Optimization of Locally Resonant Metafoundations for the Protection of Industrial Tanks and Small Modular Reactors Subjected to Low-Frequency Seismic Waves

Industrial process plants and power plants are crucial components of modern infrastructures, playing a pivotal role in sustaining communities through the provision of essential goods and services. These facilities contain critical equipment and structures vulnerable to damage or failure when exposed to seismic excitations without protection measures. Robust seismic protection ensures the preservation of structural integrity and functionality, guaranteeing the uninterrupted delivery of vital services like electricity generation, water treatment, and manufacturing. Consequently, seismic protection measures for these plants enhance overall community resilience and safety, mitigating potential disruptions and harm in the face of earthquakes. Based on these insights, a novel seismic protection system, known as metafoundation (MF), is revisited and enhanced. Geared towards offering cost-effective, modular, and multidirectional protection to critical infrastructure components, the investigation delves into the exploration and implementation of novel nonlinearities and mechanisms to finite locally resonant MFs in order to obtain further improvements. The thesis commences by elucidating the principles of periodic lattices and lattice-based acoustic metamaterials, the foundational concept of finite locally resonant MFs, using both analytical and numerical met-hodologies, followed by some experimental validation. Theoretical exploration encompasses one-dimensional linear and nonlinear metamaterials featuring local resonance properties, via resonators. By incorporating nonlinear mechanisms, such as the Bouc-Wen and Duffing oscillators, the study delves into unique nonlinear wave dynamics and evolving dispersion characteristics. Notably, the focus intensifies on bistable Duffing oscillators as the primary cell spring, and the reliability of numerical simulations is confirmed through experimental validation. Transitioning from theoretical frameworks to practical applications, the finite lattices has been analysed. The effectiveness of MFs under seismic loading relies significantly on the seismic input. Consequently, both natural and synthetic three-directional accelerograms — where the former were generated through a physics-based ground motion model — were utilized for performance assessment and, crucially, for optimization purposes. The inherent locally resonant property of MFs necessitates careful tuning of resonator parameters, as mistuning can lead to notable performance degradation. Optimization strategies encompassed frequency domain and time domain approaches for linear and nonlinear MFs, respectively. In the frequency domain, the Power Spectrum Density (PSD) functions of ground motions were considered alongside the transfer function of MF-superstructure coupled systems to quantify responses. The optimization was achieved through solving the multi-variable, multiobjective optimization problem, facilitated by a specialized algorithm based on sensitivity analysis. In the time domain, conversely, optimization focused on energy dissipation through time history analyses. To streamline computational efficiency, experimental design methods and Kriging models were employed. The pursuit of enhanced performance and novelty, required intricate nonlinear mechanisms in conjunction with MFs to be considered. The columns of MF were substituted with bistable ones. In another application instead, to enhance vertical seismic protection, unit cells featuring vertical quasi-zero-stiffness mechanisms were interconnected in series with locally resonant unit cells. Moreover, to improve performance and minimize MFs’ voluminous size —needed for low-frequency attenuation — the incorporation of novel inerters to resonators was considered. The implemented strategies based on 3D modelled MFs, were applied to a storage tank of a process plant and two in-design stage Small Modular Reactor (SMR) buildings. Detailed time history analyses revealed that MFs can effectively meet targeted performance objectives of the coupled systems. This includes achieving performance levels comparable to conventional isolation solutions for horizontal seismic excitation, while also safeguarding the superstructure against vertical actions and resultant rocking motions. Finally, it was shown that MFs offer a viable solution aligned with the primary development objective of SMRs, facilitating modular standardization for deployment in beyond-design earthquake locations without additional resistance of the superstructure.