Reduced Order Models and Localized Nonlinearity: An Approach to the Design of Meta-Structures
Impact events on soil media cause vibrations that propagate all around the impact site. These vibrations can be mitigated by the construction of suitable buried barriers. A recent proposal suggests of realizing them by meta-structures characterized by a n
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Abstract Impact events on soil media cause vibrations that propagate all around the impact site. These vibrations can be mitigated by the construction of suitable buried barriers. A recent proposal suggests of realizing them by meta-structures characterized by a nonlinear response. Their design requires repeated analyses of the whole system made of soil and barriers. A simplification is achieved by building the reduced order model of the linear system and incorporating the nonlinear effects as suitable external actions.
1 Introduction As often occurred in the last decades, scientific neologisms are first acquired by electronics, where the term meta-structure means a structure based upon metamaterials and meta-material denotes any material that obtains its electromagnetic properties from its structure rather than from its chemical composition. But in Wikipedia (https://en.wikipedia.org/wiki/Metamaterial#Structural) one also reads: “Structural metamaterials provide properties such as crushability and light weight. Using projection micro-stereolithography, microlattices can be created using forms much like trusses and girders”. Starting from this point of view, one easily reaches a quite different concept, still named meta-structure, as adopted in [1], where the authors “propose to use an array of resonating structures (herein termed a “metastructure”) buried around sensitive buildings to control the propagation of seismic waves”. Thus the topic addressed by the last term in the title is clarified. Just for sake of completeness, this term is also used by modern painters (http://www. blackbookgallery.com/meta-structures) and in a socio-epistemological context [2]. The idea of buried barriers in vibration mitigation is not new and implementations are mainly associated with the traffic induced vibration [3–5]. This was synthesized by the FP7 research project RIVAS (http://www.rivas-project.eu/index. php?id=8), which recently celebrated its closure conference. But extensions to the
F. Casciati () Department of Civil Engineering and Architecture, University of Pavia, via Ferrata 3, Pavia, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2017 H. Irschik et al. (eds.), Dynamics and Control of Advanced Structures and Machines, DOI 10.1007/978-3-319-43080-5_21
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protection from seismic [6], machine foundation [7] or blast [8] generated waves are easily found in the literature. Also the technology insight in this barrier is quite broad and spans from passive [9] to active [10] solutions. Once the concept has been introduced, the next step is how to design such a technological solution to the problem of vibration mitigation. The numerical model has to simulate soil–structure interaction [11] and, as usual in these cases, the size of the problem is quite large. On the other side, the barriers are better designed to behave in a nonlinear way, making the problem nonlinear. Thus standard model order reduction (MOR) schemes [12] could not be adopted, since they only hold fo
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