Reduced-Order Models for Vibration Analysis, Parameter Identification and Passive Control of Civil Engineering Structures

Adequate mathematical models are essential for investigating the static and dynamic behaviors of structures; it would be useful to employ efficient models that require limited computational effort and can be readily adapted to address a wide range of problems. In the framework of civil engineering structures, almost all of them have one element in common: they are composed of beams. They are always present in bridges, either as main structural components or as secondary elements; furthermore, the largest part of buildings, both residential and industrial, is composed of beams (and columns as well), especially those constructed in reinforced concrete or steel. Thus, because of their central role in structures, different aspects of them are analyzed in the Thesis, investigating new features especially in nonlinear dynamics, with complementary points of view, but always aimed at a thorough understanding of the mechanical behavior. Moreover, being the main purpose of the Thesis the development of efficient models to study linear and nonlinear systems, modeling aspects related to other types of structural elements are considered too, like cables and three-dimensional frames. For the former, a nonlinear model is used and the interaction of the cable with vortices that shed from its surface is investigated, whereas for the latter a model, based on the homogenization of the building to a Timoshenko beam, is used to get modal properties comparable with those experimentally found. Consequently, reduced-order models are developed for the different types of structures, existing models are extended to incorporate new features and comparisons are made with results obtained from experimental data, when available, to validate the accuracy of the models and to test their limits. In general, each chapter of the Thesis corresponds to a main structural system – beams, cables or three-dimensional frames – where new problems are addressed and interesting findings are obtained in both linear and nonlinear fields, proving the importance of having models that are both simple and rigorous. The main original contributions of the Thesis are in order of appearance: the comparison of analytical results, obtained for Thin-Walled Beams modeled through the Generalized Beam Theory, with those found on full-scale viaducts, the vibration control of this kind of beams using a Nonlinear Energy Sink, the introduction of a newly developed model-based procedure to identify parameters of nonlinear continuous systems, the extension of an analytical formulation for the suspended cable subjected to Vortex-Induced Vibrations using the Multiple Scale Method directly on the non-discretized equations and, finally, the implementation of some new features on the homogenization technique to model three-dimensional frames in order to compare their modal properties to those of full-scale buildings. The results reveal new and significant findings, and several additional aspects remain to be explored.