Tensioned String Research Articles

Buckling of Columns Subjected to a Central Force Produced by a Tensioned String

The paper is concerned with a new buckling problem of columns subjected to a central force produced by the tension of a string. The central force can be characterized by having a movable center fixed on the deformed axis of a column at its intermediate position. Equilibrium equations of the column, together with the boundary conditions and the conditions of continuity, lead to the characteristic determinant. The characteristic determinant yields the buckling load, and then the buckling mode. If the intermediate center is set at the midspan of the column, the characteristic equation yields a double root. The double root makes buckling mode indeterminate. This fact is an interesting aspect of the present buckling problem. The imperfection method is applied to discuss a possible buckling mode. Experiment of the column was conducted to check the theoretical prediction. The theoretical buckling load and the corresponding buckling modes are compared with the experimental results to find a good agreement between the theory and the experiment.

Moderately large amplitude vibrations of a constant tension string: a numerical experiment

Moderately large amplitude vibrations of a constant tension string: a numerical experiment

Extended Scale Relativity, p-Loop Harmonic Oscillator, and Logarithmic Corrections to the Black Hole Entropy

An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit scales delineating the asymptotic regimes (Planck scale region and a smooth region of a quantum point oscillator). In the most interesting Planck scale regime, the solution recovers in an elementary fashion some basic relations of string theory (including string tension quantization and string uncertainty relation). It is shown that the degeneracy of the first collective excited state of the p-loop oscillator yields not only the well-known Bekenstein–Hawking area-entropy linear relation but also the logarithmic corrections therein. In addition we obtain for any number of dimensions the Hawking temperature, the Schwarschild radius, and the inequalities governing the area of a black hole formed in a fusion of two black holes. One of the interesting results is a demonstration that the evaporation of a black hole is limited by the upper bound on its temperature, the Planck temperature.

Monopoles and strings in noncommutative gauge theory

We study some non-perturbative aspects of noncommutative gauge theories. We find analytic solutions of the equations of motion, for noncommutative U(1) gauge theory, that describe magnetic monopoles with a finite tension string attached. These solutions are non-singular, finite and sourceless. We identify the string with the projection of a D-string ending on a D3-brane in the presence of a constant B-field.

A new system for the measurement of displacements of the human body with widespread applications in human movement studies

This paper reports the development, construction and use of a new system for the measurement of linear kinematics in one, two or three dimensions. The system uses a series of rotary shaft encoders and inelastic tensioned strings to measure the linear displacement of key anatomical points in space. The system is simple, inexpensive, portable, accurate and flexible. It is therefore suitable for inclusion in a variety of motion analysis studies. Details of the construction, calibration and interfacing of the device to an IBM PC computer are given as is a full mathematical description of the appropriate measurement theory for one, two and three dimensions. Examples of the results obtained from the device during gait, running, rising to stand, sitting down and pointing with the upper limb are given. Finally it is proposed that, provided the constraints of the system are considered, this method has the potential to measure a variety of functional human movements simply and inexpensively and may therefore be a valuable addition to the methods available to the motion scientist.

Measurement of Restitution Behavior of Strings and Rigid Body.

The relationship between restitution behavior of strings and its mechanical properties was measured and discussed. An impact test device that could control the initial tension and impact velocity on speed area of less than 10 m/s was developed for measuring the restitution behavior of hammer and tensioned strings. About this device, influence to the measurement results of mass and materials of the hamnler and slipping on the clamps was examined. Using this device, restitution behavior of tennis strings was measured. A dynamic restitution model considering tensile viscoelasticity of materials was suggested with approximating it by Voigt model. The restitution behavior was simulated by numerical computation. In experimental range for all samples, coefficient of restitution increases with initial tension and decreases with initial velocity, and when the mass of a hammer is small, the coefficient becomes big. The calculation results of the model could show the tendency of experimental results well.

高張力ロッドを用いたテンション構造のシステム化に関する研究

Although cables are most popular as material, steel rods are also used as tensile members in tension structures for long time in history. In this paper, required quality for the tension strings and their connections are discussed by defining tension structures as structural-system hierarchy composed of various levels of elements. Their required quality items are chosen through historical review including bridges and glass wall structures, and through their hierarchical studies using parabolic tension elements defined as sub-systems. Several type of connections for high-strength tension rods are proposed and selected for satisfying these requirements, followed by application for practical projects.

A static drilling riser model using free boundary conditions

A static three-dimensional analytical method for drilling risers experiencing large displacements and slip at the top joint is presented. The riser is described in cylindrical coordinates as a three-dimensional tensioned string, without bending or torsional stiffness. The vertical vessel displacement is not taken into account. The equilibrium configuration is obtained from the stationary condition of the total potential energy functional. Kinematic boundary conditions are introduced for the radial displacement only. The riser orientation at the top directly follows from the natural boundary conditions based on the variational treatment of the energy functional.

VIBRATION SUPPRESSION BY USING SELF-ARRANGING MASS: EFFECTS OF ADDING RESTORING FORCE

The potential of using self-arranging sliding mass for vibration damping is considered. Earlier studies have demonstrated the effect of freely sliding mass: vibrations of a structure may decrease when forces of non-linear interaction cause a mass to slide along it. However, when the mass stops sliding at an equilibrium point, a new resonance frequency is created that cannot be damped by further sliding. This study suggests adding passive restoring forces for returning the mass to a prescribed position at small levels of vibration. The effect of this is considered numerically and analytically for a simple study case: a spring-loaded point mass sliding on a tensioned string. The arrangement is shown to damp resonant vibrations, although the damped response may, under certain conditions, be beating or chaotic. Frequency responses are derived analytically for a number of cases, including slow frequency-sweeps across resonance. The suggested device is shown to limit vibrations due to parametric resonance. Sliding mass tends to be most effective in damping high amplitudes, thus complementing other passive or active control strategies that are typically most effective at low amplitudes.

Piano escapement action

An escapement action (200) for a piano includes a hammershank (132) having a first end mounted to pivot relative to the piano and a second end carrying a hammer (130) to strike a tensioned string (140) of the piano, with a knuckle (150) disposed therealong between the first and second ends. A repetition support (110) bearing against a key (102) of the piano is mounted to pivot relative to the piano in response to depression of the key (102). A jack (120) has a first portion extending from a pivot connection (121) with the repetition support and defines a jack surface disposed for engagement with a knuckle (150) surface, the jack (120) arranged for escape of the jack surface from engagement with the knuckle surface during depression of the key (102). A spring (160) urges the jack toward an "at rest" position with the jack surface in engagement with the knuckle surface. A jack retainer assembly (204) dependent from the hammershank (132) between the second end and the knuckle includes a cushion surface (210) positioned to retain the jack (120) in "at rest" position in opposition to force of the spring.

The response of a non-uniformly tensioned circular string to a moving load

Abstract A non-uniformly tensioned circular string on a damped elastic foundation is acted upon by a moving concentrated load. This configuration can be viewed as a very simplified representation of a spinning rectangularly orthotropic disk acted upon by a spatially fixed force, or of a stationary orthotropic disk subjected to a circumferentially moving load. The natural frequencies and normal modes of vibration of the string on elastic foundation are determined for a range of values of the tension inhomogeneity. The response of the string to a moving load is then determined. The results indicate that there are many speeds, below the critical speed of the uniformly tensioned string, for which the forced response is large. It is anticipated that the response of this simple model to a moving load can provide insight into the behavior of the mathematically more complicated rectangularly orthotropic circular disk.

Free And Forced Response Of An Axially Moving String Transporting A Damped Linear Oscillator

The transverse response of a cable transport system, which is modelled as an ideal, constant tension string travelling at constant speed between two supports with a damped linear oscillator attached to it, is predicted for arbitrary initial conditions, external forces and boundary excitations. The exact formulation of the coupled system reduces to a single integral equation of Volterra type governing the interaction force between the string and the payload oscillator. The time history of the interaction force is discontinuous for non-vanishing damping of the oscillator. These discontinuities occur at the instants when transverse wavefronts propagating along the string interact with the oscillator. The discontinuities are treated using the theory of distributions. Numerical algorithms for computing the integrals involving generalized functions and for solution of the delay-integro-differential equation are developed. The response analysis shows a discontinuous velocity history of the payload attachment point. Special conditions leading to absence of the above discontinuities are given.

String solutions with finite tension strings in SU(2) gauge theory

We extend recent work on string solutions within the SU(2) Higgs model by showing that another class of solutions exists with equally interesting properties: the tension is finite and the string posseses plus one unit of flux.

Finite tension strings in SU(2) gauge theory

The second-order field equations of the SU(2) Higgs model are studied and a new class of string solutions is obtained. The tension is finite and scale-dependent and the strings are of minus one unit flux.

A Model Analysis of Tire Behavior Under Vertical Loading and Straight-Line Free Rolling

Abstract A structural analog, consisting of a flexible circular ring under tension with a nest of radially arranged linear springs and dampers, is developed as a pneumatic tire model. The model is concerned with the prediction of the tire's vertical load-deflection characteristics and its free rolling resistance. The mathematical formulation of the boundary of the model's region of contact with a smooth hard surface is based on approximations made using the theory of a tensioned string supported by an elastic foundation. Forces developed within the contact region are computed from geometrical considerations. The model's ring tension and radial foundation stiffnesses, as related to the tire's inflation pressure, are obtained experimentally by performing contact patch length measurements and static point-load tests on the specific tire modeled. Further, by prescribing a loss factor in the radial dampers, the model's free rolling resistance characteristics may be computed. Experimental verification conducted on a radial tire shows general agreement between the predicted and experimental vertical load-deflection characteristics for the normal working range of inflation pressure, deflection, and interacting surface curvature. The predicted rolling resistance characteristics are also found to be in good accord with experimental measurements.

Forced transverse vibrations of a submerged tensioned string

For a submerged cable, the classical equation of a vibrating string must be modified to account for added mass and damping effects. This can be done with the aid of Morison's formulae. The resulting equation is non-linear. It is solved for the case when one end of the string is forced into sinusoidal transverse motion. The first harmonic approximations for both resonant and non-resonant responses are obtained by the method of matched asymptotic expansions under the assumption that the non-dimensional damping coefficient is small.

Tension string structure for planetary entry vehicles.

This paper provides a brief description and analysis of a new ultralightweight, high-drag concept for the construction of planetary entry vehicles. This concept employs structural principles similar to those used in suspension bridges or bicycle wheel design: high-strength filamentary strings in pure tension, a central support member, and an equatorial ring that is stabilized against buckling by the forebody and afterbody strings. Preliminary designs and a manufacturing technique have been developed, and 12-in.-diam models have been constructed from trilene monofilaments with plexiglass rings and central supports. Tradeoff studies suggest that the following materials might be best for flight vehicles: strings of S glass yarn (Owens Corning Fiberglas Corp.), a toroidal ring of aluminum, and a central support of aluminum honeycomb sandwich. The negative Gaussian curvature of the axisymmetric forebody should provide aerodynamic characteristics between those of the sphere-cone and the Langley tension shell. An elastomeric material can be applied to the forebody strings to form a heat shield. Further work on this concept appears to be warranted.

Large-Amplitude Linear Vibrations of Tensioned Strings

The transverse motion of a tensioned string driven parametrically by a moving end support is examined both analytically and experimentally. The conditions required to linearize the equations of motion for vibrations over a large-amplitude range at constant frequency are developed and shown to be physically realizable.

Pantograph motion on a nearly uniform railway overhead line

Representing the line by a tensioned string supported by an elastic medium, whose spring constant varies periodically with position by a small amount, a mathematical investigation is made into the oscillations of overhead equipment produced by the passage of a pantograph. The simplicity of the representation allows analytical results to be obtained for a pantograph whose impedance is of quite general type. For the pantograph in current use, the analysis shows how the oscillations increase at certain critical speeds and how these speeds, and the magnitude of the oscillations, depend on the parameters of the pantograph/line combination.

Construction Aspects of the Pinard-Hanmer 500-Kv Transmission Line

This paper describes construction aspects of the northern 228 miles of Ontario Hydro's new 437-mile 500-kv EHV (extra-high-voltage) bundle conductor transmission line. Because of rigid specifications and new design features, new construction practices had to be developed in many areas, particularly foundation construction, tower erection, and the tension stringing of a 4-conductor bundle.