Guided waves in a stratified elastic and locally perturbed domain: theoretical and numerical aspects

This article presents new results concerning guided waves in a three‐dimensional unbounded stratified and locally perturbed elastic medium. On the one hand, we numerically show non‐monotonic dispersion curves, a phenomenon not yet encountered in fields other than elasticity. On the other hand, we prove that the infimum of the essential spectrum of the studied operator depends on the possible non‐monotonicity of such curves. This link is a new result with respect to equivalent situations coming from acoustics or electromagnetism. The numerical study underlines, besides the non‐monotonic dispersion curves, the appearance of generalized Stoneley waves. Copyright © 2000 John Wiley & Sons, Ltd.     

Propagation of guided waves in bonded composite structures with tapered adhesive layer

Adhesively bonded composites are becoming increasingly important in engineering applications due to its advantages for structural repair and integrated manufacturing of advanced composite structures. Characteristics of guided waves propagation in bonded composite structures with tapered adhesive layer are investigated in this paper. Hamilton’s principle and a semi-analytical finite element method are combined to study the wave propagation problem numerically that account for different properties of adhesive layer. Several adhesive bonded composite models are analyzed, including dimensions of adhered joints, local separation of adhesive and material degradation. Dispersion curves of different bonded states are studied numerically by accounts for effects of varying adhesive thickness. Results provided some suggestions in selecting more suitable mode for interrogating of adhesive bonded composite with different states.     

Torsional vibrations and dispersion of torsional waves in orthotropic composite rods

The Barr’s refined theory of torsional vibrations of isotropic rods of noncircular cross section is generalized for an orthotropic material. An analysis of natural frequencies of torsional vibration of free-free orthotropic prismatic rods of rectangular cross section is carried out with the help of an exact solution of the frequency equation. For orthotropic CFRP and GFRP rods, the improved theory, which takes into account the normal stresses and inertia forces in the axial direction, in some cases, predicts a noticeable raise in the natural frequencies compared with those following from the Saint-Venant classical theory. A good agreement is obtained between the experimental and calculated values of natural frequencies of torsional vibrations of rectangular quartz and fiber glass rods. The dispersion of torsional waves in an orthotropic quasi-homogeneous rod is considered. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 165–182, March–April, 2008.     

Propagation of torsional waves in a prestretched compound hollow circular cylinder

The propagation of torsional waves in a prestressed compound (bi-layered) hollow circular cylinder is in vestigated within the frame work of a piecewise homogeneous body model, with the use of a three-dimensional linerized theory of elastic waves in initially stressed bodies. The elasticity relations for components of the compound cylinder are obtained from the Murnaghan potential. Numerical investigations are performed for bronze and steel. According to the results obtained, the effect of variations in the geometric (the ratio between the thickness of the cylinder and its inner radius) and mechanical parameters on the dispersion curves are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 1, pp. 103–116, January–February, 2008.     

Asymptotic behavior of nonlinear waves in elastic media with dispersion and dissipation

In the case of nonlinear elastic quasitransverse waves in composite media described by nonlinear hyperbolic equations, we study the nonuniqueness problem for solutions of a standard self-similar problem such as the problem of the decay of an arbitrary discontinuity. The system of equations is supplemented with terms describing dissipation and dispersion whose influence is manifested in small-scale processes. We construct solutions numerically and consider self-similar asymptotic approximations of the obtained solution of the equations with the initial data in the form of a “spreading” discontinuity for large times. We find the regularities for realizing various self-similar asymptotic approximations depending on the choice of the initial conditions including the dependence on the form of the functions determining the small-scale smoothing of the original discontinuity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 240–256, May, 2006.     

Thermo-poroacoustic acceleration waves in elastic materials with voids

A model for coupled elasto-acoustic waves, thermal waves, and waves associated with the voids, in a porous medium is investigated. Due to the use of lighter materials in modern buildings and noise concerns in the environment such models for thermo-poroacoustic waves are of much interest to the building industry. Analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to industry and medicine. We present a model for acoustic wave propagation in a porous material which also allows for propagation of a thermal wave. The thermodynamics is based on an entropy inequality of A.E. Green, F.R.S. and N. Laws and is presented for a modification of the theory of elastic materials with voids due to J.W. Nunziato and S.C. Cowin. A fully nonlinear acceleration wave analysis is initiated.     

Optimized composite finite difference schemes for atmospheric flow modeling

In this paper, we use some finite difference methods in order to solve an atmospheric flow problem described by an advection–diffusion equation. This flow problem was solved by Clancy using forward‐time central space (FTCS) scheme and is challenging to simulate due to large errors in phase and amplitude which are generated especially over long propagation times. Clancy also derived stability limits for FTCS scheme. We use Von Neumann stability analysis and the approach of Hindmarsch et al. which is an improved technique over that of Clancy in order to obtain the region of stability of some methods such as FTCS, Lax–Wendroff (LW), Crank–Nicolson. We also construct a nonstandard finite difference (NSFD) scheme. Properties like stability and consistency are studied. To improve the results due to significant numerical dispersion or numerical dissipation, we derive a new composite scheme consisting of three applications of LW followed by one application of NSFD. The latter acts like a filter to remove the dispersive oscillations from LW. We further improve the composite scheme by computing the optimal temporal step size at a given spatial step size using two techniques namely; by minimizing the square of dispersion error and by minimizing the sum of squares of dispersion and dissipation errors.     

Behavior of concrete cylinders confined by carbon composite 2. Prediction of strength

The mechanical behavior of round concrete cylinders confined by a carbon-epoxy composite wrapping is analyzed concerning the increased concrete compression strength due the wrapping. It is shown that the loading trajectories in the normalized stress space fit into a single master curve for all the concrete batches and jacket thicknesses investigated. The loading paths ended at failure of the composite wrapping from the increased internal lateral pressure. The strength of the composite was determined by split-disc tests of composite rings, but the strength of composite jackets realized on concrete specimens did not reach the strength of the rings. Therefore, a coefficient of composite strength reduction was introduced. A simple formula for predicting the strength of confined concrete is derived, and a comparison with fib (fédération internationale du béton) recommendations for strength predictions is given. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 2, pp. 165–178, April–May, 2006.     

Fracture of a piezoelectric fiber/elastic matrix composite

A piezoelectric fiber/elastic matrix system subjected to axially symmetric mechanical and electric loads is considered. The fiber contains a penny-shaped crack located at its center perpendicularly to the fiber. By using the Fourier and Hankel transforms, the problem is reduced to the solution of an integral equation. Numerical solutions for the crack tip fields are obtained for various crack sizes and different fiber volume fractions. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 301–318, May–June, 2006.     

Asymptotic stability of a composite wave of two traveling waves to a hyperbolic–parabolic system modeling chemotaxis

In this paper, we study the asymptotic stability of a composite wave consisting of two traveling waves to a hyperbolic–parabolic system modeling repulsive chemotaxis. On the basis of elementary energy estimates, we show that the composite wave is asymptotically stable under general initial perturbations, which are not necessarily zero integral. As an application, we obtain a similar result for this system in the presence of a boundary. Copyright © 2013 John Wiley & Sons, Ltd.     

Propagation of TM waves in a Kerr nonlinear layer

TM electromagnetic waves propagating through a nonlinear homogeneous isotropic unmagnetized dielectric layer located between two homogeneous isotropic half-spaces are studied. The nonlinearity in the layer obeys the Kerr law. The problem is reduced to a system of nonlinear ordinary differential equations. A dispersion relation for the propagation constants is derived. The results are compared with those in the case of a linear layer.     

On the propagation of Lamb waves in a sandwich plate made of compressible materials with finite initial strains

The propagation of flexural Lamb waves in a prestrained sandwich plate made from compressible highly elastic materials is investigated within the scope of a piecewise homogeneous body model by utilizing TLTEWISB. The mechanical relations of layer materials are described by a harmonic-type potential, and numerical results are obtained for the first and second vibration modes. According to the results, the influence of problem parameters and of the initial stretching strain along the layers on the wave propagation speed is examined. The asymptotic values of the speed are considered in the cases of short and long wavelengths, and the influence of the initial strains on these asymptotic (limit) values are also analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 231–244, March–April, 2008.     

Fitting enclosing cylinders to data in R n

A simple iterative algorithm is given for finding a stationary point of the (non-convex) problem of finding the smallest enclosing (n–d)-cylinder to discrete data in R ⁿ , that is a cylinder whose axis is a d-dimensional linear manifold. An important special case is the problem of finding the smallest enclosing (usual) cylinder, when n=3 and d=1. The method is based on the solution of a sequence of second order cone programming problems, which can be efficiently solved by interior point methods and for which good software packages are available.     

Transient analysis of thermo-elastic waves in thick hollow cylinders using a stochastic hybrid numerical method,considering Gaussian mechanical properties

This article attempts to study the stochastic coupled thermo-elasticity of thick hollow cylinders subjected to thermal shock loading considering uncertainty in mechanical properties. The thermo-elastic governing equations based on Green–Naghdi theory (without energy dissipation) are stochastically solved using a hybrid numerical method (combined Galerkin finite element and Newmark finite difference methods). The mechanical properties are considered as random variables with Gaussian distribution, which are generated using Monte Carlo simulation method with various coefficients of variations (COVs). The effects of uncertainty in mechanical properties with various coefficients of variations on thermo-elastic wave propagation are studied in detail. Also, the maximum, mean and variance of temperature, displacement and stresses are illustrated across thickness of cylinder in various times.     

Travelling waves in lattice dynamical systems

For a class of one‐dimensional lattice dynamical systems we prove the existence of periodic travelling waves with prescribed speed and arbitrary period. Then we study asymptotic behaviour of such waves for big values of period and show that they converge, in an appropriate topology, to a solitary travelling wave. Copyright © 2000 John Wiley & Sons. Ltd.     

Behavior of concrete cylinders confined by a carbon composite 3. Deformability and the ultimate axial strain

Results of an experimental investigation into the mechanical properties of concrete cylinders confined by a carbon-epoxy composite wrapping are presented. It is shown that, for all the con fined con crete spec i mens tested, the loading paths in the normalized stress space follow a single master curve, what ever the concrete strength and confinement intensity. At stresses in the confined concrete exceeding the strength of plain concrete, the tangent modulus was found to depend on the slope angle of the master curve and the asymptotic value of the differential Poisson ratio (the first derivative of the lateral strain with respect to the axial one). Formulas for predicting the ultimate axial strain and the tangent modulus are derived and compared with the corresponding fib (fédération internationale du béton) recommendations. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 433–448, July–Au gust, 2006.     

A relaxed model and its homogenization for nematic liquid crystals in composite materials

We analyse a model for equilibrium configurations of composite systems of nematic liquid crystal with polymer inclusions, in the presence of an external magnetic field. We assume that the system has a periodic structure, and consider the relaxed problem on the unit length constraint of the nematic director field. The relaxation of the Oseen–Frank energy functional is carried out by including bulk as well as surface energy penalty terms, rendering the problem fully non‐linear. We employ two‐scale convergence methods to obtain effective configurations of the system, as the size of the polymeric inclusions tends to zero. We discuss the minimizers of the effective energies for, both, the constrained as well as the unconstrained models. Copyright © 2004 John Wiley & Sons, Ltd.     

Dynamics of breather waves and rogue waves on a soliton background in the coupled Hirota systems

Based on the Darboux-dressing transformation, the new localized wave solutions of the coupled Hirota systems are constructed with a detailed derivation. Furthermore, by using Taylor series expansions for the trigonometric and exponential functions of our obtained exact breather solution, the N-order rogue wave solutions are also expressed explicitly. Besides, the dynamics of these rogue wave solutions are illustrated with some vivid graphics.     

Mechanics of composite materials in fuel cell systems

The science and technology that are fundamental to the concept of composite materials are also the foundation for the construction and function of fuel cells and fuel cell systems. The present paper outlines this relationship in the context of the physics and chemistry that are enabled by the specific selection and arrangement of constituents of the functional composite fuel cell. General principles of operation are described, and fundamental issues are defined that must be addressed by the composites community if the fuel cell science and engineering is to advance. Examples of several types of functional composite fuel cells are presented, with emphasis on polymer electrolyte (PEM) and solid-oxide (SOFC) systems. Specific needs for continued research are identified.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 3–16, January–February, 2005.