Wave Propagation In Multilayered Structures Research Articles

Symmetry Aspects in the Use of Multilayered Substrates for SAW Devices.

Multilayered structures extensively studied as a novel type of substrates for surface acoustic wave (SAW) devices are characterized by an asymmetry of wave propagation: acoustic wave characteristics generally change with inversion of propagation direction or interchange of top/bottom surfaces in one of the layers, though separately each material is symmetric for such inversions. In this article, the matrix formalism known as an effective tool for theoretical and numerical investigation of acoustic wave propagation in multilayered structures is applied to explain the existence of asymmetry and analyze its relation to the symmetry and orientations of combined materials. This phenomenon is illustrated by the examples of layered structures combining LiTaO3 (LT) plate with quartz or Si, previously reported as potential substrates for SAW devices with improved performance. Asymmetry arises from anisotropy of combined materials and occurs even when one of these materials is non-piezoelectric. It was estimated numerically as a variation of SAW resonator characteristics with substrate or plate inversion and was analyzed as a function of plate or substrate orientation. In particular, it was shown that "polarity inverted" structure enabling alternative resonator performance for the same material layers can be obtained either by an interchange of top/bottom surfaces of a piezoelectric plate or by inversion of propagation direction in a substrate. Asymmetry decreases with the introduction of an isotropic layer at the plate-substrate interface.

Modeling and numerical study of the influence of imperfect interface properties on the reflectance function for anisotropic multilayered structures

The demand for the development of non-destructive techniques aiming to assess the reliability of adhesively bonded structures has greatly increased these recent years. The multilayered plates investigated can suffer from different defects, such as delaminations, inclusions and microcracks at interfacial areas. The aim of this paper is to study the effect of imperfect interfaces on the wave propagation in multilayered structures that represent the typical architecture of components present in several industrial fields. This study is based on the calculation of both the reflectance function and the guided waves dispersion curves for an anisotropic multilayer where two metallic layers are bonded together by an adhesive layer made of an epoxy resin. Comparisons were performed in order to evaluate numerically the influence of several properties of the adhesive layer on the resonance modes of the multilayer. In addition, an imperfect porous interface layer model is implemented in order to simulate different adherence qualities between the metallic layers.

Modeling and numerical study of the influence of imperfect interface properties on the reflection coefficient for isotropic multilayered structures

The microelectronics industry is expressing an increased demand for the development of non-destructive tools and methods for health control and diagnostics in multilayered structures. The purpose of these tools is to detect problems such as delaminations, inclusions and microcracks. The aim of this paper is to study the effect of imperfect interfaces on the wave propagation in multilayered structures. This type of structure represents the typical architecture of many microelectronic components. This study will be based on the calculation of the reflection coefficient and the guided waves dispersion curves. The investigated structure is an isotropic trilayer where two metallic layers are bonded together by an adhesive layer made of an epoxy resin. Comparisons were performed in order to evaluate numerically the influence of several properties of the adhesive layer on the guided waves behavior. In addition, an imperfect viscoelastic interface layer model [1] has been implemented in order to simulate different adherence qualities between the metallic layers.

Analysis of Guided Wave Propagation in a Multi-Layered Structure in View of Structural Health Monitoring

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.

Using the Finite Product Method for solving eigenvalue problems formulated in cylindrical coordinates

Analysis of free/forced wave propagation in multi-layered structures and structures under heavy fluid loading constitute classical problems of fluid-structure interaction. These waveguides and many similar ones support infinitely many waves and in some cases e.g. at high-frequency excitations or in near-field analysis it is necessary to account for a large number of them. Finding the dispersion curves from these transcendental dispersion relations is not a trivial task due to their ill-conditioned/unstable nature as well as numerical algorithms ability to solve transcendental equations. These issues can, however, be circumvented by using the Finite Product Method (FPM). The FPM is generic and has been used to solve dispersion equations of homogeneous waveguides derived in Cartesian coordinates with sine/cosine functions. However, it is yet to be formulated in cylindrical coordinates when Bessel functions are involved in dispersion equations. We focus in this paper on extending the method to the cylindrical problems and compound waveguides illustrated here by a fluid-filled cylindrical shell. The great advantage of the FPM is that it reduces the transcendental dispersion equation to a polynomial one easily solved by numerical algorithms but more importantly it delivers only authentic roots of the dispersion equation i.e. no spurious roots as often encountered when using Taylor approximations etc.

Multilayered structures using thin plates of LiTaO3 for acoustic wave resonators with high quality factor

Multilayered substrates, including thin plates of LiTaO3 (LT) bonded to silicon (Si) or glass wafers either directly or via intermediate layers, were numerically investigated as potential materials for surface acoustic wave (SAW) resonators with high quality (Q)-factor required for the next generation of mobile communication systems. The propagation velocities and electromechanical coupling coefficients of shear horizontally (SH) polarized acoustic waves were estimated as functions of LT orientation and thicknesses of all layers in LT/Si, LT/SiO2/Si, LT/glass, LT/AlN/glass and structures with several pairs of SiO2/AlN layers between LT and the glass wafer. Optimal combinations of cut angle, LT and electrode thicknesses, as well as the number and thicknesses of intermediate layers, required for the construction of resonators with improved performance were observed for each analyzed structure. In the resonators employing LT/Si and LT/SiO2/Si structures with 30°YX - 48°YX LT cuts, high electromechanical coupling k2, reaching 11.6%, can be combined with high velocities up to 4000 m/s, zero TCF at the resonant frequency and Q-factors that are considerably higher than in the LSAW filters using regular LT substrates. To understand the loss mechanisms that limit resonator Q-factors in LT/glass, mechanical displacements that accompany wave propagation in multilayered structures were visualized. Investigation of the nature of acoustic modes and their transformations with number and thicknesses of the layers revealed that the low-velocity glass wafer can be used as a supporting substrate if an intermediate AlN layer or alternating pairs of low- and high-velocity layers, for example SiO2/AlN, are introduced between LT and the glass wafer.

One-dimensional time-domain finite-element modelling of nonlinear wave propagation for non-destructive evaluation

This one-dimensional time-domain finite-element model achieves accurate quantitative modelling of ultrasonic wave propagation in multi-layered structures. First, a sinusoidal wave toneburst is sent into a single layer of material exhibiting inherent material nonlinearity characterised by the nonlinear parameter β and thick enough for the toneburst received in through transmission to be resolved. The signal processing protocol that yields the theoretically correct quantitative value of β involves measuring the received toneburst for several propagation distances as well as the use of scaling factors taking into account the fast Fourier transform implementation, input signal windowing and material damping. Using that model configuration, model parameters (element size, time step, frequency step, input pressure, etc.) are then optimised and chosen quantitatively to generate accurate results. Finally, these model parameters are used for cases of interest where the configuration is not such that the exact β value can be obtained – e.g. thinner sample, pulse-echo etc. but where confidence in the results remains. This quantitative model that can be used for multi-layered structures provides a tangible resource useful to NDE engineers: a new prediction tool expected to enable them to choose the experimental set-up, driving frequency and post-processing method that would optimise kissing bond detection capability.

3D simulations and experiments of guided wave propagation in adhesively bonded multi-layered structures

Understanding guided wave propagation in multi-layered plates and interaction with discontinuities can be difficult, as well as the interpretation of the ultrasonic signals. Propagation of guided waves can be studied analytically solving the equations of motion with the proper boundary conditions; nevertheless analytical models can be difficult to solve for complex multi-layered structures or having inner discontinuities. The problem can be efficiently studied using numerical techniques. Simulation of guided wave propagation in multi-layered structures, for ultrasonic waves in the MHz range, is solved here with the finite element analysis based on an explicit integration rule to solve the equations of motion in a dynamic analysis. Simulation allows a better understanding of propagation and interference phenomena by creating a window of observation in the multi-layered plate. Numerical results determined for a three-layer Al plate, without or with discontinuities, matched very well with experiments, providing an efficient tool to visualize and extract significant information in the transmitted waves and to optimize wave mode and configuration for a rigorous ultrasonic inspection.

Characterization of surface acoustic wave propagation in multi-layered structures using extended FEM/SDA software

This paper describes the characterization of SAW propagation in layered substrate and overlayered structures. The software based on the finite element method and spectral domain analysis was newly developed and applied to the characterization of SAW propagation under an infinitely-long Al interdigital transducer on a rotated Y-cut LiTaO(3)/sapphire substrate. Because of the finite LiTaO(3) thickness, a series of spurious resonances appears. It is shown that the excitation strength of the spurious resonances changes with frequency as well as the rotation angle, which reflects the frequency and rotation angle dependence of the energy leakage. Next, the analysis was carried out for SAWs propagating in a SiO(2) layer/Al IDT/42 degrees YX-LiTaO(3) structure. It is shown that the influence of the SiO(2) layer is significantly dependent on the location where the SiO(2) layer is deposited. In particular, it is shown that when the SiO(2) layer is deposited only on top of the electrodes, the SAW reflectivity increases compared with when the SiO(2) layer is deposited between and on top of electrodes.

Investigation of nonlinear wave propagation in multilayered structures containing left-handed layers—a delta-function approach

We investigate nonlinear wave propagation in multilayered structures containing left-handed layers. A delta-function description is used for the dielectric function of the structure. This model enables us to calculate the transmission coefficient of the structure using a 2-dimensional map. The special characteristics of wave propagation emerging from the inclusion of nonlinear left-handed layers in multilayered structures are elaborated by plotting global transmission diagrams. Optical bistability is studied both in the case of self-focusing and defocussing nonlinearity.