Wave field produced in a composite laminate by a concentrated surface force (original) (raw)
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Journal of Applied Mechanics, 2005
This study is motivated by the need for an efficient and accurate tool to analyze the wave field produced by localized dynamic sources on the surface or the interior of isotropic plates and anisotropic composite laminates. A semi-analytical method based on the wave number integral representation of the elastodynamic field is described that reduces the overall computational effort significantly over other available methods. This method is used to calculate the guided wave field produced in a thin unidirectional graphite/epoxy composite laminate by a dynamic surface point load. The results are compared with those obtained from a finite element analysis, showing excellent agreement, except for minor differences at higher frequencies. A recently discovered feature of the calculated surface motion, namely, a spatially periodic “phase reversal” of the main pulse with propagation distance, is observed in both cases. The present work is expected to be helpful in developing impact damage mon...
NDT & E International, 2000
Stiffness and damping properties of viscoelastic materials are given by the real and imaginary components, respectively, of the material constants. A new technique is proposed to experimentally measure the real and imaginary components of anisotropic (and isotropic) viscoelastic plates. Main advantage of this technique is that material properties of thin plates can be measured where many other techniques fail. Material properties are obtained by numerically inverting the transmitted ultrasonic fields, obtained for different incident angles. Simplex inversion algorithm is applied to initial estimates of plate thickness and plate properties. By this iterative technique the values of the unknown parameters (material properties and plate thickness) are continuously modified to give better agreement between the experimental and theoretical transmitted fields. After a certain number of iterations the speed of convergence of the Simplex scheme is significantly reduced. To improve the accuracy of convergence the Newton-Raphson inversion technique is adopted at that point. By this technique material properties of different types of plates are measured. These is a glass plate (isotropic plate with no damping), a polymer plate (isotropic plate with damping), and glass fiber reinforced epoxy plates with different fiber orientations (anisotropic plates with damping). Both real and imaginary components are successfully measured for all these plates. In a relative scale the measurement error for the imaginary components is higher. Reliability of the measured material constants of fiber reinforced epoxy plates is verified by the method of invariance. All experiments are carried out in the frequency range that is appropriate for satisfying two conditions-the specimen homogeneity and the plane wave conditions. ᭧
Application of 2D elastic Rayleigh waveform inversion to ultrasonic laboratory and field data
Near Surface Geophysics, 2016
In addition to geophysical applications from the near surface to a global scale, seismic full-waveform inversion can be applied to ultrasonic data on the centimetre and decimetre scales for nondestructive testing of pavements, facades, plaster, sculptures, and load-bearing structures such as pillars or core samples from boreholes, which can consist of geo-materials and non-geomaterials. Classical non-destructive testing approaches are based on the inversion of body-wave travel times to deduce P-wave velocity models. In contrast, surface waves (especially Rayleigh waves) are well suited to quantify surficial alterations of material properties, e.g., due to weathering. Furthermore, ultrasonic measurements of test samples with known material parameters close the gap between synthetic tests or analytical solutions and field data applications to estimate the accuracy of seismic modelling and inversion codes. Due to the scale invariance of the problem, the full-waveforminversion approaches developed on the ultrasonic scale are also applicable to larger scale geophysical problems. In this paper, we demonstrate the potential of two-dimensional Rayleigh waveform inversion on the ultrasonic scale using two data examples acquired with a single-fold, low-coverage acquisition geometry. For a simple homogeneous Plexiglas block in a controlled laboratory environment, we discuss the accuracy of visco-elastic Rayleigh wave modelling, as well as the sensitivity of two-dimensional elastic full-waveform inversion with respect to small data residuals. While the inversion is restricted to the recovery of the S-wave velocity model, a passive visco-elastic modelling approach with a homogeneous average Q s-model is required in order to describe amplitude loss and dispersion of the Rayleigh wave. The applicability of this approach under field conditions is illustrated for an ultrasonic data example from the weathered sandstone facade of the Porta Nigra in Trier (Germany). In addition to a random medium resolution analysis of the full-waveforminversion result, we particularly emphasise the importance of lateral model smoothing to mitigate small-scale inversion artefacts and to avoid erroneous interpretations. The estimated two-dimensional S-wave velocity anomalies correlate well with prominent surficial weathering effects in the upper about 3 cm. ity models from Rayleigh wave data by fitting phase slownessfrequency spectra (multi-channel analysis of surface waves MASW). Bohlen et al. (2004), Kugler et al. (2007), and Wilken and Rabbel (2012) extended this approach to create 1.5D S-wave velocity models for marine Scholte wave data by using local slant stacks. The extension to the 2D surface-wave inversion using local optimisation methods is a challenging task, due to potential cycle-skipping problems in case of the strongly dispersive surface wave field in the time domain. Masoni et al. (2013, 2014a,b) and Pérez Solano, Donno, and Chauris (2014) increased the robustness of 2D surface-wave inversion by defining new cost functions in different data domains. A 2D time-domain Gauss-Newton Rayleigh-wave FWI was developed by Tran and McVay (2012) for geotechnical site charac
Advances in Radio Science, 2005
This paper presents recent advances and future challenges of the application of different linear and nonlinear inversion algorithms in acoustics, electromagnetics, and elastodynamics. The presented material can be understood as an extension of our previous work on this topic. The inversion methods considered in this presentation vary from linear schemes, like the Synthetic Aperture Radar (SAR) applied electromagnetics and the Synthetic Aperture Focussing Technique (SAFT) as its counterpart in ultrasonics, and the linearized Diffraction Tomography (DT), to nonlinear schemes, like the Contrast Source Inversion (CSI) combined with different regularization approaches. Inversion results of the above mentioned inversion schemes are presented and compared for instance for time-domain ultrasonic data from the Fraunhofer-Institute for Nondestructive Testing (IZFP, Saarbrücken, Germany). Convenient tools for nondestructive evaluation of solids can be electromagnetic and/or elastodynamic waves...
A spectrally formulated plate element for wave propagation analysis in anisotropic material
Computer Methods in Applied Mechanics and Engineering, 2005
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.
Wave propagation in inhomogeneous layered media: solution of forward and inverse problems
Acta Mechanica, 2004
Wave propagation in anisotropic inhomogeneous layered media due to high frequency impact loading is studied using a new Spectral Layer Element (SLE). The element can model functionally graded materials (FGM), where the material property variation is assumed to follow an exponential function. The element is exact for a single parameter model which describes both moduli and density variation. This novel element is formulated using the method of partial wave technique (PWT) in conjunction with linear algebraic methodology. The matrix structure of finite element (FE) formulation is retained, which substantially simplifies the modeling of a multi-layered structure. The developed SLE has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation in the frequency domain as its interpolation function. The mass distribution is modeled exactly, and, as a result, the element gives the exact frequency response of each layer. Hence, one element may be as large as one complete layer which results in a system size being very small compared to conventional FE systems. The Fast-Fourier Transform (FFT) and Fourier series are used for the inversion to the time/space domain. The formulated element is further used to study the stress distribution in multi-layered media. As a natural application, Lamb wave propagation in an inhomogeneous plate is studied and the time domain description is obtained. Further, the advantage of the spectral formulation in the solution of inverse problems, namely the force identification and system identification is investigated. Constrained nonlinear optimization technique is used for the material property identification, whereas the transfer function approach is taken for the impact force identification.
2010
The necessity of the aerospace industry to reduce the cost, but to keep good safety standards has brought to the improvement of Structural Health Monitoring (SHM) applications. The objective of a SHM system is to allow an easily an low-cost detection of damages, before critical levels. As the diffusion of composite materials poses relevant problem regarding damage tolerance and damage detectability, SHM is one of the most promising technique for the development of lighter, more efficient and more reliable structures. Guided waves are one of the most interesting instruments for damage identification, basing on in-situ actuation and acquisition and on the possibility to correlate anomalies in wave propagation with internal damage. Modeling this kind of waves with a versatile approach as the Finite Elements (FE) allows great improvements in the SHM field of research, because this approach can reduce the experimental analyses and thus the development costs of a SHM system. Since the complex nature of the guided waves, especially in composite laminates, a validation of these FE models must be provided. This is the objective of this thesis. To accomplish this task the results obtained by the FE models are compared with the ones provided by another numerical technique expressly developed to model waves in plates. Such a technique is known as Semi-Analytical Finite Element (SAFE). This comparison is only possible after a particular post-processing technique, which involve the recursive use of the Fourier transform, of the displacements measured in the FE models. Finally these data are compared with the ones obtained from an experimental analysis of three different type of laminates. Since the results of the FE, of the SAFE and of the experiments are very similar, it is demonstrated that the FE models provided are well-suited to represent wave propagation in composite plates.