Wave-based structural identification for real honeycomb sandwich structures has become an important research focus. However, most existing wave-based identification methods suffers from experimental uncertainties and a limited frequency range of applicability. To this end, we present a new wave-based structural identification framework, which includes two promising material identification methods – linear and nonlinear – suitable for honeycomb sandwich structures. The advantages of the identification process are reflected on two aspects: Firstly, the Algebraic Wavenumber Identification (AWI) technique reliably extracts complex wavenumbers over a wide frequency range under stochastic conditions, serving as input for the identification process. Secondly, a novel frequency-dependent, stepwise estimation strategy is proposed for honeycomb sandwich structures, greatly enhancing the precision of material parameter determination. Noteworthy, the proposed structural identifications enable the recovery of both equivalent dynamic and static mechanical properties. The experimental applications on a real beam, plate, and shell are presented. Key results show that (1) The proposed stepwise strategy reduces the relative error of wavenumbers of the tested beam to below 3.5%, improving parameter accuracy and ensuring estimation success; (2) For the tested plate, the estimated Young's modulus of skins, shear modulus of the core, and dynamic Hooke's matrix demonstrate satisfied precision; (3) It is the first to extract mechanical parameters of real curved structures using wave-based propagation parameters.

Accurate real material modeling is essential for structural dynamic analysis and design. Reliable structural parameters estimation, involving geometric and material parameters, is a key prerequisite, yet many existing methods primarily address homogenized material properties, which is inadequate for multilayer composites with complex geometrical core. To this end, this paper introduces a robust wave-based approach to structural parameter identification of individual layers, using only full-field displacement data. Specifically, the Algebraic K-Space Identification 2D technique (AKSI 2D) initially extracts wavenumber space (k-space) from measured structural responses, while surrogate optimization subsequently aligns this experimental k-space with the Wave Finite Element Method (WFEM)-derived numerical k-space to estimate structural parameters. The superiority of the proposed identification method stems from: (1) the ability of the AKSI 2D to automatically and accurately identify wavenumbers in any wave propagation direction from displacement fields on 2D grids, even in noisy environments, eliminating the need for complex filtering and specific point layouts; (2) the capacity of the WFEM in modeling wave propagation within multilayer structures with complex geometries, using unit cell-based operations within finite element software; and (3) the efficiency of the surrogate optimization in solving high-dimensional problems by finding the global minimum with high computational efficiency. To validate the accuracy of the proposed method, the structural parameters of each layer in two numerical cases, a four-layer laminated carbon fiber panel and a kelvin cell-based sandwich composite panel, are estimated. The inverted structural parameters show good agreement with the reference values, with an averaged relative error of less than 3.5%, even when a high level of white noise is added to the simulated displacement field. In addition, the structural parameters of a real parallelogram core sandwich panel is updated experimentally. These studies confirm that the proposed approach aligns with the intuitive decision-making of structural engineers for material characterization and modeling, offering adaptability for diverse structural design tasks.

A robust inverse method for the complex wavenumber space (complex k-space) extraction is essential for structural vibration and damping analysis of two-dimensional structures. Most existing methods suffer from extracting the reliable complex k-space of plates in the presence of realistic uncertainties, especially for plates with low damping properties. To this end, this paper presents a new method for extracting the dispersion and damping characteristics of two-dimensional periodic structures using only the full-field displacement fields as input. The proposed method, the Algebraic K-Space Identification 2D technique (AKSI 2D), is an extension of the Algebraic Wavenumber Identification technique to solve two-dimensional problems. The optimised formulas are developed within the algebraic identification framework, which allows the extraction of all the properties of the complex k-space in a comprehensive way. The proposed method is validated numerically and experimentally, and its performances are compared with other popular k-space identification methods under different uncertainty conditions. The test cases cover analytically solved isotropic fields to numerically solve orthotropic fields and finally experimental measurements. The different cases show promising results and demonstrate that the proposed method is a robust tool to characterise the wave propagation of two-dimensional structures under stochastic structural and constitution conditions.

The dataset presented contains the experimental structural response, in the frequency domain, of a suspended steel plate to a point force excitation. The plate is excited by a mechanical point force generated by a Brüel & kJær shaker with a white noise signal input from 3.125 Hz to 2000 Hz. The out-of-plate displacement fields on a 2D grid were measured using a Polytec PSV-400 Scanning Vibrometer. Finally, the displacement fields are acquired by a Fourier analyser connected to a sampler. The dataset provided is a useful resource for researchers to study the structural dynamic behaviour of large thin plates in the frequency domain and to validate the effectiveness of wavenumber identification methods. Its value has been illustrated in the research paper “Algebraic K-Space Identification 2D technique for the automatic extraction of complex k-space of 2D structures in presence of uncertainty” [1]. The data collection was carried out during three weeks in April 2022 at the Ecole Central de Lyon.

This paper proposes an inverse method to characterize wave and energy propagation in curved structures, addressing the challenges of accurately obtaining dispersion curves, wavenumber space, and damping loss factors caused by their complex dynamics. The proposed method, Generalized Algebraic K-Space Identification (GAKSI) technique, is developed within the algebraic identification framework, enables the extraction of complex wavenumbers of multidimensional signals from full-field measured maps for the first time. By introducing iterated integrals and multivariate Laplace transform, the method can effectively filter signal noise, enhancing the accuracy of extracted wave propagation parameters. In this paper, the proposed method is applied to isotropic open shells with different geometric parameters and a real honeycomb cylindrical shell. Extracted results are compared with those from the reference methods. An in-depth analysis compares the characterization of shells and plates under varying signal noise levels. The findings demonstrate that the proposed method achieves high precision even under noisy conditions: the relative error for the extracted wavenumber converges to around 2.5% when the signal-to-noise ratio (SNR) exceeds 5, while the relative error for the extracted damping loss factor converges to approximately 5.5% when the SNR exceeds 10. Furthermore, the observations reveal that curvature-induced bending-membrane coupling enhances the damping properties, with this effect becoming more pronounced as the wave propagation direction transitions from the axial to the circumferential direction. These findings validate the capability of proposed method to characterize dispersion and damping properties in curved structures, offering promising potential for further applications in structural analysis, such as structural optimization and design.

The full model parameters estimation of heterogeneous multilayer composites (HMC), involving geometric parameters and static-dynamic viscoelastic properties, has attracted considerable attention for both damage diagnosis and the design of new materials. However, this remains a challenge in current research due to the complexity involved in identifying special layers. To this end, we developed a robust wave-based method to estimate the structural parameters of each layer in HMCs using full-field displacement data. The method follows a two-stage inversion process. In Stage I, it estimates geometric and elastic parameters, and in Stage II, it determines damping properties. These parameters can be static, dynamic, linear, nonlinear, or mixed. The objective is to optimize the identification process by combining the multi-scale wave and energy propagation modeling and characterization numerical methodology that automatically incorporates the limited knowledge on both the used predicted Finite Element model (whatever its complexity) and experimental data (inevitably noisy). The Condensed Wave Finite Element Method with Contour Integral solver (CWFEM-CI) is proposed to model wave and energy propagation in mesoscopic predicted models by solving a nonlinear eigenvalue problem. It enables complex wavenumber extraction in arbitrary directions while reducing computational cost through model order reduction approach, Component Mode Synthesis (CMS). At the macroscopic scale, Algebraic K-Space Identification 2D (AKSI 2D) is applied to retrieve complex wavenumbers from real materials, serving as reference data for inverse optimization. By embedding iterated integrals into the mathematical foundation of the method, signal noise is effectively suppressed, thereby ensuring accurate material identification. Finally, the identification problem is formulated and solved iteratively using the surrogate optimizer, which minimizes the difference between predicted and experimental wave propagation parameters. The accuracy and effectiveness of the proposed method are validated through numerical experiments on linear elastic, nonlinear viscoelastic, and heterogeneous multilayer models, using both synthetic and real full-field data.

This paper presents a new method for extracting the dispersion characteristics of two-dimensional periodic structures. The proposed method, the Algebraic K-Space Identification 2D (AKSI 2D) technique, is developed under the algebraic identification framework, allowing the extraction of all properties of the complex k-space in a coherent manner. The proposed method is validated numerically and experimentally, and its performances are compared with other popular k-space identification methods under different uncertainty conditions. The test cases cover isotropic analytically solved fields to numerically solved orthotropic fields and finally experimental measurements.

The extraction of experimental wavenumbers through wavenumber identification methods holds a pivotal role in addressing realistic material identification. The robustness of wavenumber identification methods under practical conditions significantly influences the accuracy of estimated material properties. Thus, this study aims to propose two identification procedures, integrating two wave-based structural identification methods with the Algebraic Wavenumber Identification (AWI) technique, to precisely estimate the equivalent static and dynamic properties of honeycomb sandwich structures, respectively. The AWI method can identify reliable wavenumbers using structural response, serving as input for wave-based linear-and nonlinear-structural identification methods. Moreover, a novel frequency-dependent stepwise estimation strategy is proposed to significantly improve the estimation accuracy. This paper presents an application of the proposed identification procedures on material properties estimation of a real honeycomb sandwich beam.