Multiresolution finite wavelet domain method for efficient modeling of guided waves in composite beams

Dimitriou, Dimitris K.; Nastos, Christos V.; Saravanos, Dimitris A.

doi:10.1016/j.wavemoti.2022.102958

Cited by 7 publications

(5 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, if the same procedure was performed using any single-resolution method such as the FE, and then perform wavelet decomposition to the results in order to get the respective "coarse" and "fine" solutions, the following issues would rise: i) those models are much slower than the MR-FWD simulations, as indicated in [15], [16].…”

Section: Optimization Process and Resultsmentioning

confidence: 99%

“…The MR-FWD method utilizes both the scaling and wavelet functions of the Daubechies wavelet family as basis functions, forming a hierarchical approach that involves two types of solution components: the coarse and the fine components. The method has evinced remarkable computational benefits in transient dynamic simulations of rods [14], Timoshenko beams [15] and high-order layerwise strips [16]. On top of the computation efficiency of the method, additional benefits have been manifested due to the sensitivity and localization properties of the utilized Daubechies wavelets [17].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Guided Wave Based Damage Identification in Composite Strips Using Inverse Multiresolution Wavelet Methods

Dimitriou,

Saravanos

2023

10th ECCOMAS Thematic Conference on Smart Structures and Materials

View full text Add to dashboard Cite

An inverse procedure for damage identification based on guided waves using the multiresolution finite wavelet domain method is presented. The forenamed method utilizes Daubechies wavelet and scaling functions for the approximation of state variables and as such, it involves two types of solutions, the coarse and the fine solutions. In that way, the multiresolution nature of the method can be utilized for efficient damage estimation in experimental applications since the fine solutions of the method have manifested remarkable localization capabilities and high sensitivity to damage. In order to fully take advantage of the additional functionalities of the multiresolution method, full-field displacement measurements of the guided wave propagation phenomenon are employed. Wavelet decomposition using Daubechies wavelets is now applied on the measurements in each different time step. The decomposition will lead to an approximation and a detail component that are directly comparable to the coarse and fine solution of the multiresolution simulation, respectively. Therefore, several multiresolution models can be created using the same Daubechies wavelets as the decomposition of the experimental data, so as to compare the simulation results with the measured ones. Numerical results evince that comparing the detail component of the experiments with the fine solution of the simulations, and their respective wavenumber spectra, using appropriate metrics can lead to efficient damage identification. In such manner, an optimization process can be conducted, utilizing the cross-correlation of both the structural responses and their wavenumber content for the definition of the objective function, in order to characterize the investigated damaged composite strip cases. This procedure can lead to more sensitive and accurate damage estimation due to the advantages of the multiresolution analysis.

show abstract

Section: Optimization Process and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Guided Wave Based Damage Identification in Composite Strips Using Inverse Multiresolution Wavelet Methods

Dimitriou,

Saravanos

2023

10th ECCOMAS Thematic Conference on Smart Structures and Materials

View full text Add to dashboard Cite

show abstract

“…[102] Nastos and associates introduced the Daubechies WMM, applying it to composite plate dynamic analysis, [103] transient wave analysis of elastic solids, [104] and wave analysis of composite beams. [105] Dimitriou et al implemented this technique to analyze the propagation of guided waves within layerwise beam structures. [185] Meanwhile, Liu et al applied the method address 2D elastic issues.…”

Section: Other Wavelet Methodsmentioning

confidence: 99%

“…[105] Dimitriou et al implemented this technique to analyze the propagation of guided waves within layerwise beam structures. [185] Meanwhile, Liu et al applied the method address 2D elastic issues. [186] Extensive studies on wavelet-based numerical algorithms reveal that pure wavelet algorithms encounter difficulties in managing nonlinear terms and boundary conditions.…”

Section: Other Wavelet Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Application of Wavelet Methods in Computational Physics

Wang,

Liu,

Zhou

2024

Annalen der Physik

View full text Add to dashboard Cite

The quantitative study of many physical problems ultimately boils down to solving various partial differential equations (PDEs). Wavelet analysis, known as the “mathematical microscope”, has been hailed for its excellent Multiresolution Analysis (MRA) capabilities and its basis functions that possess various desirable mathematical qualities such as orthogonality, compact support, low‐pass filtering, and interpolation. These properties make wavelets a powerful tool for efficiently solving these PDEs. Over the past 30 years, numerical methods such as wavelet Galerkin methods, wavelet collocation methods, wavelet finite element methods, and wavelet integral collocation methods have been proposed and successfully applied in the quantitative analysis of various physical problems. This article will start from the fundamental theory of wavelet MRA and provide a brief summary of the advantages and limitations of various numerical methods based on wavelet bases. The objective of this article is to assist researchers in choosing the appropriate numerical methodologies for their particular physical issues. Furthermore, it will explore prospective advancements in wavelet‐based techniques, offering valuable insights for researchers committed to enhancing wavelet numerical methods in the field of computational physics.

show abstract

Exploring the inherent capacity of the multiresolution finite wavelet domain method to provide convergence indicators in transient dynamic simulations

Dimitriou,

Saravanos

2024

Computers & Structures

View full text Add to dashboard Cite

Multiresolution finite wavelet domain method for efficient modeling of guided waves in composite beams

Cited by 7 publications

References 60 publications

Guided Wave Based Damage Identification in Composite Strips Using Inverse Multiresolution Wavelet Methods

Guided Wave Based Damage Identification in Composite Strips Using Inverse Multiresolution Wavelet Methods

Application of Wavelet Methods in Computational Physics

Exploring the inherent capacity of the multiresolution finite wavelet domain method to provide convergence indicators in transient dynamic simulations

Contact Info

Product

Resources

About