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Cui, D., Ichchou, M., Zine, A. and Atalla, N. (2024) Multi-Scale Dynamics and Nonlinear Eigenvalue Problem of Heterogeneous Metastructures Using a Wave Finite Element Scheme and Modal Strain Energy Method. In: Belhaq, M., Ed., Advances in Nonlinear Dynamics and Control of Mechanical and Physical Systems, Springer, 141-152. https://doi.org/10.1007/978-981-99-7958-5_11

has been cited by the following article:

• TITLE: Physical Investigation on Robust Algorithms for Inverse Problems of Heterogeneous Metastructures

  AUTHORS: Dongze Cui, Rafael Da Silva Raqueti, Najib Fazail, Da Chen

  KEYWORDS: Heterogeneous Metastructures, Wave Propagation, Inverse Wavespace Identification Frameworks, Green’s Function Correlation (GFC), Algebraic Wavenumber Identification (AWI), Damping Loss Factor (DLF)

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.8, August 29, 2025

  ABSTRACT: A typical inverse problem, identifying the wavespace for metastructures from measurements of displacement fields, is crucial to understanding the dynamic properties of metastructures and the optimal design of vibroacoustic performance. The validity examination of inverse methods for heterogeneous metastructures is still an open question, especially for those showing wave coupling effects. The present study examines the robustness and accuracy of different inverse methods for extracting the complex wavespace. We compare the nonlinear Inhomogeneous Wave Correlation (IWC) method and its extension, the Green’s Function Correlation (GFC) framework, with the linear Algebraic Wavenumber Identification (AWI) framework. Direct wave-based methodologies are employed to assess both the precision of these techniques and the influence of wave coupling on the inverse methods’ robustness. The study starts by evaluating the precision of all methods through Highly Contrasted Dissipative Structures (HCDS) with rheological viscoelastic material. Then, the limitation of GFC due to the assumption of the elastic formulation is demonstrated by the sandwich plate with thick soft cores.