Multi-scale wave propagation modelling for two-dimensional periodic textile composites

In this article, a method for wave propagation analysis of textile composites at a mesoscopic level is presented for the first time in the vibro-acoustic and ultrasonic frequency range. The method combines a reduction method, allowing for computational cost saving, and the Wave Finite Element Method (WFEM), associating the Periodic Structure Theory (PST) and standard Finite Element Method (FEM). The PST allows to model only a unit cell of a periodic structure for analyzing the wave propagation properties of the entire structure. A comparison of standard vibrational analysis of textile composite structures, using homogenized properties, is compared with the presented method. It is shown for different types of weaves that using the standard method results in errors in the dispersion curves.

This paper addresses the question of damage detection of cylindrical structures using finite element and periodic structure theory. The structure is modeled considering two waveguides connected through a coupling element, simulated as the defect. Wave characteristics in the waveguides are evaluated using a Wave Finite Element method (W.F.E.M) based on the analysis of the anomalies which affect the elastic wave travelling in the structure. Reflection and transmission coefficients of the wave modes which are incident to the coupling element are provided by a diffusion matrix. Then forced response of the pipe with and without transversal defect is predicted using wave decomposition. Numerical examples are given. These concern an isotropic pipe, for which dispersion curves are provided and diffusion coefficients in presence of a transversal and a longitudinal defect are predicted.

On a coupling between the Finite Element (FE) and the Wave Finite Element (WFE) method to study the effect of a local heterogeneity within a railway track

Phononic crystals can develop defects during manufacturing that alter the desired dynamic response and bandgap behavior. This frequency behavior change can enable successful defect inspection if the characteristic defect response is known. In this study, the behavior of a defective square unit cell comprising a freed and shortened leg is studied using a wave finite element method and an approximate continuous-lumped model to elucidate the defect induced qualitative dynamical features. These metrics are a computationally inexpensive alternative to modeling a defective unit cell within a large pristine array entirely in finite elements. The accuracy of these models is validated by comparing the result to a full finite element model. The impact of a shortened unit cell leg on the behaviors of an infinite array of defective cells and a finite array with a single defect are successfully predicted through dispersion curves and frequency response functions, respectively. These methods reveal defect-induced modes that split the local resonance bandgap of the pristine cell, as well as new anti-resonances resulting from the shortened leg. The study uses both approaches to evaluate the effect of defects in complex phononic crystal geometries and provides a comparative evaluation of the results of each model.

Vibration based methods are commonly deployed to detect structural damage using sensors placed remotely from potential damage sites. Whilst many such techniques are modal based there are advantages to adopting a wave approach, in which case it is essential to characterise wave propagation in the structure. The Wave Finite Element method (WFE) is an efficient approach to predicting the response of a composite waveguide using a conventional FE model of a just a short segment. The method has previously been applied to different structures such as laminated plates, thinwalled structures and fluid-filled pipes. In this paper, the WFE method is applied to a steel reinforced concrete beam. Dispersion curves and wave mode shapes are first presented from free wave solutions, and these are found to be insensitive to loss of thickness in a single reinforcing bar. A reinforced beam with localised damage is then considered by coupling an FE model of a short damaged segment into the WFE model of the undamaged beam. The fundamental bending, torsion and axial waves are unaffected by the damage but some higher order waves of the cross section are significantly reflected close to their cut-on frequencies. The potential of this approach for detecting corrosion and delamination in reinforced concrete beams will be investigated in future work.

A flexible numerical approach for non-destructive ultrasonic testing based on a time-domain spectral-element method: Ultrasonic modeling of Lamb waves in immersed defective structures and of bulk waves in damaged anisotropic materials

As an important part of long-range nondestructive testing and structural health monitoring technology, ultrasonic guided wave technology has been used in a wide range of applications in aerospace, petrochemical, transportation, and other fields. This paper extends the previously developed wave finite element method by introducing the prestressing effect in Murnaghan hyperelastic materials and solving the dispersion curves of prestressed waveguide structures. Furthermore, this paper proposes a mode-tracking algorithm based on image sequential alignment that can achieve the multi-mode classification of guided wave dispersion curves and compare the changes in propagation characteristics of different guided wave modes. The results reveal that the change in guided wave phase velocity produced by prestressing is related to the applied stress, frequency-thickness product, and propagation direction and that the susceptibility of different guided wave modes to prestress varies. Finally, the model approach is validated by comparing its predictions to theoretical results from the literature, which match remarkably well. This study is an important guideline for the preferential selection of environmentally insensitive guided wave modes and excitation frequencies, correction of detection signals, and accurate assessment of engineering structure damage information in ultrasonic guided wave technology engineering applications.

Wave Characteristics Analysis of Three-Dimensional Braided Composite Structures Based on Wave Finite Element Method

Propagation of Rayleigh-Lamb waves in multilayered plates through a multiscale structural model

The aim of this study was to evaluate the effect of manufacturing induced in-plane tow misalignment and out-of-plane tow crimp on the mechanical properties of a heavy-tow unidirectional non-crimp fabric (UD-NCF) composite. The elastic constants and failure onset (strength) are predicted by employing a multiscale computational approach. Micro-scale finite element (FE) models that explicitly represent the fibers and matrix within the tow microstructure were used to predict the effective properties of the tow. Meso-scale FE models comprised of the homogenized tows and surrounding matrix were used to predict the properties of a UD NCF composite lamina. Four meso-scale models, identified as ideal, crimp, misalignment and real, were considered in this study. No manufacturing defects were represented in the ideal model, while out-of-plane crimp, in-plane misalignment and both out-of-plane crimp and in-plane misalignment were accounted for in the crimp model, misalignment model and real model, respectively. Predicted lamina stiffness based on the real model are found to be in an excellent agreement with available experimental data, which was not always the case for the other three models. The longitudinal and transverse strength predictions are found to be dependent on the chosen local failure criteria for each model. Max-stress and Puck’s fiber failure criteria provide an excellent estimate of longitudinal strength while the Puck’s inter-fiber failure and Tsai-Hill criteria predict transverse strength with good accuracy. The feasibility to accurately predict the mechanical properties of heavy tow non-crimp fabric composites by incorporating their inherent micro-structural defects is demonstrated in this study.

The wave propagation in sandwich plate rows with cellular core is analyzed and controlled. Honeycomb core materials of different geometry placed periodically along the structure introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands (stop bands). The location and the extension of the stop bands can be optimized by proper selection of the geometrical and physical properties of the core. An optimal configuration of the core can be identified to design passive sandwich structures, which are stable and quiet over desired frequency bands. A theoretical model is developed to describe the wave propagation characteristics and the vibrations of a three-layered sandwich plate simply supported along its longitudinal edges. The core properties of the plate change periodically along the plate length. The wave propagation characteristics are estimated by analyzing the transfer matrix of each cell of the resulting periodic structure. The transfer matrix is also properly recast to obtain the cell's dynamic stiffness matrix and to formulate a spectral finite element model for the periodic sandwich plate. The spectral finite element model allows predicting the dynamic behavior of the structure with a significantly reduced number of elements as compared to conventional finite elements. The numerical model is used to predict the dynamic response of the considered class of plates and to study their propagation and attenuation characteristics for various core configurations. The presented numerical results demonstrate the simplicity and the effectiveness of the proposed treatment, which reduces the transmission of waves and the plate vibrations over specified frequency bands without the need of additional passive or active control devices. Such unique characteristics can be employed to design lightweight composite panels behaving as mechanical filters. The filtering capabilities of such passive composite panels can be properly modified and optimized to fit required transmissibility levels over desired frequencies without compromising the size and the weight of the structure.

: The principal goal of this research is to advance the technology of structural health management (SHM) for composite structures. Wave propagation based methods have shown promise for SHM of composite structures. The spectral finite elements (SFE) method is highly suitable for wave propagation analysis due to its frequency domain approach which yields models that are many orders smaller than conventional FEM. Wavelet spectral finite element (WSFE) method overcomes the wrap around problem to accurately model 2-D plate structures of finite dimensions. The specific accomplishments of the research are: developed WSFE model for damaged composite plate with transverse crack; validated WSFE modeling of Lamb wave propagation in healthy composite plates through experimental measurements; implemented baseline-free Damage Force Indicator method for delamination detection using dynamic stiffness matrix from WSFE model of healthy plate; developed Modified Time Reversal method for Lamb wave based baseline-free damage diagnostics; and investigated effect of tone burst center frequency on instantaneous phase based delamination detection.

The ‘finite element’ technique is used to investigate numerically the guiding of elastic surface waves by ridges with a view to application in microwave electronics and in seismology. The technique is applied first to other problems with a cylindrical geometry such as the propagation of waves along bars and plates where existing theoretical and experimental results are available for comparison. Finally ridged structures are considered. Dispersion curves and displacement functions are obtained for the lowest mode which is the only one which may, under suitable circumstances, propagate unattenuated. Our results indicate that only the lowest antisymmetric mode is properly trapped by the ridge and that this occurs in a certain frequency range.

Model order reduction (MOR) techniques have been used in structural dynamics for over sixty years as a quick and effective way to examine the dynamic behavior of complex finite element (FE) models. Various macroscopic phenomena arise from the physics and mechanics of the underlying microstructure, and MOR approaches can be employed in conjunction with the multiscale computational homogenization approach, which is deriving local macroscopic constitutive responses from underlying microstructure; to predict the dynamic behavior of heterogeneous macrostructures. The accuracy and efficiency of the most representative approaches from dynamic condensation, component mode synthesis (CMS), and general model reduction (GMR) methods are compared in this paper. The techniques considered are Guyan and the improved reduced system (IRS) from classical dynamic condensation, Craig-Bampton (CB) and enhanced Craig-Bampton (ECB) from CMS, IRS-based substructuring, GMR, and GMRPlus. All the substructuring methods employ primal assembly at the boundary interface of the substructures. The accuracy and computing efficiency of the techniques are compared in-depth using real-world engineering problems, and the effect of the number of substructures on the accuracy and computational cost is also examined.

Understanding the effects of ground-borne vibration on buildings is becoming increasingly important as pressure grows to construct high-quality buildings on existing urban sites, which are often close to busy roads or railways. The motivation behind the work presented here is the development of a computational model that enables engineers to evaluate the effectiveness of isolating buildings. This paper presents one component of such a model, namely a new three-dimensional model for modelling the propagation of ground-borne vibration through a piled foundation. A row of piles is considered, with the piles modelled using the solutions for an elastic bar and Euler beam, and the soil represented by an elastic half-space. The model is comprehensive in that it accounts for the longitudinal and transverse motion of the piles due to both external pile-head loads and interaction between neighbouring piles through wave propagation in the surrounding soil. Computational efficiency is achieved by assuming that the row comprises an infinite number of identical piles and using a combination of the boundary element method and periodic structure theory.