Linear random operator equations in mathematical physics. II
Stochastic, random and ordinary Green function relations for two point correlation functions in mathematical physics
Adomian, G.↗
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Linear random operator equations in mathematical physics. III
Wave equations for motion in stochastic medium, using linear random operator theory
Adomian, G.↗
Effect of randomly fluctuating pressure gradients, with arbitrarily specified power spectrum and probability density, on flow in channels
Random fluctuating longitudinal pressure gradient effect on steady incompressible channel flow for arbitrary power spectrum and probability density
Perlmutter, M.↗
Reflection of signals from a randomly oscillating conducting plane
Point source average signal reflection from conductive plane in random oscillation
Liu, C. H.↗
Design properties of randomly reinforced fiber/resin composites
The pseudoisotropic laminate analogy is used in conjunction with fiber composite micro and macromechanics to predict the thermal and mechanical properties of planar randomly reinforced fiber composites (PRRFC). Theoretical results are presented for boron/epoxy, Thornel-50/epoxy, and S-glass/epoxy PRRFC. The results show that the thermal and elastic properties depend on both constituent materials and the fiber volume ratio. The strength depends also on the type of applied stress.
Chamis, C. C.↗
The generation of random numbers on the IBM 360/44
A summary is presented of the generation and testing of random numbers on the IBM 360/44 computer. Various generators and statistical tests are considered.
Speed, F. M.↗
Fatigue failure of materials under broad band random vibrations
The fatigue life of material under multifactor influence of broad band random excitations has been investigated. Parameters which affect the fatigue life are postulated to be peak stress, variance of stress and the natural frequency of the system. Experimental data were processed by the hybrid computer. Based on the experimental results and regression analysis a best predicting model has been found. All values of the experimental fatigue lives are within the 95% confidence intervals of the predicting equation.
Huang, T. C.↗
Uniform random number generators
Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.
Farr, W. R.↗
Design properties of randomly reinforced fiber composites
The pseudoisotropic-laminate analogy is used in conjunction with fiber composite micro- and macromechanics to predict the thermal and mechanical properties of planar randomly reinforced fiber composites (PRRFC). Theoretical results are presented for boron/aluminum, boron/epoxy, Thornel-50/epoxy, and S-glass/epoxy PRRFC. The results show that the thermal and elastic properties depend on both constituent materials and the fiber volume ratio. The strength depends also on the type of applied stress. In general, no simple ratio exists between the properties of unidirectional fiber composites and those of PRRFC. The data are presented in convenient graphical form to serve as an aid for design and/or analysis and also for further research in PRRFC. The residual stresses and the impact resistance are also theoretically examined.
Chamis, C. C.↗
An evaluation of random analysis methods for the determination of panel damping
An analysis is made of steady-state and non-steady-state methods for the measurement of panel damping. Particular emphasis is placed on the use of random process techniques in conjunction with digital data reduction methods. The steady-state methods considered use the response power spectral density, response autocorrelation, excitation-response crosspower spectral density, or single-sided Fourier transform (SSFT) of the response autocorrelation function. Non-steady-state methods are associated mainly with the use of rapid frequency sweep excitation. Problems associated with the practical application of each method are evaluated with specific reference to the case of a panel exposed to a turbulent airflow, and two methods, the power spectral density and the single-sided Fourier transform methods, are selected as being the most suitable. These two methods are demonstrated experimentally, and it is shown that the power spectral density method is satisfactory under most conditions, provided that appropriate corrections are applied to account for filter bandwidth and background noise errors. Thus, the response power spectral density method is recommended for the measurement of the damping of panels exposed to a moving airflow.
Bhat, W. V.↗
Wave propagation in a random medium
A simple technique is used to derive statistical characterizations of the perturbations imposed upon a wave (plane, spherical or beamed) propagating through a random medium. The method is essentially physical rather than mathematical, and is probably equivalent to the Rytov method. The limitations of the method are discussed in some detail; in general they are restrictive only for optical paths longer than a few hundred meters, and for paths at the lower microwave frequencies. Situations treated include arbitrary path geometries, finite transmitting and receiving apertures, and anisotropic media. Results include, in addition to the usual statistical quantities, time-lagged functions, mixed functions involving amplitude and phase fluctuations, angle-of-arrival covariances, frequency covariances, and other higher-order quantities.
Lee, R. W.↗
Relabeling of finite element meshes using a random process
An algorithm is presented to relabel automatically the nodes of an arbitrary finite-element mesh. The purpose of such relabeling is to reduce the bandwidth of the master stiffness matrix produced by the finite-element method. The algorithm uses a random process for the relabeling. Computing time is reduced substantially, compared to systematic methods.
Roberts, E., Jr.↗
Hybrid computer optimization of systems with random parameters
A hybrid computer Monte Carlo technique for the simulation and optimization of systems with random parameters is presented. The method is applied to the simultaneous optimization of the means and variances of two parameters in the radar-homing missile problem treated by McGhee and Levine.
White, R. C., Jr.↗
Fatigue failure of materials under narrow band random vibrations. I.
A novel approach for the study of fatigue failure of materials under the multifactor influence of narrow band random vibrations is developed. The approach involves the conduction of an experiment in conjunction with various statistical techniques. Three factors including two statistical properties of the excitation or response are considered and varied simultaneously. A minimum of 6 tests for 3 variables is possible for a fractional f actorial design. The four coefficients of the predicting equation can be independently estimated. A look at 3 predicting equations shows the predominant effect of the root mean square stress of the first order equation.
Huang, T. C.↗
Local theorems in strengthened form for lattice random variables.
Investigation of some conditions which are sufficient for a sequence of independent integral-valued lattice random variables to satisfy a local theorem in strengthened form. A number of theorems giving the conditions under which the investigated sequence satisfies a local theorem in strengthened form are proven with the aid of lemmas derived by Kruglov (1968).
Mason, J. D.↗
Design properties of randomly reinforced fiber/resin composites.
The pseudoisotropic laminate analogy is used in conjunction with fiber composite micro and macromechanics to predict the thermal and mechanical properties of planar randomly reinforced fiber composites (PRRFC). Theoretical results are presented for boron/epoxy, Thornel-50/epoxy, and S-glass/epoxy PRRFC. The results show that the thermal and elastic properties depend on both constituent materials and the fiber volume ratio (FVR). The strength depends also on the type of applied stress.
Chamis, C. C.↗
Physical interrelation between Fokker-Planck and random walk models with application to Coulomb interactions.
A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.
Englert, G. W.↗
Local theorems for nonidentically distributed lattice random variables.
Derivation of local limit theorems for a sequence X sub n of independent integral-valued lattice random variables involving only a finite number of distinct nondegenerate distributions. Given appropriate sequences A sub n and B sub n of constants such that 1/B sub n (X sub 1 +
Mason, J. D.↗