D. Turhan

Propagation of transient out-of-plane shear waves in viscoelastic layered media

Abstract Propagation of two-dimensional transient out-of-plane shear waves in multilayered viscoelastic media is investigated. The multilayered medium consists of N different isotropic, homogeneous and linearly viscoelastic layers with more than one discrete relaxation time. The top surface of the layered medium is subjected to dynamic out-of-plane shear tractions; whereas, the lower surface is free or fixed. A numerical technique is employed to obtain the solution, which combines the Fourier transform with the method of characteristics. The numerical results are displayed in curves denoting the variations of the shear stresses with time at different locations. These curves reveal clearly the scattering effects caused by the reflections and refractions of inclined waves at the boundaries and at the interfaces of the layers. The curves also display the effects of viscous damping in the wave profiles. By suitably adjusting the material constants, the curves for the case of elastic layers are also obtained as a special case. The curves further show that the numerical technique applied in this study is capable of predicting the sharp variations at the wave fronts.

Transient wave propagation in layered media conducting heat

Abstract Transient wave propagation in thermoelastic layered composites consisting of alternating isotropic, homogeneous and linearly elastic high-strength reinforcing and low-strength matrix layers is investigated. The layers of the composite medium can be plane, cylindrical or spherical. The inner surfaces of the composite bodies are subjected to uniform time dependent dynamic inputs. A common formulation is employed for the three types of layered media. The generalized theory of thermoelasticity is used, with thermal relaxation predicting finite wave speeds for thermal disturbances. The method of characteristics is employed to obtain the solutions. Curves are plotted denoting the variations of normal stresses with time at different locations and variations of stresses along the thicknesses of the bodies at different times. The curves reveal the thermal and geometric dispersions in the wave profiles and the effects of reflections and refractions at the boundaries and the interfaces of the layers.

Transient waves in viscoelastic cylindrical layered media

Propagation of two-dimensional transient waves in viscoelastic cylindrical layered media is investigated. The cylindrical multilayered medium consists of N different isotropic, homogeneous and linearly viscoelastic layers with two discrete relaxation times. A numerical technique which combines the complex Fourier series with the method of characteristics is employed to obtain the solutions. The numerical results are displayed in curves denoting the variations of the stress and displacement components with time at different locations. These curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces of the layers, and the effects of viscous damping in the wave profiles. The curves further show that the numerical technique applied is capable of predicting the sharp variations in the field variables in the neighbourhood of the wave fronts. By suitably adjusting the material constants, the results for the special cases of elastic layers and viscoelastic layers with one relaxation time (standard linear solid) are also obtained. Furthermore, solutions for some special cases are compared with the available solutions in the literature and a good agreement is found.

Finite element solution for reflection of plane harmonic waves from the free surface of a half-space

Abstract Reflection of harmonic elastic waves from the free surface of a half-space is investigated using the finite element technique. The waves are assumed to be planar and the half-space is represented by bilinear finite elements of rectangular shape. Before treating the reflections of plane longitudinal and vertical shear waves, the wave propagation in an infinite medium is given in a way which will be directly applicable to the subsequent reflection problem. Numerical results are reported for various values of the wavelength, the angle of incidence and the grid dimensions of the finite elements. Special attention is paid to the representability of the homogeneous medium by the finite elements in such wave propagation problems and to suitable grid dimensions. Finally attention is drawn to two types of solution which do not appear in the exact solution of the reflection problem.

Transient response of inhomogeneous thermoelastic media to a dynamic input

A problem involving a half-space or an infinite space with a cylindrical or spherical cavity subjected to a uniform dynamic input on its surface is studied. The material is elastic and has an inhomogeneity in the direction perpendicular to the boundary surface for the half-space problem and an inhomogeneity in the radial direction for the problem with a cylindrical or spherical cavity. The numerical results, obtained when the dynamic input is a step pressure, indicate that the wave profiles are influenced by two kinds of dispersions: one caused by thermal effects and the other by inhomogeneity. The influence of thermal dispersion is observed more pronouncedly along the initial portion of wave profiles. Compared to the homogeneous case the inhomogeneities in which Lamés constants increase and decrease with the distance measured from the boundary have respectively amplifying and attenuating effects on both the axial stress and velocity.ZusammenfassungDas Problem der gleichmässigen dynamischen Belastung an den Grenzen eines halbunendlichen Körpers oder eines unendlichen Körpers mit einem zylindrischen oder sphärischen Halbraum wurde untersucht.Der Körper ist elastisch und enthält Inhomogenitäten, im halbunendlichen Körper in der Richtung senkrecht zur Grenzebene und im unendlichen Körper mit Hohlräumen in radialer Richtung. Die numerischen Ergebnisse, die für eine Belastung nach einer Schritt-Funktion erzielt wurden, zeigen dass die Profile der Ausbreitungswellen von zwei Streuungen beeinflusst sind: die erste ist eine Folge der thermischen Effekte, die zweite eine solche der Inhomogenitäten. Der Effekt der thermischen Zerstreuung ist im anfänglichen Bereich der Profile stärker. Im Vergleich zum homogenen Fall hat die Zu-beziehungsweise die Abnahme der Laméschen Konstanten mit dem Abstand von der Grenze erhöhenden beziehungsweise vermindernden Einfluss sowohl auf die axiale Spannung als auch auf die Geschwindigkeit.

Propagation of out-of-plane shear waves in an elastic layer

Abstract In this study, a general approximate theory which has been proposed for the dynamic behavior of viscoelastic plates and layered composites is assessed by considering the propagation of out-of-plane shear waves in an elastic layer. This somewhat simple problem was chosen for assessment because the solution using the exact theory can be obtained numerically with good accuracy. The approximate equations of the problem are integrated by employing the method of characteristics whereas the exact equations are solved by a transform technique together with the method of characteristics. From a comparison of the approximate and exact results, it is found that the approximate theory can predict very well the transient waves propagating in a layer and their geometric dispersions due to reflections at the boundaries, and that it is capable of describing the sharp variations at wave fronts.

Wave propagation in anisotropic non-homogeneous thermoviscoelastic media

Abstract Propagation of waves in linear anisotropic non-homogeneous thermoviscoelastic media is investigated by employing the basic ideas of the theory of singular surfaces and of ray theory. The characteristic equation governing the wave velocities, and the decay and growth equations describing the change of the strength of the discontinuity as the wave front moves in the medium are obtained. The results then are reduced to the case of isotropic materials. The decay and growth equations for this case are integrated along the rays and the general solutions are obtained. The factors affecting the decay and growth, namely the effects of inhomogeneity, geometry of the wave front, material internal friction and thermomechanical coupling, are discussed.

Dynamic Response of Viscoelastic Cylinders Enclosed in Filament Wound Cylindrical Composites

In this study, transient dynamic response of viscoelastic cylinders enclosed in filament wound cylindrical composites will be investigated. The body consists of n+1-layers, the inner layer being viscoelastic, while the outer fiber reinforced composite medium consists of η-different generally orthotropic, homogeneous and elastic layers. The governing field equations ( [1], [2] [5]) of viscoelasticity and anisotropic elasticity will be applied to each layer. The material of the viscoeiastic layer is modelled as standard linear solid. Solutions for the case of an ablating inner surface are obtained as well. The numerical results are displayed in curves denoting the variations of circumferential and radial stresses with time at different locations. The curves reveal clearly the effects of reflections and refractions at the inner and outer surfaces and the interfaces between the layers. Furthermore, the effects of damping, geometric dispersion and ablating inner boundary are clearly seen in the curves.

Two-dimensional Transient Shear Wave Propagation In Viscoelastic Cylindrical Layered Media

In this study, propagation of two-dimensional transient shear waves in viscoelastic cylindrical layered media is investigated. The multilayered medium consists of N different isotropic, homogeneous and linearly viscoelastic layers with two discrete relaxation times. A numerical technique which combines the Fourier transform with the method of characteristics is employed to obtain the solutions. The numerical results are displayed in curves denoting the variations of the stress components with time at different locations. These curves reveal clearly the scattering effects caused by the reflections and refractions of waves at the boundaries and at the interfaces. The curves also display the effects of viscous damping in the wave profiles. The curves further show that the numerical technique applied is capable of predicting the sharp variations in the field variables in the neighbourhood of the wave fronts. By suitably adjusting the material constants, curves for the cases of elastic layers and viscoelastic layers with one relaxation time (standard linear solid) are also obtained. Solutions for some one-dimensional elastic and viscoelastic transient wave propagation problems are obtained as special cases. These solutions are compared with the existing ones in the literature and very good agreement is found.

Transient Wave Propagation in Periodically Layered Media

In this paper, transient wave propagation in periodically layered composites consisting of alternating isotropic and homogeneous high-strength reinforcing and low-strength matrix layers is investigated. First, some results from our recently published work1,2 will be given. In our recent work,1,2 the propagation of dilatational waves is investigated. The layers of the composite medium can be plane, circular cylindrical or spherical. Furthermore, the layers can be linearly thermoelastic or linearly viscoelastic. The viscoelastic material of the bodies is modelled as a standard linear solid. A common formulation is used for the three types of layered media. The bodies are subjected to uniform time-dependent dynamic inputs at their inner surfaces and the outer surfaces are either fixed or free. The composite bodies are initially at rest.