Thin Circular Ring Research Articles

Effect of Shear and Load Behavior on Ring Stability

The problem of buckling of a thin circular ring under uniform external transverse loading is investigated for the force normal to the deformed ring, the force parallel to its initial direction, and the force directed toward the initial center of curvature. Results are derived through a simple treatment within the framework of thin ring theory and without the assumption of inextensionality. It is assumed that the uniform pressure is applied quasistatically, the material is linearly elastic, and the strains are small while the rotations are moderate. In addition, the effect of transverse shear deformation is included.

Design of Surface Grinding Dynamometers

This paper discusses the application of some basic elastic theory of thin circular rings used as transducers and equations generally used in the design of a surface grinding dynamometer. Octagonal strain rings and their approximation in design application to dynamometers are presented. Examples of calculations are demonstrated. The wiring diagrams of strain gages on the dynamometer are also shown. The calibration setup, curves, and equations of calibration are dealt with. The author has a dual purpose in writing this paper: He wishes to have a record of his design experience for later reference and to share some valuable information with engineers and scientists in the field.

Buckling of thin circular rings under uniform pressure

The twist-buckling of thin rings is investigated. A simple formula for calculating the in-plane buckling of the ring with extensional effects included, is also derived. The load required for twist-buckling is found to be generally less than that for in-plane buckling.

Buckling of radially constrained circular ring under distributed loading

The paper presents first an approximate solution of the static, elastic deformation of a thin circular ring which is constrained in a rigid circular boundary and is acted upon by uniformly distributed loading along a direction in the plane of the ring. The solution is based on the assumption that the detached region is limited to a small portion of the circumference. The result of the solution is represented by a load-deflection curve which indicates the snap-buckling behavior of the ring.The system of nonlinear equation for the exact formulation has also been studied. A systematic iterative scheme is developed for its solution and is applied to a ring ofR/t equal to 100. The result compares favourably with the approximate solution.

Nonlinear Flexural Vibrations of Thin Circular Rings

The nonlinear flexural vibrations of thin circular rings are analyzed by assuming two vibration modes and then applying Galerkin’s procedure on the equations of motion. The results show that vibrations involving either a single bending mode or two coupled bending modes can occur. Theory and experiment both indicate a nonlinearity of the softening type and the existence of these coupled-mode vibrations. Test results for the steady-state response are in good agreement with the calculated values, and the deflection modes used in the analysis agree with the experimental mode shapes. The analytical and experimental results exhibit several features that are characteristic of nonliner vibrations of axisymmetric systems in general and of circular cylindrial shells in particular.

Equilibrium equation for radially loaded thin circular rings

Equilibrium equation for radially loaded thin circular rings

Small vibrations of thin incomplete circular rings

The in-plane inextensional vibrations of an incomplete circular ring of small cross section are studied by means of the classical equations of motion. Natural frequencies and modes are found for rings with clamped ends and subtended angles between 180° and 360°. A solution is given for the problem of an incomplete ring clamped at one end and given a prescribed, time-dependent displacement at the other end.

The Bending of Thin Uniform Circular Rings

IT is known that if a thin circular ring is subjected to a uniform normal loading in its own plane, of amount σ per unit length of circumference, it will become elastically unstable when σ=—3B/R3, σ being taken to be positive when acting outwards. The theory on which this result is based assumes that the cross‐sectional dimensions of the ring and the change in radius are small compared with the initial radius, and is the counterpart of the elementary buckling theory of straight compression members. If the ring is initially perfectly circular it remains so at any numerically smaller value of σ, and it remains circular for any positive value of σ.

Three Interesting Instances of Rocking

(1) Two equal thin circular rings are firmly jointed together at one point so that their planes are inclined to each other. The combination is placed on a rough horizontal plane and made to rock to-and-fro. The period is calculated and confirmed by experiment. Repetition is made with jointed disks. (2a) A right solid cone is suspended by the vertex from a fixed point on a rough vertical plane. It is made to rock through small oscillations. The period is calculated and confirmed by experiment. (2b) A right solid cone results in equilibrium on a rough plane inclined to the horizontal. It is set rocking and the period calculated and confirmed by experiment. Repetition is performed with a thin conical shell. (3) A thin circular ring is placed standing on a rough horizontal plane and leaning against a rough vertical wall. It is set rocking to-and-fro and the period calculated and confirmed by experiment. Repetition is made with leaning disks and wide bands. Variants of (3) are also performed.

Scattering of Electromagnetic Radiation by a Thin Circular Ring in a Circular Wave Guide

The scattering of a TE1, 1 wave by a thin, perfectly conducting circular ring suspended in a circular wave guide with perfectly conducting walls is considered, and approximate expressions are obtained for the scattering cross section, resonance maximum, and half-width as a function of the width of the ring.

LXXXVI.The large deflexions of a thin circular ring

LXXXVI.<i>The large deflexions of a thin circular ring</i>

On the modern development of Faraday's conception of electricity

Thin elastic circular rings can be subject to various loading profiles when used to stiffen long pipes or aboveground cylindrical storage tanks. Specific nonuniform loading profiles have been used by many researchers in theoretical analyses. However, real loading patterns may deviate slightly from the theoretical approximation. The sensitivity of rings to initial imperfections is highlighted in this work. This study investigates the effect of small imperfections in nonuniform loading of the cosine form. A Duffing-type nonlinear differential equation was solved using a perturbation technique to describe the effects of a “follower” loading normal to a ring with large deformations. It is found that the lower buckling mode will govern with the existence of any magnitude of imperfection corresponding to the shape of the fundamental mode.