PSI - Issue 78

Alessandro Contento et al. / Procedia Structural Integrity 78 (2026) 1975–1982

1977

Fig. 1. Rigid rocking block from Housner (1963).

Rigidly fixed elements, on the other hand, are subject to vibrations more akin to oscillatory systems. In this case, the main concern is the transmission of inertial forces to the structure and connections, which may lead to localized damage or detachment of parts. The behavior depends on the stiffness of the connections, the natural frequency of the element, and the transmitted seismic acceleration. Lastly, elements equipped with isolation or damping devices, such as elastomeric bearings or tuned mass dampers, exhibit a mitigated response due to energy dissipation and reduced acceleration transmission. However, their behavior can be highly nonlinear and dependent on parameters such as vertical stiffness, damping characteristics, and the dynamics of the isolation system. These different mechanisms require specific analyses capable of capturing both dynamic and nonlinear effects, in order to properly assess the seismic vulnerability and safety of NSEs. 2.2. Analytical and numerical models for seismic response evaluation Various analytical and numerical models have been developed to understand and predict the seismic response of NSEs, each with specific advantages and limitations. Traditional analytical models often represent elements as systems with limited degrees of freedom, such as Single Degree of Freedom (SDOF) systems. These models are useful for rapid assessments and for qualitative understanding of the response, but can be inadequate for elements with complex geometries or significant nonlinear behaviors, such as rocking with repeated impacts. Numerical models, on the other hand, offer a more detailed and flexible representation, capable of incorporating geometric nonlinearities, base contact interactions, nonlinear damping, and three-dimensional effects. Finite element methods are commonly used to realistically simulate the behavior of machinery, installations, or complex architectural components. However, these models require significant computational resources and careful calibration of parameters, especially for modeling dampers and isolators. In recent years, attention has also shifted to semi-empirical or hybrid models, which combine experimental data with numerical simulations to enhance predictive capability and robustness. Additionally, updated dynamic models based on laboratory testing - such as those developed by Frost and Cacciola (2023, 2024) - have shown improved ability to predict the onset of rocking and the overall response of elastomeric isolators. In summary, the choice of the most suitable model depends on the evaluation objective, the complexity of the element, and the available resources. Often, a balance between detail and simplicity is necessary for practical applications. 2.3. Experimental techniques for characterizing the seismic response of NSEs The importance of experimental techniques for studying the seismic behavior of NSEs has grown significantly in recent decades, as empirical data allow for the validation and improvement of analytical and numerical models. Among the most widely used experimental methods are laboratory tests on scaled models and full-scale tests. Laboratory tests make it possible to reproduce controlled and repeatable loading conditions using shaking tables or vibration platforms. These experiments are essential for analyzing specific phenomena, such as rocking initiation or elastomeric isolator response. However, one of the main challenges is the correct representation of geometric and dynamic scaling, which must adhere to strict similitude laws to ensure real-world applicability. Full-scale tests,