Deflections and Moments Due to a Concentrated Load on a Cantilever Plate of Infinite Length

1950 ◽  
Vol 17 (1) ◽  
pp. 67-72 ◽  
Author(s):  
T. J. Jaramillo
Keyword(s):  
Constant Width ◽  
Arbitrary Point ◽  
Free Edge ◽  
Practical Significance ◽  
Infinite Length ◽  
Cantilever Plate ◽  
Concentrated Load ◽  
Numerical Examples ◽  
Improper Integrals ◽  
Special Case

Abstract This paper contains an exact solution in terms of improper integrals for the deflections and moments due to a transverse concentrated load acting at an arbitrary point of an infinitely long cantilever plate of constant width and thickness. The solution is transformed into series form by means of contour integration, and is illustrated by numerical examples. In particular, comparisons are made with the known solution (1) for the special case where the load is applied at the free edge of the plate. The results obtained are of practical significance in connection with the design of certain types of monorail cranes.

Cantilever Plate With Concentrated Edge Load

1937 ◽  
Vol 4 (1) ◽  
pp. A8-A10 ◽  
Author(s):  
D. L. Holl
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Finite Length ◽  
Finite Differences ◽  
Free Edge ◽  
Cantilever Plate ◽  
Transverse Stress ◽  
Longitudinal Stress ◽  
Concentrated Load ◽  
Clamped Edge

Abstract The author gives, by the method of finite differences, an approximate solution of the problem of a finite length of a cantilever plate which bears a concentrated load at the longitudinal free edge. All the boundary conditions are taken into account, and the plate action is determined approximately at all points of the plate. The author points out that a secondary maximum transverse stress occurs at the clamped edge nearest the loading point, and that the longitudinal stress is greatest directly under the loading point.

The Uniform Distribution of a Fluid Flowing Through a Perforated Pipe

1950 ◽  
Vol 17 (4) ◽  
pp. 431-438
Author(s):  
Willard M. Dow
Keyword(s):  
Fluid Flow ◽  
High Capacity ◽  
Practical Significance ◽  
Linear Rate ◽  
Gaseous Fuels ◽  
Extended Range ◽  
Flow Through ◽  
Perforated Pipe ◽  
Special Case ◽  
Theoretical Results

Abstract A theoretical analysis is made of the flow through a perforated pipe with a closed end for the special case of a constant linear rate of discharge along the length of the pipe. The results of the fluid-flow considerations are applicable to many practical manifold systems. The practical significance of the results with respect to pipe burners for gaseous fuels is emphasized as the results make possible the design of simple high-capacity and extended-range pipe burners of industrial importance. The capacity of commercially available pipe burners may be increased several hundred per cent. The validity of the theoretical results was verified by experiment.

Acceleration Analysis of Platform-Type Manipulators

1996 ◽  
Author(s):  
Maher G. Mohamed
Keyword(s):  
Stewart Platform ◽  
Algebraic Manipulation ◽  
Analysis Procedure ◽  
Compact Form ◽  
Numerical Examples ◽  
Acceleration Field ◽  
Center Point ◽  
Planar Manipulators ◽  
Acceleration Analysis ◽  
Special Case

Abstract The screw algebra is used to efficiently derive expressions in compact form for both the angular accelerations of the moving links and the linear accelerations of points on the links of platform-type manipulators. The analysis employs the property that the acceleration state of the manipulator platform can be determined by considering the acceleration states of the links of only one — any one — of the manipulator legs. The obtained expressions provide an ease in symbolic and algebraic manipulation. The analysis is then extended to specify the acceleration center point of ithe nstantaneous motion of the manipulator platform. The acceleration center point is then used in expressing the distribution of the acceleration field of the platform instant motion which is important in manipulator synthesis. The special case of planar manipulators is studied and simpler expressions are derived. Numerical examples are presented for the analysis of a 3-DOF planar platform-type and of a 6-DOF spatial “Stewart Platform” manipulators to illustrate the analysis procedure.

scholarly journals Optical axes of catadioptric systems including visual, Purkinje and other nonvisual systems of a heterocentric astigmatic eye

2010 ◽  
Vol 69 (3) ◽  
Author(s):  
W. F. Harris
Keyword(s):  
Visual System ◽  
Optical Axis ◽  
The Other ◽  
Optical Systems ◽  
Numerical Examples ◽  
Straight Line ◽  
Optical Axes ◽  
Catadioptric Systems ◽  
Reflecting Surfaces ◽  
Special Case

For a dioptric system with elements which may be heterocentric and astigmatic an optical axis has been defined to be a straight line along which a ray both enters and emerges from the system.  Previous work shows that the dioptric system may or may not have an optical axis and that, if it does have one, then that optical axis may or may not be unique.  Formulae were derived for the locations of any optical axes.  The purpose of this paper is to extend those results to allow for reflecting surfaces in the system in addition to refracting elements.  Thus the paper locates any optical axes in catadioptric systems (including dioptric systems as a special case).  The reflecting surfaces may be astigmatic and decentred or tilted.  The theory is illustrated by means of numerical examples.  The locations of the optical axes are calculated for seven optical systems associated with a particular heterocentric astigmatic model eye.  The optical systems are the visual system, the four Purkinje systems and two other nonvisual systems of the eye.  The Purkinje systems each have an infinity of optical axes whereas the other nonvisual systems, and the visual system, each have a unique optical axis. (S Afr Optom 2010 69(3) 152-160)

scholarly journals Buckling Of The Stiffened Flange Of The Thin-Walled Member At Longitudinal Stress Variation

2015 ◽  
Vol 61 (3) ◽  
pp. 149-168
Author(s):  
A. Szychowski
Keyword(s):  
Boundary Conditions ◽  
Free Edge ◽  
Cantilever Plate ◽  
Longitudinal Stress ◽  
Stress Variation ◽  
Buckling Modes ◽  
Load Distributions ◽  
Edge Stiffener ◽  
Thin Walled ◽  
Elastically Restrained

AbstractBuckling of the stiffened flange of a thin-walled member is reduced to the buckling analysis of the cantilever plate, elastically restrained against rotation, with the free edge stiffener, which is susceptible to deflection. Longitudinal stress variation is taken into account using a linear function and a 2nd degree parabola. Deflection functions for the plate and the stiffener, adopted in the study, made it possible to model boundary conditions and different buckling modes at the occurrence of longitudinal stress variation. Graphs of buckling coefficients are determined for different load distributions as a function of the elastic restraint coefficient and geometric details of the stiffener. Exemplary buckling modes are presented.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

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.

A Mechanical Model of Helical Elements in Textured Yarns

1976 ◽  
Vol 46 (4) ◽  
pp. 278-283 ◽  
Author(s):  
M. Konopasek
Keyword(s):  
Differential Equations ◽  
Mechanical Model ◽  
Mechanical Characteristics ◽  
Functional Relationship ◽  
Three Dimensional ◽  
Infinite Length ◽  
Fiber Properties ◽  
Helical Angle ◽  
Limiting Case ◽  
Special Case

The helical model of the spontaneously collapsed filaments in twist-textured yarns is defined as reflecting the limiting case of a free-filament segment with infinite length (or number of coils) between two reversal points. The fundamental relationships linking fiber properties and parameters of the texturing process with geometrical and mechanical characteristics of the helices are derived directly from the differential equations of the three-dimensional elastica. Bicomponent and similar fibers are interpreted as a special case of twist-textured filaments with original (permanently set) helical angle equal to π/2; for this case an explicit functional relationship between contraction and stretching force is obtained.

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