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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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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 +
Development of a method for computing the mean-square response of linear systems to nonstationary random excitation of the form given by y(t) = f(t) x(t), in which x(t) = a stationary process and f(t) is deterministic. The method is suitable for application to multidegree-of-freedom systems when the mean-square response at a point due to excitation applied at another point is desired. Both the stationary process, x(t), and the modulating function, f(t), may be arbitrary. The method utilizes a fundamental component of transient response dependent only on x(t) and the system, and independent of f(t) to synthesize the total response. The role played by this component is analogous to that played by the Green's function or impulse response function in the convolution integral.
This paper discusses the merits of employing the new computer-controlled random environment control systems for fast and efficient large-scale data analysis when they are not being used for test control. Hardware and software requirements are stated. Several of the more familiar frequency functions are defined from the Fourier coefficients, the main product of the Fourier processors used in these control systems. Another function, the probability density function, is defined and suggestions for its application are made. An analysis example is presented. Some programming tips are listed, and the accuracy and reliability of frequency analysis measurements are considered.
Planar randomly reinforced fiber composites (PRRFC) is pseudoisotropic laminate with large number of ply orientation combinations where strength is function of these ply orientation combinations. Laminate theory can be applied to determine strength of PRRFC, and in conjunction with composite micro- and macromechanics can predict mechanical properties of PRRFC's with any fiber/matrix combination.
It is necessary to place number of sensors at different positions in sound field to determine actual sound intensities to which test object is subjected. It is possible to determine whether specification is being met adequately or exceeded. Since excitation is of random nature, signals are essentially coherent and it is impossible to obtain true average.
Mathematical formulation is based on cumulative-damage hypothesis and experimentally-determined stress-corrosion characteristics. Under both stationary random loadings, mean value and variance of cumulative damage are obtained. Probability of stress-corrosion fracture is then evaluated, using principle of maximum entropy.
A complete user and programmer guide for the REPRI program is presented. This program was developed to perform mission concept, subsystem capability, and experiment support compatibility studies for a space station. The program utilizes Monte Carlo techniques to randomly schedule events in discrete intervals. Resources, logistics, cost, and space station volume are considered.
When charged particles move in a random magnetic field superimposed upon a relatively large constant field, their pitch angle distribution can be calculated to any desired precision by an iterative approximation procedure. Improved knowledge of the pitch angle distribution and of the characteristic time for relaxation of anisotropy leads to an accurate expression for the coefficient of diffusion parallel to the mean field.
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