements aim to address specific challenges, such as increased isolation performance, improved robustness, and compatibility with its unique underground environment. One aspect to be improved is the Active Platform (AcP) which will mitigate seismic noise in low frequency regime. The AcP is accommodated at the base of the SA and it is positioned on top of the base-tower within an Ultra-High Vacuum (UHV) environment. It consists of a Bottom Ring supported by three mechanical structures known as “feet”, each housing custom-designed vertical piezoelectric actuators (PZAs). This thesis focuses specifically on the mechanical characterization and redesign of foot structure. Starting from the existing AdV design, a detailed analysis was carried on to critically evaluate and revise the design. Chapter 1 provides an overview of the ambitious ET Project, which involves the construction of a large-scale (around 10 km per arm) underground laser interferometer. Chapter 2 describes the SA outlining its subsystems, which includes the Safety Structure (whose base also serves as the interface between the SA and the vacuum system), the feet (the focus of this thesis), the Inverted Pendulum (IP), sensors and actuators (namely LVDTs and accelerometers), the Filter chain (“Filter 0”, “standard filters”, and “Filter 7”), the last suspension stage or “Payload”, and the associated control electronics. Chapter 3 focuses on the IP and AcP, providing a detailed description of the foot structure and its PZA. Chapter 4 presents the analyses performed, which include the development of a rheological model of the foot, finite element method (FEM) simulations, and experimental tests. The results are thoroughly discussed and critically evaluated. Chapter 5 outlines the redesign process for the foot structure, guided by the findings from the previous chapter. The proposed new design and its validation through FEM simulations are presented in detail. Chapter 6 concludes the thesis summarizing the key findings, discussing proposed next steps, and identifying potential future developments.