scholarly journals Instability of Cylindrical Shells Subjected to Axisymmetric Moving Loads

1966 ◽  
Vol 33 (2) ◽  
pp. 289-296 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Cylindrical Shell ◽  
Constant Velocity ◽  
Broad Class ◽  
Infinite Length ◽  
Functional Difference ◽  
Moving Loads ◽  
Loading Function ◽  
Double Laplace Transform ◽  
Special Cases ◽  
The Stability

Using a Donnell-type nonlinear theory and the stability in the small concept of Poincare´, the instability of an infinite-length cylindrical shell subjected to a broad class of axisymmetric loads moving with constant velocity is studied. Special cases of the general loading function include the moving-ring, step, and decayed-step loads. The analysis is carried out with a double Laplace transform, functional-difference technique. Numerical results are presented for the case of the moving-ring load.

Stability of Cylindrical Shells Under Moving Loads by the Direct Method of Liapunov

1967 ◽  
Vol 34 (4) ◽  
pp. 991-998 ◽  
Author(s):  
G. A. Hegemier
Keyword(s):  
Constant Velocity ◽  
Local Stability ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Functional Space ◽  
Moving Loads ◽  
The Stability ◽  
Shell Axis

The stability of a long, thin, elastic circular cylindrical shell subjected to axial compression and an axisymmetric load moving with constant velocity along the shell axis is studied. With the aid of the direct method of Liapunov, and employing a nonlinear Donnell-type shell theory, sufficient conditions for local stability of the axisymmetric response are established in a functional space whose metric is defined in an average sense. Numerical results, which are presented for the case of a moving decayed step load, reveal that the sufficient conditions for stability developed here and the sufficient conditions for instability obtained in a previous paper lead to the actual stability transition boundary.

Response of Cylindrical Shells to Moving Loads

1964 ◽  
Vol 31 (1) ◽  
pp. 105-111 ◽  
Author(s):  
J. P. Jones ◽  
P. G. Bhuta
Keyword(s):  
Cylindrical Shell ◽  
Constant Velocity ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Moving Loads ◽  
Coupling Effects ◽  
Influence Coefficients ◽  
Pressure Pulses

The response of a circular cylindrical shell subjected to a moving ring load with a constant velocity has been examined in detail when both longitudinal and transverse coupling effects are included. It is found that the correction in the bending resonance velocity resulting from the inclusion of longitudinal coupling effects is small. The results of the analysis may be used as influence coefficients to determine, by means of Duhamel integrals, the displacements and stresses produced by varying pressure pulses.

scholarly journals On a Generalization of One-Dimensional Kinetics

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1264
Author(s):  
Vladimir V. Uchaikin ◽  
Renat T. Sibatov ◽  
Dmitry N. Bezbatko
Keyword(s):  
Exact Solution ◽  
Asymptotic Behavior ◽  
Constant Velocity ◽  
Telegraph Equation ◽  
Material Derivative ◽  
Symmetric Random Walk ◽  
One Dimensional ◽  
Special Cases ◽  
Fractional Telegraph Equation ◽  
Asymmetric Case

One-dimensional random walks with a constant velocity between scattering are considered. The exact solution is expressed in terms of multiple convolutions of path-distributions assumed to be different for positive and negative directions of the walk axis. Several special cases are considered when the convolutions are expressed in explicit form. As a particular case, the solution of A. S. Monin for a symmetric random walk with exponential path distribution and its generalization to the asymmetric case are obtained. Solution of fractional telegraph equation with the fractional material derivative is presented. Asymptotic behavior of its solution for an asymmetric case is provided.

Light-Induced Metastable Defects in a-Si:H: Towards an Understanding

1985 ◽  
Vol 49 ◽  
Author(s):  
Martin Stutzmann ◽  
Warren B. Jackson ◽  
Chuang Chuang Tsai
Keyword(s):  
Amorphous Silicon ◽  
Mechanical Stress ◽  
Hydrogenated Amorphous Silicon ◽  
Material Parameters ◽  
Kinetic Behaviour ◽  
Proposed Model ◽  
Special Cases ◽  
The Stability ◽  
Hydrogenated Amorphous

AbstractThe dependence of the creation and the annealing of metastable dangling bonds in hydrogenated amorphous silicon on various material parameters will be discussed in the context of a recently proposed model. After a brief review of the kinetic behaviour governing defect creation and annealing in undoped a- Si:H, a number of special cases will be analyzed: the influence of alloying with O, N, C, and Ge, changes introduced by doping and compensation, and the role of mechanical stress. Finally, possibilities to increase the stability of a-Si:H based devices will be examined.

The Behavior of Long Beams Under Impact Loading

1950 ◽  
Vol 17 (1) ◽  
pp. 27-34
Author(s):  
P. E. Duwez ◽  
D. S. Clark ◽  
H. F. Bohnenblust
Keyword(s):  
Plastic Deformation ◽  
Cross Sections ◽  
Constant Velocity ◽  
Bending Moment ◽  
Infinite Length ◽  
Longitudinal Impact ◽  
Deflection Curve ◽  
Transverse Impact ◽  
Cold Rolled ◽  
Annealed Copper

Abstract This paper presents the results of a theoretical and experimental investigation of the plastic deformation of long beams which are subjected to a concentrated transverse impact of constant velocity. In the theoretical analysis, the beam is supposed to be of infinite length, and plane cross sections are assumed to remain plane. The bending moment is assumed to depend on the curvature according to a function that is obtained from the stress-strain curve of the material. The theory neglects both the lateral displacement of the cross sections against each other due to the shearing force and the rotary kinetic energy of the motion of the beam. The theory shows that a strain is not propagated along a beam at constant velocity, as in the case of longitudinal impact. The strain depends on the ratio between the square of the distance from the point of impact and the time. This is correct regardless of the shape of the moment - curvature curve. If certain approximations are applied to the bending moment - curvature curve, the theory provides a method of computing the deflection curve of a beam at any instant during impact. An experimental study has been made in which the deflection curves of long simply supported beams have been obtained during impact. The deflection characteristics of a cold-rolled steel and an annealed-copper beam have been computed by approximating the bending moment - curvature curves. It is shown that for materials such as cold-rolled low-carbon steel, for which plastic deflection is localized at the point of impact, the observed deflection curve is closely approximated by computing a curve based on the assumption that the beam remains elastic. For a soft material like annealed copper, plastic deformation extends over a relatively large distance from the point of impact and, taking plastic deformation into account, a satisfactory agreement is obtained between theory and experimental results.

scholarly journals Final coalgebras as greatest fixed points in ZF set theory

1999 ◽  
Vol 9 (5) ◽  
pp. 545-567 ◽  
Author(s):  
LAWRENCE C. PAULSON
Keyword(s):  
Fixed Points ◽  
Set Theory ◽  
Theorem Prover ◽  
Infinite Length ◽  
Special Cases ◽  
Definition Of ◽  
Recursive Definitions ◽  
Ordered Pairs

A special final coalgebra theorem, in the style of Aczel (1988), is proved within standard Zermelo–Fraenkel set theory. Aczel's Anti-Foundation Axiom is replaced by a variant definition of function that admits non-well-founded constructions. Variant ordered pairs and tuples, of possibly infinite length, are special cases of variant functions. Analogues of Aczel's solution and substitution lemmas are proved in the style of Rutten and Turi (1993). The approach is less general than Aczel's, but the treatment of non-well-founded objects is simple and concrete. The final coalgebra of a functor is its greatest fixedpoint.Compared with previous work (Paulson, 1995a), iterated substitutions and solutions are considered, as well as final coalgebras defined with respect to parameters. The disjoint sum construction is replaced by a smoother treatment of urelements that simplifies many of the derivations.The theory facilitates machine implementation of recursive definitions by letting both inductive and coinductive definitions be represented as fixed points. It has already been applied to the theorem prover Isabelle (Paulson, 1994).

Mathematical aspects of trapping modes in the theory of surface waves

1987 ◽  
Vol 183 ◽  
pp. 421-437 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Bound States ◽  
Constant Width ◽  
Minimum Energy ◽  
Horizontal Cylinder ◽  
Linear Operators ◽  
Inviscid Fluid ◽  
Infinite Length ◽  
Horizontal Canal ◽  
Special Cases ◽  
Characteristic Modes

A horizontal canal of infinite length and of constant width and depth contains inviscid fluid under gravity. The fluid is bounded internally by a submerged horizontal cylinder which extends right across the canal and has its generators normal to the sidewalls. Suppose that the fluid is set in motion by a surface pressure varying across the canal, then some of the energy is radiated to infinity while some of the energy is trapped in characteristic modes (bound states) near the cylinder. The existence of trapping modes in special cases was shown by Stokes (1846) and Ursell (1951); a general treatment, given by Jones (1953), is based on the theory of elliptic partial differential equations in unbounded domains. In the present paper a much simpler treatment is given which uses only the theory of bounded symmetric linear operators together with Kelvin's minimum-energy theorem of classical hydrodynamics.

scholarly journals Revisiting the stability of quadratic Poincaré gauge gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Jose Beltrán Jiménez ◽  
Francisco José Maldonado Torralba
Keyword(s):  
Effective Action ◽  
Gauge Theories ◽  
Homogeneous Part ◽  
Scalar Theory ◽  
Poincare Group ◽  
Additional Dimension ◽  
Special Cases ◽  
The Stability ◽  
Gauge Gravity ◽  
Two Sectors

Abstract Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence of these pathological couplings results in a theory where either the axial sector or the torsion trace becomes a ghost. We conclude that imposing ghost-freedom generically leads to a non-dynamical torsion. We analyse however two special choices of parameters that allow a dynamical scalar in the torsion and obtain the corresponding effective action where the dynamics of the scalar is apparent. These special cases are shown to be equivalent to a generalised Brans–Dicke theory and a Holst Lagrangian with a dynamical Barbero–Immirzi pseudoscalar field respectively. The two sectors can co-exist giving a bi-scalar theory. Finally, we discuss how the ghost nature of the vector sector can be avoided by including additional dimension four operators.

scholarly journals Structure and Uncertainty in Discrete Choice Models

2003 ◽  
Vol 11 (4) ◽  
pp. 316-344 ◽  
Author(s):  
Curtis S. Signorino
Keyword(s):  
Discrete Choice ◽  
Private Information ◽  
Statistical Models ◽  
Broad Class ◽  
Choice Models ◽  
Discrete Choice Models ◽  
Social Scientists ◽  
Sources Of Uncertainty ◽  
Special Cases

Social scientists are often confronted with theories in which one or more actors make choices over a discrete set of options. In this article, I generalize a broad class of statistical discrete choice models, with both well-known and new nonstrategic and strategic special cases. I demonstrate how to derive statistical models from theoretical discrete choice models and, in doing so, I address the statistical implications of three sources of uncertainty: agent error, private information about payoffs, and regressor error. For strategic and some nonstrategic choice models, the three types of uncertainty produce different statistical models. In these cases, misspecifying the type of uncertainty leads to biased and inconsistent estimates, and to incorrect inferences based on estimated probabilities.

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