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In this paper, a method is presented for the numerical computation of dispersion properties and mode shapes of guided waves in plate structures. The formulation is based on the Scaled Boundary Finite Element Method. The through-thickness direction of the plate is discretized in the finite element sense, while the direction of propagation is described analytically. This leads to a standard eigenvalue problem for the calculation of wave numbers. The proposed method is not limited to homogeneous plates. Multi-layered composites as well as structures with continuously varying material parameters in the direction of thickness can be modeled without essential changes in the formulation. Higher-order elements have been employed for the finite element discretization, leading to excellent convergence for complex structures. It is shown by numerical examples that this method provides highly accurate results with a small number of nodes while avoiding numerical problems and instabilities.
In this paper the Scaled Boundary Finite Element Method (SBFEM) is applied for the simulation of Lamb waves in cracked plates. This method is highly advantageous to study the interaction of different Lamb wave modes with cracks as the crack is not discretized and no refinement is required around the crack tip. Numerical examples are presented for the reflection of the fundamental symmetric and antisymmetric modes from cracks of different depth. The spatial Fourier transformation is employed to calculate the amplitudes of reflected Lamb wave modes. The results reveal possibilities to obtain details of the crack geometry in non-destructive testing and structural health monitoring applications.
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method
(2012)
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
Lamb waves are a common tool in the field of non-destructive testing and are widely used for materialcharacterisation. Further, the increasing computational capability of modern systems enables the Simulation of complex and detailed material models. This work demonstrates the possibility of simulating an adhesive-bonded multilayer system by characterising each layer individually, and introduces an Approach for determining the dispersive behaviour of acoustic waves in a multilayer system via real measurements.
Interdigital transducers (IDTs) are a well-known tool for excitation of surface acoustic waves. The use of IDTs is versatile, but they are most commonly employed as actuators for excitation of ultrasonic guided waves (UGWs). However, they are still a relatively new technology, which leaves many possibilities for future research, especially in the scope of newly emerging structural health monitoring (SHM) systems. IDTs offer low weight, design flexibility and beam directivity, which make them ideal candidates for employment in such systems.
Due to the IDTs’ and waves’ complexity, problems often cannot be described analytically, therefore they require numerical solutions and experimental validations. In this contribution, a novel, simple use of IDTs, in the scope of SHM is described. Firstly, numerical findings acquired with finite element method are presented. To validate those results, experiments in a plate-like waveguide are carried out. A good agreement between them is found. The results show the potential of the IDTs in yet another prospective application, which could be attractive for adoption in the future.
Structural health monitoring (SHM) is a term that groups together techniques adopted to evaluate in a continued fashion the structural integrity and degradation of technical appliances. SHM is particularly attractive for components that are difficult to access or expensive to take off-line. Among many other techniques, SHM can be performed using ultrasonic guided waves (UGW) which have an advantage of traveling over Long distances. Various guided wave modes exist along with many methods for their generation and sensing, e.g by means of interdigital transducers (IDT). This contribution is dedicated to the design and characterization of a flexible piezopolymerbased IDT which allows for the selective excitation of UGW, resulting in more straightforward data analysis. The designed IDT was characterized using a 3D Laser Doppler Vibrometer (3D LDV) in the air to identify and analyze the IDT’s Vibration modes. Then the transducer was mounted on an aluminum plate, and the generated wavefield was measured with the 3D LDV.
According to this investigation, we demonstrate that it is possible to selectively excite desired guided wave mode, namely the A0 mode, suppressing the excitation of the S0 mode. Moreover, the measured wavefield allows for analysis of the directivity of the designed IDT. All in all the results show good correlation between theoretical predictions and measured values, thus allowing to use the current design in terms of selective excitation as it is.
Lamb waves are widely used for non-destructive evaluation of material parameters as well as for detection of defects. Another application of Lamb waves is quality control of adhesive joints.
Researchers are currently investigating shear horizontal and zero-group velocity modes for characterisation of the adhesive bonding strength. In a new approach, Lamb wave mode repulsion is used to obtain the coupling strength between different layers to characterise the adhesive bonding strength. The modes of the individual layers become coupled in the multilayered systems forming particular regions, the so-called mode repulsion regions. This study investigates these modes and their interaction in two-layered plate-like structures with varying coupling strength both numerically, with the Scaled Boundary FEM, and experimentally
Guided waves (GW) are of great interest for non-destructive testing (NDT) and structural health monitoring (SHM) of engineering structures such as for oil and gas pipelines, rails, aircraft components, adhesive bonds and possibly much more. Development of a technique based on GWs requires careful understanding obtained through modelling and analysis of wave propagation and mode-damage interaction due to the dispersion and multimodal character of GWs. The Scaled Boundary Finite Element Method (SBFEM) is a suitable numerical approach for this purpose allowing calculation of dispersion curves, mode shapes and GW propagation analysis. In this article, the SBFEM is used to analyse wave propagation in a plate consisting of an isotropic aluminium layer bonded as a hybrid to an anisotropic carbon fibre reinforced plastics layer. This hybrid Composite corresponds to one of those considered in a Type III composite pressure vessel used for storing gases, e.g., hydrogen in automotive and aerospace applications. The results show that most of the wave energy can be concentrated in a certain layer depending on the mode used, and by that damage present in this layer can be detected. The results obtained help to understand the wave propagation in multi-layered structures and are important for further development of NDT and SHM for Engineering structures consisting of multiple layers.
Damage Quantification in Aluminium-CFRP Composite Structures using Guided Wave Wavenumber Mapping
(2019)
The use of composite materials is associated not only with the advantages of weight reduction and improved structural performance but also with the risk of barely visible impacts or manufacturing damages. One of the promising techniques for the detection and characterisation of such damages is based on ultrasonic guided wave propagation and analysis. However, the multimodal nature and dispersive behaviour of these waves make their analysis difficult. Various signal processing techniques have been proposed for easier interpretation of guided wave signals and extraction of the necessary information about the damage. One of them is the wavenumber mapping which consists of creating a cartography of the wavenumber of a propagating mode over an inspected area, using a dense wavefield acquisition measured for example with a scanning laser Doppler vibrometer. This technique allows both the quantification of the in-plane size and the depth of damage, for example, impact-induced delamination in composite laminates.
In this contribution, wavenumber mapping is applied to a delaminated aluminium-CFRP composite structure which corresponds to composite-overwrapped pressure vessels used for storing gases in aerospace and automotive industries. The analysis of experimental data obtained from measurements of guided waves propagating in an aluminium-CFRP composite plate with impact-induced damage is performed. The output of the imaging is a three-dimensional representation of the delamination induced by the impact. Good agreement between conventional ultrasonic testing and guided wave damage mapping can be found.
The dispersive properties of Lamb waves can be utilised for material characterisation because the frequency-wavenumber-relationship, as well as the group velocity, depend on material parameters. These dependencies make a non-destructive estimation of an elastic constant possible. This preliminary study investigates the sensitivity of dispersion curves caused by a change in elastic constants. The Scaled Boundary Finite Element Method is used to compute special dispersion curves, which show the sensitivity value of the frequency and group velocity as a colour value. This representation allows for easy identification of patterns and local effects. Two sets of dispersion curves are presented, one set for a steel plate and the other set for a plate made of a carbon fibre reinforced polymer. In general, we notice that the sensitivity often increases with the frequency and that higher-order modes seem to be more suitable for material characterisation. Moreover, specific modes respond to material changes while others are relatively unaffected, which must be taken into consideration for material characterisation.