Scattering of antiplane shear wave by a propagating crack at the interface of two dissimilar elastic media

An analysis of the scattering of horizontally polarized shear wave by a semi-infinite crack running with uniform velocity along the interface of two dissimilar semi-infinite elastic media has been carried out. The mixed boundary value problem has been solved completely by the Wiener-Hopf technique. The effect of different values of the material parameter, the angle of incidence of incident wave and the crack propagation velocity on the stress intensity factor have been illustrated graphically.     

Scattering of guided SH-wave by a partly debonded circular cylinder in a traction free plate

A solution of the scattering problem of guided SH-wave by a partly debonded circular cylinder centered in a traction free plate has been set up. The plate is divided up into three regions with two imaginary planes perpendicular to the plate walls. In the central region where the partly debonded cylindrical obstacle is posted, the wave field is expanded into the cylindrical wave modes and Chebyshev polynomials. In the other two exterior regions the fields are expanded into the plate wave modes. A system of fundamental equations to solve the problem is obtained according to the traction free boundary condition on the plate walls and the continuity condition of the traction and the displacement across the imaginary planes. The approximate numerical method termed mode-matching technique is used to construct a matrix equation to obtain curves showing the coefficient of reflection and transmission versus the ratio of the cylinder’s radius to the plate’s half-thickness and the angular width of the debonded region. A comparison of the numerical results between the welded interface condition and the debonded interface condition is made, and the results are discussed.     

Scattering of plane harmonic waves on a cylindrical cavity with an elliptical cross section in an orthotropic medium

The diffraction of a plane longitudinal harmonic wave on a cavity with a smooth curvilinear cross section in a rectilinearly orthotropic medium is solved by using small perturbations in the elastic moduli and introducing generalized wave potentials. Results are presented from a numerical analysis of the dynamic stresses in the near diffraction field and at the boundary of an elliptical cavity including variations in the relative incident wavelength, eccentricity of the cavity, and degree of anisotropy of the medium. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 102–110, 1999.     

Scattering of an incident acoustic wave by an elastic sphere in a shallow water

The scattering of acoustic waves by an elastic sphere in a shallow ocean wave guide is investigated taking into account the shear waves which can exist in addition to compressional waves in scatterers of solid material. Expressions for the scattered waves are given. Numerical values for a quantity called the farfield form function for various depth are presented in graphical forms.      

Deformation of a composite plate on an elastic foundation by local loads

Bending of an elastic annular composite plate with a light filler lying on an elastic foundation is considered. The plate is subjected to local loads. To describe the kinematics of the package, asymmetric across its thickness, the hypotheses of broken normal is accepted. The reaction of foundation is described based on the Winkler model. A system of equilibrium equations is constructed, and its exact solution in displacements is found. Numerical solutions for a metal-polymer sandwich plate are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 109–120, January–February, 2007.     

Stress intensity factors for a finite plate with an inclined crack by boundary collocation

In this paper, we combine the Muskhelishvili＇s complex variable method and boundary collocation method, and choose a set of new stress function based on the stress boundary condition of crack surface, the higher precision and less computation are reached. This method is applied to calculating the stress intensity factor for a finite plate with an inclined crack. The influence of θ （the obliquity of crack） on the stress intensity factors, as well as the number of summation terms on the stress intensity factor are studied and graphically represented.     

The wave field generated by a centre of rotation in an unbounded elastic medium with a semi-infinite conical crack

The dynamic stress intensity factor at the edge of a semi-infinite conical crack when the medium is loaded by a non-stationary centre of rotation is determined. A centre of rotation is understood to be a set of four forces of equal magnitude that act in the same plane and form pairs having the same direction of rotation.¹ If the magnitude of these forces is time dependent, i.e., their application is non-stationary, they form a non-stationary centre of rotation. The solution of the problem required the use of methods of integral transformations and discontinuous solutions, which reduced the problem to an integral differential equation in Laplace transform space. The combined use of the orthogonal polynomial method and time discretization to solve the equation enabled a formula for the stress intensity factor to be obtained.     

Mathematical model for crack arrest of an infinite plate weakened by a finite and two semi-infinite cracks

The problem of an unbounded plate weakened by three quasi-static coplanar and collinear straight cracks: two semi-infinite cracks and a finite crack situated symmetrically between two semi-infinite cracks, is investigated. The plate is subjected to uniform unidirectional in-plane tension at infinite boundary. Developed plastic zones are arrested by distributing cohesive yield point stress over their rims. The solution is obtained using complex variable technique. Closed form analytic expressions are derived for load bearing capacity and crack-tip-opening displacement (CTOD). A case study is presented for CTOD and load bearing capacity versus crack length, plastic zone length and inter-crack distance etc. Results are presented graphically and analyzed.     

Propagation of waves in a micropolar elastic layer with stretch immersed in an infinite liquid

The effect of liquid on the propagation of waves in a micropolar elastic layer with stretch has been investigated. The frequency and wave velocity equations for symmetric and antisymmetric vibrations are derived. Propagation of monochromatic waves in a micropolar elastic layer with stretch is discussed. Results of this analysis reduce to those without stretch.     

Mathematical modelling of unsteady flow of a Sisko fluid through an anisotropically tapered elastic arteries with time-variant overlapping stenosis

In the present investigation, we have studied the influence of heat and chemical reactions on blood flow through anisotropically tapered elastic artery with time-variant overlapping stenosis. The nature of blood in small arteries are analyzed mathematically by considering it as a Sisko fluid. The analysis is carried out for an artery with a mild stenosis. Analytical expressions for the axial velocity, the stream function, the temperature distribution, the concentration of fluid, the pressure gradient, the resistance impedance and the wall shear stress distribution have been computed numerically and the results were studied for various values of the physical parameters, such as the Sisko parameter b^∗, the power index n, the taper angle ?  , the maximum height of stenosis δ^∗${\delta }^{\ast }$, the Soret number S_r, the Brickmann number B_r, the total mass of the vessel and the surrounding tissues M and the longitudinal contributions of the viscous and elastic constraints to the total tethering C and K respectively. The obtained results show that the magnitude of the axial velocity is higher for a Newtonian fluid than that for a Sisko fluid and it decreases by increasing of the power index n also the transmission of axial velocity curves through a tethered tube is substantially higher than that through the free tube. The wall shear stress distribution and resistance impedance profiles with the time have an oscillation form through the tapered overlapping stenosed arteries and this oscillation decaying as the time increases. The temperature profile increase by increasing the Sisko parameter b^∗ and the power index n   but the concentration profile has an opposite behavior as compared to the temperature profile. For a fixed flux, the magnitude of the pressure drop for a shear-thinning fluid (n<1)$(n<1)$ is much larger than that through a shear-thickening (n>1)$(n>1)$. The stream lines separate and the trapping bolus appear by increasing the maximum height of the stenosis δ^∗${\delta }^{\ast }$. The trapping bolus increase in size toward the line center of the tube as the power index n increases and it appear gradually by increasing the Sisko parameter b^∗. Finally the size of trapped bolus for the stream lines in the free isotropic tube is smaller than those in the tethered tube.     

Mathematical study of the small oscillations of an incompressible and inviscid liquid under zero gravity in a container of revolution with elastic bottom and anchored edge

In this paper, the Authors study the small oscillations of an inviscid liquid under zero gravity in a container of revolution with elastic bottom, considered as a membrane or a plate, and anchored edge. They obtain the equations of the displacements of the free surface and the bottom and they reduce these equations to a functional equation in a suitable Hilbert space. By using the methods of Functional Analysis the Authors prove the existence of the small oscillations. Research partially supported by GNFM, MURST (Italy).     

Propagation of perturbations in a two-layer rotating fluid with an interface excited by moving sources

Propagation of small perturbations in a two-layer inviscid fluid rotating at a constant angular velocity is studied. It is assumed that the lower density fluid occupies the upper unbounded half-space, while the higher density fluid occupies the lower unbounded half-space. The source of excitation is a plane wave traveling along the interface of the fluids. An explicit analytical solution to the problem is constructed, and its existence and uniqueness are proved. The long-time wave pattern developing in the fluids is analyzed.     

Propagation of perturbations in a two-layer stratified fluid with an interface excited by moving sources

Propagation of small perturbations in a two-layer inviscid stratified fluid is studied. It is assumed that the higher density fluid occupies the lower unbounded half-space, while the lower density fluid occupies the upper unbounded half-space. The source of the excitation is a plane wave traveling along the interface of the fluids. An explicit analytical solution to the problem is constructed, and its existence and uniqueness are proved. The long-time wave pattern developing in the fluids is analyzed.     

Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core

The effect of partially filled poly ethylene (PE) foam core on the behavior of torsional buckling of an isotropic, simply supported piezoelectric polymeric cylindrical shell made from polyvinylidene fluoride (PVDF), and subjected to combined electro-thermo-mechanical loads has been analyzed using energy method. The shell is reinforced by armchair double walled boron nitride nanotubes (DWBNNTs). The core is modeled as an elastic environment containing Winkler and Pasternak modules. Using representative volume element (RVE) based on micromechanical modeling, mechanical, electrical and thermal characteristics of the equivalent composite were determined. Critical buckling load is calculated using strains based on Donnell theory, the coupled electro-thermo-mechanical governing equations and principle of minimum potential energy. The results indicate that buckling strength increases substantially as harder foam cores are employed i.e. as E_c/E_s is increased. The most economic in-fill foam core is at η = 0.6, as cost increases without much significant improvement in torsional buckling at higher η’s.