Periodic structures provide filtering behavior for vibrations, as a result of the repetition in space of unit blocks, or unit cells. In general, they are characterized by an internal mechanical impedance mismatch, so that waves are reflected and transmitted every time a discontinuity is present. The global behavior given by waves superposition is their cancellation, only for specific frequency ranges, generally called stop-bands or band-gaps. The variation of non-dimensional parameters shows how these attenuation regions move in the frequency domain: the correspondent diagrams are the main tools for the design problem and are known as band-maps. The selection of the geometrical, physical and elastic properties of the unit cell is therefore dependent on the designer experience and nothing can be said about the optimality of the proposed solution. Numerical methods are used for the selection of the best cell geometry, in order to get optimal attenuation. Generally, this is a time consuming approach. In this paper, an new method is presented, based on how the waves are reflected and transmitted at cells interface. Both beam and rod case studies are investigated. The algorithm allows matching between band-gap central frequency and the desired value, while the designed attenuation is optimal there, under certain physical and geometrical constraints. Moreover, the design of the bandgap location has been decoupled from the design of the magnitude of attenuation. This approach is purely analytic, therefore the computational efforts required are minimum. In order to validate the analytical model, a passive periodic beam has been manufactured. Its real frequency response is therefore compared to the expected one.
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ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
September 18–20, 2017
Snowbird, Utah, USA
Conference Sponsors:
- Aerospace Division
ISBN:
978-0-7918-5826-4
PROCEEDINGS PAPER
An Optimal Method for Periodic Structures Design
Emanuele Riva,
Emanuele Riva
Politecnico di Milano, Milano, Italy
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Gabriele Cazzulani,
Gabriele Cazzulani
Politecnico di Milano, Milano, Italy
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Edoardo Belloni,
Edoardo Belloni
Politecnico di Milano, Milano, Italy
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Francesco Braghin
Francesco Braghin
Politecnico di Milano, Milano, Italy
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Emanuele Riva
Politecnico di Milano, Milano, Italy
Gabriele Cazzulani
Politecnico di Milano, Milano, Italy
Edoardo Belloni
Politecnico di Milano, Milano, Italy
Francesco Braghin
Politecnico di Milano, Milano, Italy
Paper No:
SMASIS2017-3837, V002T03A021; 8 pages
Published Online:
November 9, 2017
Citation
Riva, E, Cazzulani, G, Belloni, E, & Braghin, F. "An Optimal Method for Periodic Structures Design." Proceedings of the ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 2: Modeling, Simulation and Control of Adaptive Systems; Integrated System Design and Implementation; Structural Health Monitoring. Snowbird, Utah, USA. September 18–20, 2017. V002T03A021. ASME. https://doi.org/10.1115/SMASIS2017-3837
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