The Dynamics of Impulsively and Randomly Varying Systems

1963 ◽  
Vol 30 (1) ◽  
pp. 25-30 ◽  
Author(s):  
J. C. Samuels
Keyword(s):  
Cylindrical Shell ◽  
Integral Equations ◽  
Multiple Scattering ◽  
Critical Level ◽  
Circular Cylindrical Shell ◽  
Mean Square ◽  
The Mean ◽  
Light Integral ◽  
Multiple Scattering Of Light ◽  
Mean Square Solution

By a method, related somewhat to a technique used in the theory of he multiple scattering of light, integral equations are derived for the mean and mean-square solution of systems undergoing random changes. These equations are in essential agreement with similar equations derived elsewhere in the literature by completely different methods. The theory developed herein is applied to the analysis of a circular cylindrical shell under random end thrusts. It is found that the shell buckles when the mean-square value of the fluctuation of the end thrusts exceeds a certain critical level determined by damping.

Correlation Parameters for Eliminating the Effect of Pulse Shape on Dynamic Plastic Deformation

1970 ◽  
Vol 37 (3) ◽  
pp. 744-752 ◽  
Author(s):  
C. K. Youngdahl
Keyword(s):  
Plastic Deformation ◽  
Cylindrical Shell ◽  
Pulse Shape ◽  
Circular Cylindrical Shell ◽  
Strong Dependence ◽  
Uniform Pressure ◽  
Concentrated Force ◽  
Total Impulse ◽  
The Mean ◽  
Mean Time

The solutions to four classical problems in dynamic plasticity—the circular plate under uniform pressure, the reinforced circular cylindrical shell under uniform pressure, the free-free beam with a central concentrated force, and the circular cylindrical shell with a ring load—are examined to determine the effect of pulse shape on final plastic deformation. It is found that there is a strong dependence on pulse shape for pulses which have the same total impulse and maximum load; however, the effect of the pulse shape is virtually eliminated if the pulses have the same total impulse and “effective load.” The “effective load” is defined as the impulse divided by twice the mean time of the pulse, where the mean time is the interval between the onset of plastic deformation and the centroid of the pulse.

scholarly journals Linear filtering with fractional Brownian motion in the signal and observation processes

1999 ◽  
Vol 12 (1) ◽  
pp. 85-90 ◽  
Author(s):  
M. L. Kleptsyna ◽  
P. E. Kloeden ◽  
V. V. Anh
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Wiener Process ◽  
Integral Equations ◽  
Hurst Index ◽  
Mean Square ◽  
Linear Filtering ◽  
Observation Process ◽  
The Mean ◽  
Filtering Problem

Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1) and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process.

VII.—Some Contributions to the Theory of Random Walk and Multiple Scattering of Particles

1971 ◽  
Vol 69 (2) ◽  
pp. 115-124
Author(s):  
A. J. Allnutt ◽  
R. Fürth
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Multiple Scattering ◽  
Three Dimensional ◽  
Mean Square ◽  
Cubic Lattice ◽  
First Approximation ◽  
The Mean ◽  
Random Walk Theory ◽  
Lateral Displacements

SynopsisA theory of the random walk with “persistence” of movement of a point in a three-dimensional cubic lattice is presented from which explicit expressions for the moments of the distribution function for the displacements of an ensemble of points after N steps for any arbitrary initial average velocity are derived. The results are applied to the problem of small angle multiple scattering of particles on their passage through a material medium, and formulae for the mean square of the lateral displacements are obtained which, in first approximation, have the form of the expressions, generally used for evaluating the experimental results but, in higher approximation, indicate a deviation from this relationship for greater thickness of matter.Another approach to the same problem of multiple scattering is further presented which is based on Kramer's stochastic differential equation for the distribution function for the position and velocities of an ensemble of particles in phase space. By this method formulae for the mean square of the scatter angles, the lateral displacements and the correlation products between these are derived. The first of these expressions shows again characteristic deviations from the usual ones for greater thickness of matter, the second coincides essentially with the expression obtained from the random walk theory.

Wide-Band Random Axisymmetric Vibration of Cylindrical Shells

1979 ◽  
Vol 46 (2) ◽  
pp. 417-422 ◽  
Author(s):  
I. Elishakoff ◽  
A. Th. van Zanten ◽  
S. H. Crandall
Keyword(s):  
Circular Cylindrical Shell ◽  
Time History ◽  
Wide Band ◽  
Axisymmetric Vibration ◽  
Mean Square ◽  
Mean Square Response ◽  
History Of ◽  
Cross Correlations ◽  
The Mean ◽  
Band Limited

Analytical and numerical results are reported for the random vibrations of a uniform circular cylindrical shell excited by a ring load which is uniform around the circumference and random in time. The time history of loading is taken to be a stationary wide-band random process. The shell response is essentially one-dimensional but differs qualitatively and quantitatively from the response distributions for point-excited uniform strings and beams because of the large modal overlaps at the low end of the spectrum of shell natural frequencies. The contributions from the modal cross-correlations (which can usually be neglected for strings and beams) introduce an asymmetry into the distribution of mean-square response and can alter the magnitude of the local response considerably. For example, in a thin shell with a radius-to-length ratio of 0.5 the contribution to the mean-square velocity at the driven section due to the modal cross-correlations can be more than three times that due to the modal autocorrelations when the excitation is a band-limited white noise which includes 81 modes.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document