Wave Propagation In Composite Structures Research Articles

Efficient layerwise multiphysics spectral element model for delaminated composite strips with PWAS transducers

Efficient structural element-based models are essential for fast simulations of wave propagation in composite structures for model-based and physics-informed data-driven structural health monitoring. This article introduces the first efficient multiphysics time-domain spectral structural element for wave propagation analysis of beam and panel-type composite structures with piezoelectric transducers (patch or full layers) containing delaminations. A general framework is presented to model multiple delaminations and transducer patches located arbitrarily. The intact host and patch transducer-bonded laminates and sub-laminates between delaminations are modelled separately using an electromechanically coupled efficient layerwise zigzag theory (ZIGT) for kinematics and a piecewise quadratic variation for the electric potential across piezoelectric layers. The high-order spectral element (SE) features a virtual electric node to model equipotential surfaces of piezoelectric transducers apart from the usual physical nodes having mechanical and internal electric degrees of freedom. A hybrid point-least squares continuity approach is employed to maintain continuity at the intersections of delaminated sub-laminates or the patch-bonded laminate with the host laminate. The model’s performance in capturing electroelastic waves’ interaction with delamination is examined with reference to the conventional finite element (FE) solution based on the ZIGT, continuum-based FE solutions, and the SE solution based on a non-layerwise version of the laminate theory. Finally, the model is used to examine the impact of interfacial location and size of delaminations on wave propagation behaviour.

Impact Identification Method for Structural Health Monitoring of Stiffened Composite Panels using Passive Sensing Systems

Identification of impact and its resulting damage is a complex inverse inferential procedure. Estimating the magnitude of an impact from sensor data is challenging and still needs to be fully understood. Furthermore, only a few studies have solved practical impact identification problems relevant to real-world structures with different geometries and structural inhomogeneities (e.g. variable thicknesses and stiffeners). Accordingly, the current research presents an impact categorisation analysis using passive measurements from piezoelectric (PZT) sensors for a geometrically complex composite aircraft part. Intermediate-mass impact tests were performed on a stiffened thermoplastic composite plate to generate signals representing various impact scenarios that may occur during the lifetime of an aircraft. The impacts were applied at critical locations, including the mid-bay, on top of the stringer, and at different thicknesses. This study investigated the effect of structural features on wave propagation in composite structures. The experimental results demonstrate that these features significantly change the wave field and, consequently, affect sensor readings. To differentiate between pristine and damaged states, an impact signal categorisation approach was employed. This analysis shows that a passive sensing system can categorise the impact using the transmitted energy from a time-domain signal. However, the spectral energy values showed low efficiency in categorising impacts. Overall, the results highlight the importance of considering structural features when deploying sensor systems for structural health monitoring and provide valuable insights into the effectiveness of impact identification and damage detection in realistic composite structures.

Influence of Initial Stress on Love Wave Propagation in Composite Structures

Influence of Initial Stress on Love Wave Propagation in Composite Structures

Analysis of Elastic Pulse Dispersion in Periodically Layered Composite Rods using Wave Finite Element Method

Numerical analysis of wave propagation in composite structures needs large-scale computation which is not feasible in practice. This paper investigates the possibility of applying a wave finite element method (WFEM) to composite structure. The key feature of the WFEM is its capability of accurately analyzing the discontinuities in stress wavefront along with the discontinuities in velocities and strains. In addition, the numerical analysis of the WFEM is unconditionally stable and reduces numerical computation. This paper studies a periodically layered composite rod to analyze the dispersion and propagation of stress waves using the WFEM. The numerical results are compared with other numerical/analytical solutions, paying attention to the accuracy of computing the strong discontinuities in the stress wavefront as well as the dispersion of pulses in a heterogeneous elastic rod. It is shown that the WFEM can be used as an affordable tool for numerically solving wave propagation in composite structures.

Data-driven model identification of guided wave propagation in composite structures

This paper shows the applicability of data-driven model identification to describe guided wave propagation in composite structures. The model identified can be useful to predict waveform or further conditions considering the dynamics of wave propagation in composites media, mainly when the geometry or boundary conditions are complex and make it very difficult to propose an analytical model. Thus, the main purpose of this paper is to use a simple autoregressive with exogenous terms model to fit the experimental data assuming different frequencies of excitation and the effect of temperature changes. An example using a composite plate is performed in this paper to show the steps and applicability. After these analyses, the results obtained demonstrate the practical benefits of the black-box model for modeling of guided wave propagation in complex composite structures for aeronautical applications.

Dispersion of polarized shear waves in viscous liquid over a porous piezoelectric substrate

This article aims to study the propagation of polarized shear horizontal waves in viscous liquid layer resting over a porous piezoelectric half-space. An analytical solution is proposed using the separation of variables method. The dispersion relation is obtained using the proper boundary conditions for both electrically open and short cases in determinant form. The numerical example and graphical representation are provided in support of the findings. Dynamic response of affecting parameters (e.g. layer’s width, mass density, piezoelectric constant, dielectric constant, viscous coefficient, and dielectric coupling between the two phases of the porous aggregate) has been presented through graphs. It is observed that the phase velocity of considered wave remarkably affected by these parameters. Moreover, obtained result is matched with the existing result. Findings may contribute significantly toward optimization of surface acoustic wave devices and other liquid sensors. Moreover, this study may be utilized to frame a theoretical model for the problems of shear horizontal wave propagation in composite structures, involving piezoelectric medium.

A constitutive model for the analysis of second harmonic Lamb waves in unidirectional composites

In recent research on Structural Health Monitoring (SHM) guided waves, especially nonlinear Lamb waves, turned out to be a suitable means for monitoring material deterioration in thin-walled structures. In the corresponding numerical simulations on wave propagation the nonlinear elastic theory by Murnaghan is often implemented, which requires 14 material parameters for transversely isotropic materials. Enhancing an existing linear strain energy potential, a new nonlinear hyperelastic transversely isotropic material model is introduced which reduces the number of independent material parameters to six. In order to verify the applicability of the presented material model with respect to the simulation of nonlinear wave propagation in composite structures, and the generation of higher harmonic wave modes, the existence of a power flux from the fundamental to the higher harmonic mode is investigated analytically and numerically. Analytical considerations show that this power flux exists like in Murnaghan’s theory. For the numerical validation the S0–S0 mode pair in the low frequency range is used. Therefore, the amplitude of the second harmonic wave mode is oscillating with increasing propagation distance. This behavior is in excellent agreement with the theoretical prediction. It is shown further, that even for an oscillating behavior the amplitude of the second harmonic mode can be approximated by a linear curve fit over a considerably propagation distance and hence shows a quasi cumulative behavior. Therefore, the introduced material model is an advantageous alternative to Murnaghan’s theory to simulate the second harmonic Lamb wave generation due to in composite structures.

Unified nonlocal rational continuum models developed from discrete atomistic equations

In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type of enrichment can be useful in a wide range of mechanical problems such as localization of strain and damage in many quasibrittle structures, size effects in microscale elastoplasticity, and multiscale modeling of materials. A novel technique of transforming a discrete differential expression into an exact equivalent rational continuum derivative form is developed considering the Taylor’s series transformation of the continuous field variables and traveling wave type of solutions for both the discrete and continuum field variables. An exact equivalent continuum rod representation of the 1D harmonic lattice with the non-nearest neighbor interactions is developed considering the lattice details. Using similar enrichment technique in the variational framework, other useful higher-order equations, namely nonlocal rational Mindlin–Herrmann rod and nonlocal rational Timoshenko beam equations, are developed to explore their nonlocal properties in general. Some analytical and numerical studies on the high frequency dynamic behavior of these novel nonlocal rational continuum models are presented with their comparison with the atomistic solutions for the respective physical systems. These enriched rational continuum equations have crucial use in studying high-frequency dynamics of many nano-electro-mechanical sensors and devices, dynamics of phononic metamaterials, and wave propagation in composite structures. These new models can help to circumvent the biggest problem regarding size and time restrictions in many atomistic simulations.

Simplified Modeling of Impact Damage for Numerical Simulation of Lamb Wave Propagation in Composite Structures

Simplified Modeling of Impact Damage for Numerical Simulation of Lamb Wave Propagation in Composite Structures

Simulation of Lamb Wave Propagation in Composite Structures Based on the Finite Element Stacked Shell Method

Monitoring of structural integrity of a component is very important, especially for the damage sensitive laminated composite structures. Among the Structural Health Monitoring (SHM) techniques, the Acousto-Ultrasonic (AU) technology is very promising. However, the accurate simulation of Lamb wave propagation is a very demanding task, in terms of computational cost. In the present study, in the frame of Finite Element method, the stacked-shell methodology is proposed for the simulation of Lamb wave propagation in composite laminated panels. The results of the stacked-shell approach are initially evaluated with respect to experimental results; the method is subsequently applied to undamaged and damaged composite laminated panels, in order to assess its efficiency and accuracy in the simulation of Lamb wave-based damage detection techniques.

Guided waves in a stiffened composite laminate with a delamination

The integrity of safety-critical structural composites can be enhanced by the use of innovative ultrasonic nondestructive evaluation techniques. Among the various existing techniques, guided wave methods provide a good promise in terms of sensitivity to a variety of damage types or defects and the extent of the area that can be monitored, given the ability of these waves to travel relatively long distances within the structure under investigation. In comparison with isotropic metallic structures, wave propagation in composite structures presents additional complexity for effective damage identification. The material inhomogeneity, anisotropy, and the multilayered construction of composite materials lead to significant dependence of wave modes on laminate layup configurations, direction of propagation, frequency, and interface conditions. In this article, a specific structure will be analyzed with different levels of complexities in an effort to determine the propagation characteristics of the waves. The investigated structure is a stiffened composite plate of finite thickness and infinite lateral dimensions. The work is carried out using theoretical analysis, numerical modeling, and laboratory experiments. Numerical (finite element) simulations are used for more realistic models, where the geometric and material complexities present practical difficulties in direct analysis using theoretical constructs only.

Modeling of piezo-induced ultrasonic wave propagation in composite structures using layered solid spectral element

This article presents the development of a three-dimensional spectral element-based Piezo-Enabled Spectral Element Analysis code to simulate piezo-induced ultrasonic wave propagation in composite structures. Piezo-Enabled Spectral Element Analysis solves the coupled electromechanical governing equations for a given arbitrary voltage input to a piezoelectric actuator and outputs the voltage response of the piezoelectric sensors. In case of modeling laminated composites, one element per ply is computationally expensive, and smeared material properties may give inaccurate results; hence, a layered solid spectral element is introduced. Layered solid spectral element can model several plies per element and uses combined nodal quadrature and Simpson’s 1/3 integration rule for numerical integration of mechanical stiffness matrix. It is worth noting that Piezo-Enabled Spectral Element Analysis can interface with commercial finite element mesh generators such as Abaqus/CAE to model structures with complex configuration. Delaminations and debonds are modeled by separating the nodes in the damaged area to create a volume split. Experiments and simulations have been carried out to verify and validate Piezo-Enabled Spectral Element Analysis for composites. This article also presents simulations of ultrasonic wave propagation in a stiffened composite plate with delamination and debond.

Multimodal wave propagation in smart composite structures with shunted piezoelectric patches

Wave propagation in composite structures with shunted piezoelectric patches is investigated in this study. The wave finite element approach is first developed as a prediction tool for wave propagation characteristics such as dispersion curves in composite structures, and subsequently extended to consider shunted piezoelectric elements through the diffusion matrix model. A three-layered composite beam equipped with a pair of resistor–inductor shunted piezoelectric patches is modeled and analyzed carefully with these numerical techniques. Reflection and transmission coefficients of propagating waves in this smart composite structure are calculated, and the performance of shunted piezoelectric patches on the control of wave propagation is investigated numerically with the diffusion matrix model. Another finite element formulation, named modified wave finite element method, which is dedicated to the analysis of wave propagation in multilayered composite structures, is proposed and developed for considering piezoelectric elements in the structures. It is a dynamic substructuring technique that allows the dynamics of a typical layer cross section to be projected on a reduced local wave mode basis with appropriate dimensions. Results issued from this method are compared to those issued from the classical wave finite element and diffusion matrix model formulations to demonstrate the pertinence of the modelings.

Erratum to: Local interaction simulation approach for modeling wave propagation in composite structures

Erratum to: Local interaction simulation approach for modeling wave propagation in composite structures

Local interaction simulation approach for modeling wave propagation in composite structures

This paper presents a local interaction simulation approach (LISA) numerical method to analyze the guided wave propagation in composite structures. The method is based on recursive iterative equations, derived from the elastodynamic equilibrium equations. Derivation of the iterative equations is presented for a generalized orthotropic medium in a non-principal axis frame with non-uniform spatial discretizations. The new iterative equations have the capability to model generic laminated composite plates. The results show the validation of the numerical simulations through comparisons with experimental studies of laminated composite plates.

Wave propagation in composite structures

Dynamic behaviour of honeycomb-core composite structures forms the framework of this article. The wave numbers of propagative waves are the elements of comparison between a numerical method (wave finite-element method) and an experimental identification technique (inhomogeneous wave correlation). The numerical method is based on the description of the dynamics of periodic waveguides. The experimental technique uses a matching criterion with the measured displacement field to obtain the corresponding wave numbers for a wave-based description of the displacement. Both approaches are applied to a sandwich composite beam with a honeycomb core. They seem to be in quite good accordance with analytical results for the flexural wave number.

A pre-stack migration method for damage identification in composite structures

In this paper a damage imaging technique using pre-stack migration is developed using Lamb (guided) wave propagation in composite structures for imaging multi damages by both numerical simulations and experimental studies. In particular, the paper focuses on the experimental study using a finite number of sensors for future practical applications. A composite laminate with a surface-mounted linear piezoelectric ceramic (PZT) disk array is illustrated as an example. Two types of damages, one straight-crack damage and two simulated circular-shaped delamination damage, have been studied. First, Mindlin plate theory is used to model Lamb waves propagating in laminates. The group velocities of flexural waves in the composite laminate are also derived from dispersion relations and validated by experiments. Then the pre-stack migration technique is performed by using a two-dimensional explicit finite difference algorithm to back-propagate the scattered energy to the damages and damages are imaged together with the excitation-time imaging conditions. Stacking these images together deduces the resulting image of damages. Both simulations and experimental results show that the pre-stack migration method is a promising method for damage identification in composite structures.

A spectrally formulated plate element for wave propagation analysis in anisotropic material

A new spectrally formulated plate element is developed to study wave propagation in composite structures. The element is based on the classical lamination plate theory. Recently developed method based on singular value decomposition (SVD) is used in the element formulation. Along with this, a new strategy based on the method of solving polynomial eigenvalue problem (PEP) is proposed in this paper, which significantly reduces human intervention (and thus human error), in the element formulation. The developed element has an exact dynamic stiffness matrix, as it uses the exact solution of the governing elastodynamic equation of plate in frequency–wavenumber domain as the interpolating functions. Due to this, the mass distribution is modeled exactly, and as a result, a single element captures the exact frequency response of a regular structure, and it suffices to model a plate of any dimension. Thus, the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis. The fast Fourier transform (FFT) and Fourier series are used for inversion to time–space domain. This element is used to model plate with ply drops and to capture the propagation of Lamb waves.