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Communication Dans Un Congrès Année : 2023

Optimizing the bandgap region of a meta-beam with bistable resonators

Résumé

Mechanical vibrations can damage the structure’s health, typically leading to failure. Several researchers have been dedicated to developing mechanisms to avoid undesired structure vibrations. Recently, metamaterials applications showed efficiency at forbidding elastic wave propagations in a frequency band in the whole body of interest. This specific frequency domain is known as the bandgap region. A low-frequency bandgap can be obtained by tuning the resonance of resonators because of the local resonance mechanism [1]. In this context, this work studies the suppression of flexural wave propagation in a meta-beam. The system consists of a cantilever beam with nonlinear resonators uniformly spread across its body. The cantilever beam is modeled by the Euler-Bernoulli equation, and the resonators are attached using discrete mass with a bistable potential as proposed by [2]. Bandgap region is defined using the modal analysis by sweeping sine from transmissibility concerning the fixed and end node of the beam. This work aims to optimize the resonators’ nonlinear stiffness to widen the bandgap region. For this purpose, the cross-entropy (CE) method, a metaheuristic for non-convex optimization, is employed. The CE method transforms the optimization problem into an equivalent rare event estimation problem, being a global search algorithm, robust and simple [3]. The stochastic model response is approximated by a polynomial chaos expansion (PCE) surrogate model to reduce the computational cost. We identified a pattern of different stiffness values that can broaden the length of the bandgap. The presence of a nonlinearity feature can decrease the resonance peaks close to the bandgap. However, the bistability did not carry any advantage inside the bandgap region for the range values studied. References: 1. Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, P. Sheng, Science 289, 1734-1736, 2000. 2. Y. Xia, M. Ruzzene, A. Erturk, Nonlinear Dynamics 102, 1285-1296, 2020. 3. A. Cunha Jr, Nonlinear Dynamics 103, 137-155, 2021.
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Dates et versions

hal-04110738 , version 1 (30-05-2023)

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  • HAL Id : hal-04110738 , version 1

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João Pedro Norenberg, Americo Cunha Jr. Optimizing the bandgap region of a meta-beam with bistable resonators. Fifth Conference on Structural Nonlinear Dynamics and Diagnosis (CSNDD 2023), May 2023, Marrachech, Morocco. ⟨hal-04110738⟩

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