Uniaxial-strain wave-propagation experiments using shock-tube loading

A technique for studying uniaxial-strain pulse propagation is discussed. The face of a disk-shaped sample is loaded uniformly with step-function pressure by reflection of a gasdynamic shock wave. The effect of propagation through the sample on the step pulse is observed by use of measurements of the velocity of the sample's rear surface made with a capacitive transducer. Data are presented for several materials. The technique is advantageous for study of pulse dispersion mechanisms such as bulk viscoelasticity and heterogeneous microstructure.     

Some problems for viscoelastic rods

Using an approach proposed in [3],we consider some linear and nonlinear problems forviscoelastic rods.Results in [1]for linear case are affirmed more elamentarily and simplyhere.We also treat linear problem with damping term and nonlinear problem with powernonlinearity Pu~3. Some new results are established.     

Asymptotic theory of wave-propagation

A general method is presented for finding asymptotic solutions of problems in wave-propagation. The method is applicable to linear symmetric-hyperbolic partial differential equations and to the integro-differential equations for the electromagnetic field in a dispersive medium. These equations may involve a large parameter . In the electromagnetic case is a characteristic frequency of the medium. The parameter may also appear in initial data or in the source terms of the equations, in a variety of different ways. This gives rise to a variety of different types of asymptotic solutions. The expansion procedure is a ray method, i.e., all the functions that appear in the expansion satisfy ordinary differential equations along certain space-time curves called rays. In general, these rays do not lie on characteristic surfaces, but may, for example, fill out the interior of a characteristic hypercone. They are associated with an appropriately defined group velocity. In subsequent papers the ray method developed here will be applied to the analysis of transients, Cerenkov radiation, transition radiation, and other phenomena of wave-propagation.An interesting by-product of the ray method is the conclusion, derived in section 6.3, that the theory of relativity imposes no restriction on the speed of energy transport in anisotropic media.This research was supported by the Air Force Cambridge Research Laboratories, Office of Aerospace Research, under Contract No. AF 19(628)4065     

Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier–Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.     

Some critical uniaxial experiments for viscoplasticity at room temperature

An austenitic AISI Type 304 stainless steel, a ferritic A533B pressure vessel steel and a Ti-7Al-2Cb-1Ta alloy were tested using a servocontrolled MTS axial-torsion testing machine. Tests involved changes in strain rate between 10^?8 and 10^?3 s^?1 and intermittent creep periods of less than 1200 s duration.The tests show that inelastic work is not a suitable repository for modeling strain (work)-hardening and the Bauschinger effect is found to be rate dependent. Upon an increase in stress level, creep rate can decrease. This anomaly can be reproduced by a theory of viscoplasticity based on overstress previously proposed by the first author and his co-workers.     

Some comments on the higher order theories of piezoelectric,piezothermoelastic and thermopiezoelectric rods and shells

In this note, the derivations of the higher order, 1-D (or 2-D), theories are discussed for the dynamic analysis of electroelastic (i.e., piezoelectric, piezothermoelastic and thermopiezoelectric) structural elements of uniform cross-section (or uniform thickness). Certain oversights are clarified concerning the higher order theories, including their variational formulation, invariant form and uniqueness of solutions that obscure the availability of earlier contributions in the open literature. In this respect, a higher order theory with some applications by Wu et al. most recently appeared in this journal [Int. J. Solids Struct. 39 (2002) 5325] is mentioned as one of the examples.     

Large elastic deformations in thin rods

Summary In this paper an appropriate analytical treatment for the determination, through exact formulae, of large elastic deformations in thin skew-curved rods is presented. This problem is associated with a system of fifteen nonlinear, ordinary, differential equations of the first order; the unknowns of the system are the final curvature and torsion functions, as well as the generalized internal forces and displacements of the rod. Subsequently, the problem of a thin cantilever circular rod subjected to terminal co-planar forces is examined and closed formulae determining its generalized displacements are obtained. Finally, the effectiveness and the potentialities of the method are demonstrated by several numerical applications.

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Übersicht In diesem Artikel wird eine analytische Methode zur Bestimmung von großen elastischen Verformungen eines schief gekrümmten Stabes durch exakte Formeln entwickelt. Dieses Problem wird durch ein System von fünfzehn nichtlinearen, gewöhnlichen Differentialgleichungen erster Ordnung beschrieben; die Unbekannten des Systems sind sowohl die endlichen Krümmungs- und Torsionsfunktionen als auch die verallgemeinerten inneren Kräfte und Verschiebungen des Stabes. Ferner wird das Problem des dünnen beidseitig gelagerten zylindrischen Stabes, welcher koplanaren Endlasten unterliegt, untersucht, und geschlossene Formeln werden erhalten. Schließlich werden die Effektivität und die Möglichkeiten der Methode durch mehrere numerische Anwendungen dargestellt.

     

Acceleration waves in constrained elastic rods

The problem of the propagation and decay of acceleration waves in nonlinear hyperelastic rods, subject to a general class of constraints, is treated herein. The growth-decay equation, clearly showing the effect of the constraints, is derived for all waves which can propagate in the rod. For a certain class of constraints, general enough to include most of the practical applications, the wave decay equation is found to have the same form as for a rod without constraints, provided the rod is initially at rest.     

Trapped modes in bent elastic rods

We investigate the existence of trapped modes in elastic rods of constant circular cross-section that possess bends of arbitrary curvature and straighten out at infinity; such trapped modes consist of finite energy localized in regions of maximal curvature. An asymptotic model assuming smallness of dimensionless curvature is developed to describe the trapping. Existence conditions depending on Poisson’s ratio are offered, and the equations from which they derive are numerically validated. A physical explanation of why trapped modes should be expected is also given.     

Chiral effects in uniformly loaded rods

Examples of chiral materials include some auxetic materials, bones, some honeycomb structures, as well as composites with inclusions. The chiral effects cannot be described within classical elasticity. In the context of the linear theory of Cosserat elastic solids, we investigate the deformation of a chiral rod subjected to tractions on the lateral surface, to body loads, and to resultant forces and moments on the ends. The work is motivated by the recent interest in the using of the Cosserat elastic solid as model for auxetic composites, carbon nanotubes and bones. The three-dimensional problem is reduced to the study of some generalized plane strain problems. New chiral effects are presented. In the case of cylinders of arbitrary cross-section, the flexure produced by a transversal force, in contrast with the case of achiral materials, is accompanied by extension and bending by terminal couples. The body loads and the tractions on the lateral surface produce extension, flexure, torsion, bending by terminal couples and a plane strain. It is shown that a uniform pressure acting on the lateral surface of a chiral circular cylinder does not produce bending effects.     

Plectoneme formation in twisted fluctuating rods

The mechanics of DNA supercoiling is a subject of crucial importance to uncover the mechanism and kinetics of several enzymes. It is therefore being investigated using several biochemical and biophysical methods including single molecule experimental techniques. An interesting problem within this realm is that of torsional buckling and plectoneme formation in DNA as it is simultaneously put under tensile and torsional stress. Analytical solutions to this problem are difficult to find since it involves nonlinear kinematics and thermal fluctuations. In this paper we use ideas from the Kirchhoff theory of filaments to find semi-analytical solutions for the average shape of the fluctuating DNA under the assumption that there is no self-contact. The basic step in our method consists of combining a helical solution of the rod with a non-planar localizing solution in such a way that the force, moment, position and slope remain continuous everywhere along the rod. Our solutions allow us to predict the extension vs. linking number behavior of long pieces of DNA for various values of the tension and temperature. An interesting outcome of our calculations is the prediction of a sudden change in extension at buckling which does not seem to have been emphasized in earlier theoretical models or experiments. Our predictions are amenable to falsification by recently developed single molecule techniques which can simultaneously track the force-extension as well as the torque-rotation behavior of DNA.     

Wave propagation in prestrained polyethylene rods

The influence of prestrain on the propagation of mechanical waves along a slender rod of low-density unoriented polyethylene was experimentally investigated. The investigation consisted of two major parts: first, a uniaxial continuous-wave technique was used to determine the dynamic mechanical properties of the polyethylene in the form of the frequency-dependent phase velocity and damping factor for frequencies spanning the audio spectrum and for levels of uniaxial static prestrain up to 10 percent. A linear incremental dynamic viscoelastic behavior about a state of finite-static prestrain was shown to obtain over the range of strains and frequencies used. In the second part, the propagation of an incremental strain pulse along a slender rod of the same material used in the first part was investigated. With the rod in a state of static prestrain, an incremental impact-induced strain pulse was introduced into the polyethylene rod and monitored at two positions along the rod. Assuming a linear incremental dynamic viscoelastic behavior of the material, the equations necessary to describe the resulting uniaxial strain as a function of time and position along the rod are presented and the solution obtained by Fourier transform methods. The resulting Fourier inverse transform was numerically evaluated, using the material properties determined in the first part. The strain measured at the first position was used as the input boundary condition for computing the strain at the second position. Results of the continuous-wave studies indicate that the phase velocity decreases and the damping factor increases with increasing prestrain in the range of prestrains used. The change in the phase velocity with prestrain is relatively uniform over the audio-frequency range. Good correlation of the leading edges of the experimentally measured and numerically synthesized strain pulses supports the high-frequency phase-velocity data of the first part.     

Wave propagation in double helical rods

The propagation of waves in helical rods has been studied extensively. However, studying the wave propagation in double helical rods have received less attention although this can be useful in multiple fields of science and engineering. Obtaining an analytical model for a double helical rod is challenging since the curvature and tortuosity are not constant. Thus, resolving the wave behaviour analytically is nearly impossible. In this paper, wave propagation in a double helical rod will be studied using the wave and finite element method which is a technique that can be used to model homogeneous and periodic one and two dimensional structures based on the periodic structure theory. For modelling a double helical rod, the finite element model of a single turn is processed using Bloch waves. The dispersion curves and wavemodes are obtained and the similarities and differences of waves in helical and double helical rods are highlighted.     

Some experiments on the effect of isolated protuberances on flow through tubes

At various locations in the arterial system, plaques, or small relatively isolated protuberances, can develop on the inner wall of the vessel and project into the lumen. A number of investigators have suggested that the development and growth of these protuberances is related to the flow in the vicinity of the protuberance. In this study, the conditions under which the flow separates from an isolated protuberance located in a cylindrical tube were investigated. The critical Reynolds number at which separation first takes place for a given protuberance was determined. A series of tests was performed for steady flow of a Newtonian fluid through a rigid tube in which protuberances of various sizes were inserted. The results of the tests show the effect of the protuberance height and shape on the separation characteristics. In general, the results indicate that separation takes place at relatively small values of the Reynolds number; values that commonly occur in the arterial system, so that this phenomenon may be important in the study of the “coupling” between blood flow and arterial lesions.     

Residual stresses in squeeze-cast aluminum rods

The longitudinal slitting technique has been applied to determining and comparing the residual stresses in as-cast and squeeze-cast aluminum rods. Residual stresses in the squeeze-cast aluminum alloy rods are found to increase with applied punch pressures under a constant die-base thermocouple reference temperature. For the variations of residual stresses with varying die-base thermocouple reference temperatures, a peak residual stress is found to occur at a die-base thermocouple reference temperature of 100° C. A semi-empirical formula is derived for the determination of the maximum longitudinal residual stress in the tapered cylindrical as-cast aluminum alloy, from which the maximum longitudinal residual stresses for squeeze cast can be determined, using the residual-stress ratios obtained experimentally     

Helical traveling waves in elastic rods

We pose the problem on free harmonic bending vibrations of an infinite rotating tubular elastic rod with an internal fluid flow, prestressed by a torque and a longitudinal force. We show that these vibrations can only be realized as traveling circular helical waves. It is shown that, for any wavelength, there exist four waves, two having the form of a left-handed helix and the other two having the form of a right-handed helix. Each of these waves propagates in the positive and negative directions of the longitudinal rod axis at different velocities. These phenomena can manifest themselves in deep-hole drill columns.