Fiber Remodeling During Torsion of a Fiber Reinforced Hyperelastic Cylinder��Unloading Behavior

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.     

Application of the γ-Reθ Transition Model to Simulations of the Flow Past a Circular Cylinder

Based on the finite volume method, the flow past a two-dimensional circular cylinder at a critical Reynolds number (Re = 8.5 × 10⁵) was simulated using the Navier-Stokes equations and the γ-Re_θ transition model coupled with the SST k ? ω turbulence model (hereinafter abbreviated as γ-Re_θ model). Considering the effect of free-stream turbulence intensity decay, the SST k ? ω turbulence model was modified according to the ambient source term method proposed by Spalart and Rumsey, and then the modified SST k ? ω turbulence model is coupled with the γ-Re_θ transition model (hereinafter abbreviated as γ-Re_θ-SR model). The flow past a circular cylinder at different inlet turbulence intensities were simulated by the γ-Re_θ-SR model. At last, the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers were each simulated by the γ-Re_θ-SR model, and the three flow states were analyzed. It was found that compared with the SST k ? ω turbulence model, the γ-Re_θ model could simulate the transition of laminar to turbulent, resulting in better consistency with experimental result. Compared with the γ-Re_θ model, for relatively high inlet turbulence intensities, the γ-Re_θ-SR model could better simulate the flow past a circular cylinder; however the improvement almost diminished for relatively low inlet turbulence intensities The γ-Re_θ-SR model could well simulate the flow past a circular cylinder at subcritical, critical and supercritical Reynolds numbers.     

Exact Solution of the Wave‐Resistance Problem for a Submerged Cylinder. I. Linearized Theory

. We consider the problem of finding a holomorphic function in a strip with a cut ${\cal A}= \{(x,y) : \, x\in\RE,\,\,0 satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for $|x|\to\infty. We consider the problem of finding a holomorphic function in a strip with a cut satisfying some prescribed linear conditions on the boundary. The problem has a one‐parameter family of solutions in the class of sectionally holomorphic functions in ?, vanishing for . A special solution can be selected by fixing the value of the circulation around the cut. The problem is obtained by linearization of the equations of the wave‐resistance problem for a “slender” cylinder submerged in a heavy fluid and moving at uniform speed in the direction orthogonal to its generators. The results obtained, besides their own interest, are a crucial step for the resolution of the non‐linear problem. (Accepted October 14, 1998)     

Existence of a Weak Solution to a Nonlinear Fluid–Structure Interaction Problem Modeling the Flow of an Incompressible, Viscous Fluid in a Cylinder with Deformable Walls

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier–Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid–structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916–6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk–Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.     

Exact Solution of the Wave‐Resistance Problem for a Submerged Cylinder. II. The Non‐linear Problem

. We study the problem of wave resistance for a “slender” cylinder submerged in a heavy fluid of finite depth with the cylinder moving at uniform supercritical speed in the direction orthogonal to its generators. We look for a divergence‐free, irrotational flow; the boundary of the region occupied by the fluid (consisting of the free surface, the bottom and the obstacle profile) is assumed to belong to streamlines and the Bernoulli condition is taken on the free surface. The problem is transformed, via the hodograph map, into a problem set in a strip with a cut. By using a “hard” version of the inverse function theorem and by taking account of the results obtained in Part I (which we recall here), we prove the existence of a complex velocity function satisfying all the requirements of the problem. In particular, this function is continuous up to the surface of the obstacle, and the only possible singularities appear at the end‐points where the boundary is not smooth. Moreover, two stagnation points appear near to the extremities of the submerged body. (Accepted October 14, 1998)     

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

Can a monkey with a computer create art?

A computer can be programmed to search through the solution of millions of equations to find a few hundred whose graphical display is aesthetically pleasing to humans. This paper describes some methods for performing such an exhaustive search, criteria for automatically judging aesthetic appeal, and examples of the results.     

Flow of a Viscoplastic Fluid on a Rotating Disk

ＦＬＯＷＯＦＡＶＩＳＣＯＰＬＡＳＴＩＣＦＬＵＩＤＯＮＡＲＯＴＡＴＩＮＧＤＩＳＫＦａｎＣｈｕｎ（范椿）（ＩｎｓｔｉｕｉｅｏｆＭｅｃｈａｎｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ）（ＲｅｃｅｉｖｅｄＮｏｖ．２０，１９９２；Ｃｏｍｍｕｎｉｃａｔ...     

Flexural-wave-generation using a phononic crystal with a piezoelectric defect

This paper proposes a method to amplify the performance of a flexural-wave-generation system by utilizing the energy-localization characteristics of a phononic crystal(PnC) with a piezoelectric defect and an analytical approach that accelerates the predictions of such wave-generation performance. The proposed analytical model is based on the Euler-Bernoulli beam theory. The proposed analytical approach, inspired by the transfer matrix and S-parameter methods, is used to perform band-structure an...     

Stability and Self‐Oscillations of a Rotor Containing a Conducting Liquid in a Magnetic Field

This paper considers the problem of the stability in the small of the steadystate spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the buttend boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was Dpartitioned into regions with different degrees of instability is constructed. Steadystate spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steadystate spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steadystate spinning can be subcritical or supercritical.     

Oscillations of a?beam with a?time-varying mass

This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well.     

Nonlinear analysis of a structure loaded by a stochastic excitation

For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.     

Dynamical response of a pendulum driven horizontally by a DC motor with a slider–crank mechanism

Nonlinear Dynamics - The pendulum is excited horizontally by a system of a DC motor and a slider–crank mechanism. Mathematical modeling is realistic and based on experimental rig, taking into...     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Entrance of a body with a lifting force and a heat‐conducting surface into the earth's atmosphere

The problem of gliding descent of a smooth blunted body possessing a lifting force and a heatconducting surface in the Earth's atmosphere is solved. The descent trajectory is represented not only by the altitude and velocity as functions of the flight time but also by angles of attack and sideslip varying with time. Threedimensional equations of a parabolized viscous shock layer for a multispecies mixture of gases are solved jointly with a threedimensional equation of unsteady heat conduction in the solid phase.     

Paradox of a particle’s trajectory moving on a string

This paper deals with the paradoxical properties of the solution of string vibration under a moving mass. The solutions published to date are not simple enough and cannot be applied to investigations in the entire range of mass speeds, including the overcritical range. We propose a formulation of the problem that allows us to reduce the problem to a second-order matrix differential equation. Its solution is characteristic of all features of the critical, subcritical, and overcritical motion. Results exhibit discontinuity of the mass trajectory at the end support point, which has not been previously reported in the literature. The closed solution in the case of a massless string is analyzed and the discontinuity is proved. Numerical results obtained for an inertial string demonstrate similar features. Small vibrations are analyzed, which is why the effect discussed in the paper is of purely mathematical interest. However, the phenomenon results in complexity in discrete solutions.     

Resonance Waves in a Model of a Two‐Layered Liquid

With allowance for surface interaction between phases, the behavior of longwave perturbations at the interface between two layers of dissimilar liquids, which form resonance triplets described by a pseudodifferential equation, is studied.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Darcy–Brinkman–Forchheimer Porous Medium

We investigate in this article, the fully developed flow in a fluid-saturated channel filled with a Darcy–Brinkman–Forchheimer porous medium, which is conducted with an electrically varying parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. With the homotopy analysis method (HAM), a particularly effective technique in solving nonlinear problems, analytical approximation series solutions with high accuracy are derived for fluid velocity and the results are illustrated in form of figures. All these flows are new and are presented for the first time in the literature.     

Generalization of Joukowski’s Solution for a Bubble in a Channel

Fluid Dynamics - A new exact solution for the problem of potential flow of a capillary fluid past a two-dimensional bubble in a rectilinear channel is derived; the solution generalizes the known...