Vibration of beams with general boundary conditions due to a moving random load

Summary  The transverse vibrations of elastic homogeneous isotropic beams with general boundary conditions due to a moving random force with constant mean value are analyzed. The boundary conditions considered are: pinned–pinned, fixed–fixed, pinned–fixed, and fixed–free. Based on the Bernoulli beam theory, the problem is described by means of a partial differential equation. Closed-form solutions for the variance and the coefficient of variation of the beam deflection are obtained and compared for three types of force motion: accelerated, decelerated and uniform. The effects of beam damping and speed of the moving force on the dynamic response of beams are studied in detail. Received 3 December 2001; accepted for publication 30 April 2002     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.     

Supercritical flow in manholes with a bend extension

 Bend manholes of sewers with 45° deflection angles are considered. Previous results are reconsidered by introducing the so-called bend extension. It is demonstrated that the discharge capacity of the 45°- and the 90°-bend manholes is identical if the bend extension, a U-shaped straight downstream portion, is added to the 45° manhole. In addition, the effect of the bend cover is analyzed as a general means to suppress shock waves. Both bend extensions and bend covers may be added to existing structures that convey discharge close to or over the design discharge. The hydraulics of bend manholes are analyzed in detail, including the wave profiles along the inner and the outer bend walls, the complete free surface, the recirculation zone, the pressure distributions on the walls and flow in the downstream sewer. Received: 12 March 2001 / Accepted: 10 August 2001     

Instability of vibrations of a moving two-mass oscillator on a flexibly supported Timoshenko beam

Summary  Transversal vibrations of a uniformly moving two-mass oscillator on a Timoshenko beam of infinite length supported by a viscoelastic foundation are studied. By using integral transforms, the characteristic equation for the oscillator's vibrations is obtained. It is shown that the equation may have a root with a positive real part. The existence of such a root leads to the exponential increase of the amplitude of the oscillator vibrations, i.e. to instability. The reasons for the instability to occur are discussed. By employing the method of D-decomposition, the instability domains are found in the space of the system parameters. Received 30 October 2000; accepted for publication 28 March 2001     

Nonsimilar boundary-layer flow over a stationary permeable plate in a rotating fluid with a magnetic field

Summary  The nonsimilar boundary-layer flow and heat transfer over a stationary permeable surface in a rotating fluid in the presence of magnetic field, mass transfer and free stream velocity are studied. The parabolic partial differential equations governing the flow have been solved numerically by using a difference–differential method. For small streamwise distance, these partial differential equations are also solved by a perturbation technique with Shanks transformation. For uniform mass transfer, analytical solutions are obtained. The surface skin friction coefficients and the Nusselt number increase with the magnetic field, suction and streamwise distance from the leading edge of the plate except the skin friction coefficient in the y-direction which decreases with the increasing magnetic field. Received 4 December 2001; accepted for publication 24 September 2002     

On permanent long-wave distortions of a railway track due to the moving vehicle load

Summary  The paper presents a simple mathematical model which describes the evolution of the vertical profile of a railway track caused by the load arising from moving vehicles. Owing to the fact that the track ballast is not perfectly elastic, each passage of a train is accompanied by a residual deformation of the ballast. Being very small, these deformations, however, accumulate with time. It is shown that an initial imperfection in the vertical profile of the track will either grow or diminish after each passage. For given track and vehicle, the rate of growth is determined by the characteristic length of the imperfection and by the velocity of the vehicle. Received 3 February 2000; accepted for publication 19 July 2000     

On the modeling and design of piezocomposites with prescribed properties

Summary  Piezoelectric transversely isotropic matrix containing spheroidal piezoelectric inclusions with different properties and of, generally, diverse aspect ratios is considered. A full set of ten effective electrostatic constants is derived, using the method of effective field. The case, when the inclusions are circular cylinders (fibers) is analyzed in detail. The results are compared with those of several earlier works. They constitute the theoretical framework for the design of piezocomposites with prescribed overall properties. Received 3 May 2001; accepted for publication 26 June 2001     

Time dependent flow in equimolar micellar solutions: transient behaviour of the shear stress and first normal stress difference in shear induced structures coupled with flow instabilities

Recently we studied time dependent structural changes that are coupled with flow instabilities (Fischer 1998; Wheeler 1998; Fischer 2000). Within a stability analysis, a classification scheme for the feedback circuit of coupled shear-induced structure and flow instabilities was derived by Schmitt et al. (1995) and applied to our samples. Here, inhomogeneous flow layers of different concentration and viscosity are generated by shear-induced diffusion (spinodal demixing) and, as consequence, one no longer observes a homogeneous solution but a type of shear banding that is seen here for the first time. In this paper we present the behaviour of the first normal stress difference observed in the critical shear-rate regime where transient shear-induced structure is coupled with flow instability. Similar to the oscillations of the shear stresses (strain-controlled rheometer) one observes oscillations in the first normal stress difference. This behaviour indicates that elastic structures are built up and destroyed while the shear-induced structures occur and that the induced phase is more elastic than the initial one. Oscillations of shear stress and first normal stress difference are in phase and indicate that both phenomena are caused by the same mechanism. Received: 30 June 1999/Accepted: 14 December 1999     

Electrohydrodynamic instability of two superposed Walters B´ viscoelastic fluids in relative motion through porous medium

Summary  The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed viscoelastic (B′ model) dielectric fluids streaming through a porous medium is investigated. The considered system is influenced by applied electric fields acting normally to the interface between the two media, at which there are no surface charges present. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially unstable configuration, or streaming only for the potentially stable configuration, as long as perturbations in the direction of streaming are ignored. For perturbations in all other directions, there exists instability for a certain wavenumber range. The instability of this system can be enhanced (increased) by normal electric fields. In the presence of surface tension, it is found also that the normal electric fields have destabilizing effects, and that the surface tension is able to suppress the Kelvin–Helmholtz instability for small wavelength perturbations, and the medium porosity reduces the stability range given in terms of the velocities difference and the electric fields effect. Finally, it is shown that the presence of surface tension enhances the stabilizing effect played by the fluid velocities, and that the kinematic viscoelasticity has a stabilizing as well as a destabilizing effect on the considered system under certain conditions. Graphics have been plotted by giving numerical values to the parameters, to depict the stability characteristics. Received 27 March 2000; accepted for publication 3 May 2001     

Modelling of a resonant inertial oscillation within a torus

Summary  We consider the air contained in a pneumatic tyre with the purpose of investigating its inertial oscillations. We model the tyre as a torus limited by a membrane in contact with the ground. According to this model, we prove that the flow within this torus may be considered as one at low Mach number and that it is ruled by oscillations of incompressible rotating fluid. Investigating such inertial oscillations, we show that the geostrophic oscillation is resonant, and we study the resonance phenomenon. Received 6 June 2000; accepted for publication 22 November 2000     

Divergent channel flow of a liquid crystalline polymer solution

 The flow of a `model' lyotropic liquid crystal polymer, (hydroxypropyl)cellulose in water, through a rectangular channel with a divergence in the channel width, is studied by in situ light microscopy. Microscopic texture observations are related to measurements of the flow velocity field, in order to characterize the shear and elongational aspects of the flow and to examine the effects of the divergence from a narrow channel to a wide channel. A strong dependence of flow-induced texture on position in the channel is observed and is related to the interplay of shear and elongational strain. The divergence generates both a perpendicular elongational strain due to the widening of the channel, and subsequently an elongational strain along the flow direction due to the change in flow pattern from quasi-radial to unidirectional down the wide channel. Additionally side wall structure is observed to be more complex than a simple strong alignment, displaying a fine birefringent texture. Finally there is a marked dependence of the macroscopic structure on the strain history of the fluid prior to entry into the channel, indicating that very different structures of, for instance, moulded parts, can result from differences in geometry and fluid treatment prior to entry into the mould itself. Received: 12 October 1999/Accepted: 29 October 1999     

An analysis of the plane-strain compression of a three-layer strip

Summary  The problem considered here is that of the plane-strain compression of a long symmetric strip of a three-layered material between rigid, parallel, rough plates. Two combinations of layers are examined: (a) a viscoplastic material placed between two layers of a rigid/perfectly plastic material, and (b) a rigid/perfectly plastic material placed between two layers of a viscoplastic material. Closed-form solutions are presented for each combination, and qualitative differences between these solutions and solutions obtained for homogeneous materials are discussed. A possible effect of asymptotic behaviour of the solution in the vicinity of maximum-friction surfaces on the general structure of the solution is mentioned. Received 24 July 2000; accepted for publication 6 February 2001     

Thermal instability of a porous medium with relaxation and inertia in the presence of Hall effects

Summary  The thermal instability of a Rivlin–Ericksen fluid in a porous medium is considered in the presence of a uniform vertical magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has a stabilizing effect on the system, whereas the Hall current has a destabilizing effect on the system. The medium permeability has both stabilizing and destabilizing effects, depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The magnetic field (and corresponding Hall currents) introduces oscillatory modes in the system, which would be nonexistent in their absence. The sufficient conditions for the nonexistence of overstability are also obtained. Received 20 May 1999; accepted for publication 8 March 2000     

The rule of affine similitude for the force coefficients of a body oscillating in a uniformly stratified fluid

 This paper presents a study on affine similitude for the force coefficients of an arbitrary body oscillating in a uniformly stratified fluid. A simple formula is derived that gives a relation between the force coefficients for a body oscillating in homogeneous and uniformly stratified ideal fluids. In particular, it implies the existence of a universal nondimensional similitude criterion for a family of affinely similar bodies, namely, the bodies that can be transformed into each other by vertical dilation of the initial coordinate system. Theoretical results are verified by experiments with a set of spheroids having different length-to-diameter ratios. The experimental technique for evaluation of the frequency-dependent force coefficients is based on Fourier analysis of the time-history of damped oscillation tests. Received: 25 September 2000 / Accepted: 6 July 2001 Published online: 29 November 2001     

A piezoelectric-elastic body with inhomogeneities and a crack under plane electrical and anti-plane mechanical loads

Summary  In this paper, we study a two-dimensional electroelastic problem of an infinite piezoelectric body with two circular piezoelectric inhomogeneities, one of which contains a crack. We formulate the stress intensity factor (SIF) analytically and investigate it numerically. The problem is solved based on Bueckner's principle, and is reduced to a problem of a singular integral equation of the first kind with respect to the distribution function of screw dislocation. The effect of interaction between the two inhomogeneities and the crack on the electroelastic field as well as the control of the SIF by electrical loads is investigated. Received 18 April 2000; accepted for publication 24 October 2000     

Influence of unsteady wake on a turbulent separation bubble

 An experimental study was made of turbulent separated and reattaching flow over a blunt body, where unsteady wake was generated by a spoked-wheel type of wake generator with cylindrical rods. The influence of unsteady wake was scrutinized by altering the rotation direction (clockwise and counter-clockwise) and the normalized passing frequency (0 ≤ St _H  ≤ 0.20). The Reynolds number based on the cylindrical rod was Re _d =375. A phase-averaging technique was employed to characterize the unsteady wake. The effect of different rotation directions, which gave a significant reduction of x _R , was examined in detail. The wall pressure fluctuations on the blunt body were analyzed in terms of the spectrum and the coherence. Received: 15 January 2001 / Accepted: 17 July 2001     

The contact problem of a rubber half-space dented by a rigid cone apex

Summary  The smooth contact of a rubber half-space dented by a rigid cone apex is analyzed based on the large deformation theory. The problem is treated as an axially symmetric case, and the material is assumed to be incompressible. The asymptotic equations for the domain near the apex are derived. They are solved analytically for the shrinking domain, while a numerical solution is found for the expanding domain in the vicinity of the stress singularity. The purpose of this paper is not only to solve a typical problem but also to provide an analytical method to solve a large-strain problem with a singular point. Received 10 July 2001; accepted for publication 24 January 2002     

Generalized thermoelastic analysis of the stress-focusing effect in a solid cylinder under rotationally asymmetrical instantaneous thermal loading

Summary  This paper investigates the stress-focusing effect in an infinitely long cylinder under rotationally asymmetrical instantaneous thermal loading on the basis of the generalized thermoelastic Lord–Shulman (L-S) and Green–Lindsay (G-L) theories. Combined forms of the governing equations of both theories are given in a cylindrical coordinate system. The two-dimensional generalized thermoelastic problems are solved by numerical inversion of Laplace transform. Calculations have been performed to find distributions of thermal stresses on the basis of the L-S theory. Stress-focusing phenomena under different heating conditions are presented. The effects of thermomechanical coupling and relaxation time on the stress-focusing phenomena as well as the singularity of stresses are discussed. Received 15 November 2000; accepted for publication 15 November 2001