Thermoelasticity of multilayered plates with imperfect interfaces

Propagation of Lamb waves in multilayered elastic anisotropic plates is studied in the framework of combination of the six-dimensional Cauchy formalism and the transfer matrix method. The closed form secular equations for dispersion curves of Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy are obtained.

MITC technique extended to variable kinematic multilayered plate elements

Exact analysis of the propagation of acoustic waves in multilayered piezoelectric plates is performed using the transfer matrix method. A general technique for analyzing layered piezoelectric resonators under thickness and lateral field excitation is presented and is applied to the study of zinc oxide on silicon thin film resonators. Both one and two-dimensional analysis with general material anisotropy is performed, and a simplified method for incorporating thin conducting electrodes on the plate's free surfaces is presented. The general methodology described is summarized into efficient algorithms to aid in the implementation of the procedures and some computational aspects are discussed. Results are presented for cutoff behavior as well as general dispersion characteristics for two and three layered plates.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Evanescent waves are widely used in non-destructive evaluation to determine the shape and size of defects,as a result, it have become the focus of research. It is crucial to study the modal and dispersion relations of evanescent waves described by complex roots. However, it is relatively difficult to solve the roots of evanescent modes, especially for structures such as anisotropy and composites. In this paper, using the Legendre orthogonal polynomial method (LOPM), the guided wave characteristics of multilayer anisotropic elastic plates are studied by transforming the solution process into solving the eigenvalue problem of a matrix. Detailed formulas and Lamb wave dispersion diagrams are presented. The validity of LOPM is verified by comparing with the published data. Furthermore, the dispersion curves of the three-dimensional complex solutions are further drawn, and the relationship between the modes of complex and pure imaginary solutions is deeply discussed. Meanwhile, the influence of different thickness ratios on the dispersion characteristics of evanescent guided waves is also studied. Some instructive conclusions are obtained, which can guide the non-destructive testing of composite structures using evanescent waves.

The interaction of acoustic waves generated by a point source with an elastic plate immersed in acoustic fluid is considered. To estimate the range of applicability of various theoretical approaches, a hierarchy of mathematical and computer models has been developed. The models differ in the governing equations for the sounded elastic laminate structure (from a simplified Kirchhoff-Love plate to a multi-layered anisotropic composite plate obeying the full set of 3D Navier-Lame equations in each sublayer). Explicit integral representations for generated and scattered wave fields have been derived using the Fourier transform technique. In the far-field, the acoustic and guided waves are described by asymptotic representations obtained from those integrals using the stationary phase method and the residual technique. Among others, the derived solutions enable quantitative analysis of time-averaged wave energy fluxes in the considered source-structure system. Analytic representations for the total source energy and its portions carried by reflected, transmitted and guided waves have also been obtained.

The formulation of a geometrically nonlinear theory of anisotropic multilayered plates of general layups featuring interlayer slips is discussed. The theory rests on a displacement field, which accounts for an arbitrary distribution of the tangential displacements through the laminate thickness, fulfills a priori the static continuity conditions of tangential stresses at the layer interfaces, and allows for jumps in the tangential displacements so as to provide the possibility of incorporating effects of interfacial imperfection. For the interlayer displacement jump, a linear shear slip law is postulated. No a priori assumption is made on the type and order of the expansion in the thicknesswise direction of the tangential displacements. The pertinent equations of motion and consistent boundary conditions are derived by means of the dynamic version of the principle of virtual work. These are given in terms of force and moment stress resultants and in terms of generalized displacements. The generalization achieved by the proposed approach is shown by deriving, as particular cases, the recently proposed first-order and third-order models for laminated plates featuring interlayer slips

The scheme for solving of a mixed problem with general boundary conditions is proposed for a heat equation \[a(x)\frac{\partial T}{\partial \tau}= \frac{\partial}{\partial x} \left(\lambda(x)\frac{\partial T}{\partial x}\right)\] with coefficient $a(x)$ that is thegeneralized derivative of a function of bounded variation, $\lambda(x)&gt;0$, $\lambda^{-1}(x)$ is a bounded and measurable function. The boundary conditions have the form $$\left\{ \begin{array}{l}p_{11}T(0,\tau)+p_{12}T^{[1]}_x (0,\tau)+ q_{11}T(l,\tau)+q_{12}T^{[1]}_x (l,\tau)= \psi_1(\tau),\\p_{21}T(0,\tau)+p_{22}T^{[1]}_x (0,\tau)+ q_{21}T(l,\tau)+q_{22}T^{[1]}_x (l,\tau)= \psi_2(\tau),\end{array}\right.$$ where by $T^{[1]}_x (x,\tau)$ we denote the quasiderivative $\lambda(x)\frac{\partial T}{\partial x}$. A solution of this problem seek by thereduction method in the form of sum of two functions $T(x,\tau)=u(x,\tau)+v(x,\tau)$. This method allows to reduce solving of proposed problem to solving oftwo problems: a quasistationary boundary problem with initialand boundary conditions for the search of the function $u(x,\tau)$ and a mixed problem with zero boundaryconditions for some inhomogeneous equation with an unknown function $v(x,\tau)$. The first of these problems is solved through the introduction of the quasiderivative. Fourier method andexpansions in eigenfunctions of some boundary value problem forthe second-order quasidifferential equation $(\lambda(x)X'(x))'+ \omega a(x)X(x)=0$ are used for solving of the second problem. The function $v(x,\tau)$ is represented as a series in eigenfunctions of this boundary value problem. The results can be used in the investigation process of heat transfer in a multilayer plate.

Solitons, or by the original terminology waves of translation, were for the first time observed and described by Scott Russel (1845) as a special kind of the hydrodynamic waves that can arise and propagate in narrow channels. Solitons are: (i) solitary waves, resembling propagation of the wave front of shock waves; (ii) these waves can propagate without considerable attenuation, or (iii) change of form; or (iv) diminution of their speed; see, Craik (2004). It was shown later on, that motion of these waves can be described by a non-linear KdV differential equation; see the work by the originators of the KdV-equation Korteweg and de Vries (1885) and the subsequent works by Lax (1968), Miles (1981), and Zwillinger (1997), where some of the analytical solutions are presented and the main properties of the KdV equation are analyzed. Herein, we analyze the long-wave limits of Lamb waves propagating in multilayered elastic anisotropic plates at vanishing frequency 0   , or in terms of the wave number r , at 0 r  . These vanishing frequency Lamb waves satisfy conditions (i) – (iv), and thus, resemble the solitons. But, in contrast to the genuine solitons in hydrodynamics or their nonlinear analogues propagating in elastic solids; see, Eckl et al. (2004), Kawahara (1972), Kliakhandler, Porubov, and Verlande (2000), Planat and Hoummady (1989), Porubov et al. (1998), Samsonov (2001), our soliton-like waves are described by linear vectorial differential equations, known as the Christoffel equations for Lamb waves. Studies of Lamb waves, as solutions of linear equations of motion for the infinite plates, and the corresponding soliton-like linear waves traveling with the finite phase speed at vanishing frequency have quite a long history. Presumably, the first asymptotic analysis of the waves propagating at vanishing frequency in an isotropic plate with the traction-free outer planes was performed by Gogoladze (1947). He obtained an analytical expression for the phase speed of such a wave by asymptotic analysis of the approximate equation of motion related to the theory of plates based on the Bernoulli – Euler hypotheses. Later on, the similar approach and a more elaborate one allowing to consider plates with different boundary conditions at outer planes, but still based on the approximated theories of plates, were exploited by Mindlin (1951a, b, 1958, 1960), Mindlin and Medick (1959), Mindlin and Onoe (1957), Onoe (1955), and Tolstoy and Usdin (1953). The latter authors reported highly intricate behavior of the disperse curves in the vicinity of the zero frequency. See also a more recent work by Pagneux and Maurel (2001), where the dispersion relations in the complex

Thin elastic plates made of an anisotropic material (with 21 elastic moduli) and heterogeneous in the thickness direction (in partial, multilayered) are considered. A short overview of various 2D models describing deformations and vibrations of a plate is given. The classical Kirchhoff–Love and the Timoshenko–Reissner models are discussed and compared in cases of isotropic and transversely isotropic materials. A correspondence of boundary conditions of these models is established. A multilayered plate with alternating soft and hard layers is considered. By using an asymptotic expansion of the solution in a series in small thickness parameter, the 2D equations of second-order accuracy are delivered. From these equations the correct choice of parameters of the single-layered Timoshenko–Reissner model is derived, which is equivalent to a given multilayered plate. In the case of general anisotropy, a model of second-order accuracy is presented as well, and the main properties of the harmonic solutions for static problems and for free vibrations of a plate are briefly described.

Green functions of piezoelectric material with an elliptic hole or inclusion

Microstructural changes in a single crystal Ni-base superalloy induced by plastic straining

Acoustic Emission (AE) technique is non-destructive Structural Health Monitoring (SHM) technique which has the potential to detect internal damages in real time. Literature reveals that researchers have used three-dimensional (3d) Finite Element Method (FEM) to predict AE waveforms in isotropic and single-layer anisotropic plates. However, the study to predict acoustic emission waveforms using FEM in layered composites and sandwich plates is limited in literature. Modelling of such layered plates is challenging as material properties may vary from one layer to another across the plate thickness. In this study, an effort has been made for two-dimensional finite element modelling for predicting AE waveforms in layered composites and sandwich plates using a generalised refined plate theory modelling. Numerical examples are first solved for isotropic and anisotropic plates and validated with the results obtained from 3d FEM. New results are presented for multilayered composites and sandwich plates.

A two-dimensional model is developed of silicon recrystallization by nanosecond laser pulses in a silicon-on-insulator (SOI) structure with seed windows. Using this model, temperature and thermoelastic fields and phase transition behaviour are calculated. Phase transitions are described by new phase nucleation (homo- and heterogeneous) kinetics and its growth. The experimental situation is computerized using ruby laser action with 30 ns pulses and 0 to 3 J/cm2 energy density. The melting depth is shown to be greater at the edge of the seed window than in its center. This causes Si laterial epitaxy, while in the seed area the polycrystal remains. It is predicted that in the crystallization front movement along the dielectric the slope towards the dielectric increases, and the more, the lower the preheating temperature of the sample is. The thermoelastic stresses in the SOI structure are calculated before melting and after cooling, and it is shown that with higher preheating, the residual stresses in the sample are higher. The results of the computations are compared with experimental data. [Russian Text Ignored.]

The scaled boundary finite element method (SBFEM) is a semi-analytical method, whose versatility, accuracy, and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using an efficient high-order polynomial element in the SBFEM to form the approximation in the circumferential direction. The governing equations are formulated from the classical linear elasticity theory via the SBFEM technique. The scaled boundary finite element equations are formulated within a general framework integrating the influence of the distributed body source, mixed boundary conditions, contributions the side face with either prescribed surface load or prescribed displacement. The position of scaling center is considered for modeling problem. The proposed method is evaluated by solving two-dimensional linear problem. A selected set of results is reported to demonstrate the accuracy and convergence of the proposed method for solving problems in general boundary conditions.

Nondestructive testing of aerospace structures often requires their immobilization. Structural health monitoring (SHM) using guided waves (GW) can overcome this. GW propagate at long range but are diffracted by stiffeners present on typical structures. Optimally positioning sensors implies to determine the number of stiffeners GW can go through while remaining detectable. A model is developed to compute GW diffraction by a stiffener bonded to a composite plate. It hybridizes the semi-analytical finite element method for propagation and a finite element method (FE) for diffraction. Specific transparent boundary conditions minimize the size of the FE domain. Transmission-reflection coefficients are obtained as functions of the direction of incidence.