scholarly journals On the stability under shearing forces of a flat elastic strip

1924 ◽  
Vol 105 (733) ◽  
pp. 582-607 ◽  
Keyword(s):  
Bending Moment ◽  
Elastic Stability ◽  
Elastic Strip ◽  
Plate Girders ◽  
Uniform Shear ◽  
Transverse Vibrations ◽  
Annular Disc ◽  
The Stability ◽  
Limiting Case ◽  
Total Shear

1. The investigation relates to flat elastic strip, of uniform breadth, thickness and material, upon which a uniform shear is imposed by tangential tractions applied at its edges and in its plane. The tractions appear in the expression for the change of potential energy which occurs when the strip is bent, and they must therefore affect both the modes and the frequencies of its free transverse vibrations. If sufficiently intense, they will bring about a condition of limiting elastic stability, since they can neutralize, in certain types of distortion, the restoring effects of the flexural stresses. The results have some bearing on the stability of the webs of deep plate girders, which take the greater part of the total shear transmitted. The correspondence must not, however, be pressed unduly, because in a girder uniform shear will be accompanied by a varying bending moment which imposes additional stresses upon the web. It is more accurate to describe the sheared strip (of which the length, in this paper, has been assumed to be infinite) as the limiting case either of a narrow annular disc, or of a short tube, subjected to torsion. The similarity of the three problems is illustrated by the specimens shown in fig. 1, which have buckled under conditions of limiting elastic stability.

scholarly journals The elastic stability of a long and slightly bent rectangular plate under uniform shear

1937 ◽  
Vol 162 (908) ◽  
pp. 62-83 ◽  
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Stability ◽  
Stability Problems ◽  
Uniform Shear ◽  
Lines Of Curvature ◽  
The Stability

1—The problem of the elastic stability of a plane rectangular plate when subjected to uniform shear has been approximately solved for various conditions (Cox 1933; Timoshenko 1936). In the case of an indefinitely long strip an exact solution has been found (Southwell and Skan 1924), but it appears that no attempt has been made to investigate what happens if the plate is no longer plane. It is accordingly the object of this paper to consider the stability of a long strip, slightly curved, when its two side edges are subjected to uniform shear. 2—In what follows we assume that the thickness and curvature of the plate are constant, and that the edges of the plate are two generators and two lines of curvature. It is, moreover, further assumed that the plate is thin as in all similar stability problems, and that it is of such length that the boundary conditions over the two curved ends can be ignored.

scholarly journals The effect of flexural–torsional buckling on the stability of timber members: a case study

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Osama A. B. Hassan
Keyword(s):  
Axial Compression ◽  
Bending Moment ◽  
List Type ◽  
Torsional Buckling ◽  
Solution Methods ◽  
Simplified Solution ◽  
The Stability ◽  
Flexural Torsional Buckling ◽  
Building Engineering

Abstract This study investigates the stability of timber members subjected to simultaneously acting axial compression and bending moment, with possible risk for torsional and flexural–torsional buckling. This situation can occur in laterally supported members where one side of the member is braced but the other side is unbraced. In this case, the free side will buckle out of plane while the braced side will be prevented from torsional and flexural–torsional buckling. This problem can be evident for long members in timber-frame structures, which are subjected to high axial compression combined with bending moments in which the member is not sufficiently braced at both sides. This study is based on the design requirement stated in Eurocode 5. Solution methods discussed in this paper can be of interest within the framework of structural and building Engineering practices and education in which the stability of structural elements is investigated. Article Highlights This case study investigates some design situations where the timber member is not sufficiently braced. In this case, a stability problem associated with combined torsional buckling and flexural buckling can arise. The study shows that the torsional and/or flexural–torsional buckling of timber members can be important to control in order to fulfil the criteria of the stability of the member according to Eurocode 5 and help the structural engineer to achieve safer designs. The study investigates also a simplified solution to check the effect of flexural torsional buckling of laterally braced timber members.

scholarly journals The elastic stability of an annular plate

1924 ◽  
Vol 106 (737) ◽  
pp. 268-284 ◽  
Keyword(s):  
Annular Plate ◽  
Practical Interest ◽  
Middle Surface ◽  
Elastic Stability ◽  
Thin Plates ◽  
Thin Shells ◽  
Stability Equation ◽  
Inner Radius ◽  
Plane Plate ◽  
The Stability

1. Introduction and Summary. —This paper deals with the elastic stability of a circular annular plate under uniform shearing forces applied at its edges. Investigations of the stability of plane plates are altogether simpler than those necessary in the case of curved plates or shells. In the first place, as shown by Mr. R. V. Southwell, two of the three equations of stability relate to a mode of instability that is not of practical interest, and are entirely independent of the third equation which gives the ordinary mode of instability resulting in the familiar bending of the middle surface of the plate. Consequently with a plane plate there is only one equation of stability to be solved, as contrasted with the case of a shell where the three equations are dependent, and must all be solved. In the second place the theory of thin shells can be used with confidence in a plane plate problem, though a more laborious procedure is necessary to deal adequately with a shell. The only stability equation required for the annular plate is therefore deduced without trouble from the theory of thin shells, and its solution presents no difficulty in the case of uniform shearing forces. A numerical discussion is given of the stability of the plate under such forces, the “favourite type of distortion” and the stess that will produce it being obtained for plates with clamped edges in wich the ratio of the outer to the inner radius exceeds 3·2. To some extent to results have been checked by experiment, in which part of the work the viter is indebted to Prof. G. I. Taylor for his valuable help and advice. Distrtion of the type predicted by the theory took place in the two thin plates of rober different ratio of radii, which were used. The disposition of the loci of points which undergo maximum normal displace nt gives some idea of the appearance of the plate after distortion has taken pce. The points have been calculated for a plate in which the ratio of radii 4·18, and the loci are shown on a diagram, which may be compared with a potograph of a distorted plate in which this ratio is 4·3. The ratio of normal dplacements of points of the plate can be seen from contours drawn on the ne diagram. (See pp. 280, 281.)

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Characteristics of an Eigensystem Describing the Elastic Stability of a Thin Cantilever Beam

1962 ◽  
Vol 66 (623) ◽  
pp. 722-724 ◽  
Author(s):  
B. Saravanos
Keyword(s):  
Equilibrium Problem ◽  
Cantilever Beam ◽  
Elastic Stability ◽  
Additional Component ◽  
Connecting Rod ◽  
The Stability

The stability of a uniform cantilever beam subjected to an articulated tip load has been analysed as an equilibrium problem of static elastic stability. It was found there that the articulation of the connecting rod applying the tip load introduced additional component forces during the process of beam deformation.

scholarly journals Dynamics and stability of skyrmions in a bended nano-beam

2021 ◽  
Author(s):  
Anruo Zhong ◽  
Xiaoming Lan ◽  
Yangfan Hu ◽  
Biao Wang
Keyword(s):  
Energy Cost ◽  
High Mobility ◽  
Bending Moment ◽  
Elastic Fields ◽  
Spintronic Devices ◽  
Bulk Stress ◽  
The Stability ◽  
Magnetic Skyrmions ◽  
Nontrivial Topology ◽  
A Current

Abstract Magnetic skyrmions are attracting much attention due to their nontrivial topology and high mobility to electric current. Nevertheless, suppression of the skyrmion Hall effect and maintaining high velocity of skyrmions with low energy cost are two major challenges concerning skyrmion-based spintronic devices. Here we show theoretically that in a nano-beam suffering appropriate bending moment, both Bloch-type and Néel-type skyrmions move with a vanishing Hall angle under a current density smaller than that required when the bending is absent. Moreover, bending alone can be used to move skyrmions, whose velocity is solved analytically from the Thiele equation. Generally speaking, inhomogeneous elastic fields affect the stability and dynamics of skyrmions, where the local stability is dominantly determined by the local bulk stress. These findings throw new light on how to drive skyrmions straightly with lower energy cost, which is vital for utilizing skyrmions as information carriers.

Vibrations of Elastic Connecting Rod of a High-Speed Slider-Crank Mechanism

1971 ◽  
Vol 93 (2) ◽  
pp. 636-644 ◽  
Author(s):  
Peter W. Jasinski ◽  
Ho Chong Lee ◽  
George N. Sandor
Keyword(s):  
Small Parameter ◽  
High Speed ◽  
Elastic Stability ◽  
Method Of Averaging ◽  
Connecting Rod ◽  
Transverse Vibrations ◽  
Elastic Bar ◽  
The Moment ◽  
Steady State Solutions ◽  
Crank Mechanism

The research involved in this paper falls into the area of analytical vibrations applied to planar mechanical linkages. Specifically, a study of the vibrations, associated with an elastic connecting-bar for a high-speed slider-crank mechanism, is made. To simplify the mathematical analysis, the vibrations of an externally viscously damped uniform elastic connecting bar is taken to be hinged at each end (i.e., the moment and displacement are assumed to vanish at each end). The equations governing the vibrations of the elastic bar are derived, a small parameter is found, and the solution is developed as an asymptotic expansion in terms of this small parameter with the aid of the Krylov-Bogoliubov method of averaging. The elastic stability is studied and the steady-state solutions for both the longitudinal and transverse vibrations are found.

On A Formulation of the Elastic Stability Equations of Circular Cylindrical Shells Under Variable Internal Pressure

1985 ◽  
Vol 9 (2) ◽  
pp. 64-69
Author(s):  
J.L. Urrutia-Galicia ◽  
A.N. Sherbourne
Keyword(s):  
Mathematical Model ◽  
Internal Pressure ◽  
Cylindrical Shells ◽  
Direct Analysis ◽  
Elastic Stability ◽  
Equilibrium Path ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Variable Internal Pressure ◽  
The Mathematical Model

The mathematical model of the stability analysis of circular cylindrical shells under arbitrary internal pressure is presented. The paper consists of a direct analysis of the equilibrium modes in the neighbourhood of the unperturbed principal equilibrium path. The final stability condition results in a completely symmetric differential operator which is then compared with current theories found in the literature.

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