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A purely algebraic algorithm is developed for testing positive real character of real rational functions and matrices relative to the unit circle in the complex plane. Since the algorithm is entirely recursive and is performed in finite number of steps, it is suitable for machine computations.
A flight-loads measurement program on the YF-12 aircraft required the mounting of 101 strain-gauge bridges in the fuselage, fuel tanks, control surfaces, and three stations on the left wing. The sensors were to be installed primarily on titanium and were required to operate between -70 and +600 F. Strain gauges with modified Karma filaments and backings of glass-fiber reinforced epoxy resin matrices were selected and were installed with an epoxy adhesive. Attention is given to the calibration, mounting, and performance of the sensors in flight-load measurements.
Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
A general theory of finite-aperture waveguide-laser resonators is developed which represents the external reflectors by matrices that couple linearly polarized waveguide modes having the same azimuthal symmetry. The theory allows the determination of resonator efficiency, resonator frequencies, and laser near- and far-field patterns. Computations of the coupling loss for the fundamental waveguide mode as a function of mirror curvature, separation, and aperture are in good agreement with recent infinite-aperture calculations in the limit of large apertures and indicate three low-loss configurations: (1) large radius of curvature mirrors close to the guide; (2) large radius of curvature mirrors centered at the guide entrance; and (3) generally smaller curvature mirrors separated by half their curvature from the guide entrance.
Program uses combination of procedures to determine eigenfunction solutions of discrete damped structures, including spinning ones, while fully exploiting banded configuration of associated matrices.
A description is presented of two new utility programs which implement the transfer, in full precision, of arbitrary data (matrices or tables) between any of the three NASTRAN operative computers without the handling of large card decks. These computers include the CDC 6000 series, the IBM 360-370 series, and the Univac 1100 series. The data may be generated by NASTRAN or by another computer program if the NASTRAN user tape format is employed.
A cluster of boulders at Station 6 (Apollo 17 landing site) consists of breccias derived from the North Massif. Three preliminary lithologic units were established, on the basis of photogeologic interpretations; all lithologies identified photogeologically were sampled. Breccia clasts and matrices studied petrographically and chemically fall into two groups by modal mineralogy: (1) low-K Fra Mauro or high basalt composition, consisting of 50-60% modal feldspar, approximately 45% orthopyroxene and 1-7% Fe-Ti oxide; (2) clasts consisting of highland basalt composition, consisting of 70% feldspar, 30% orthopyroxene and olivine and a trace of Fe-Ti oxide.
The necessary and sufficient conditions for the decoupling of an m-input, m-output, linear time varying dynamical system by state variable feedback is described. The class of feedback matrices which decouple the system are illustrated. Systems which do not satisfy these results are described and systems with disturbances are considered. Some examples are illustrated to clarify the results.
The results of wind tunnel tests, second series of tests performed in the NASA Ames 40 x 80 foot wind tunnel, of the DH 2011 jet-flap rotor are presented and analyzed. The tests have been focused on multicyclic effects and the capability of this rotor to reduce the vibratory loads and stresses in the blades. The reductions of the vibrations and stresses at tip speed ratio of 0.4 have attained 50%. The theory shows further reductions possible, reaching 80%. The results show that the performance characteristics after the modifications introduced since 1965 remained unchanged. The domain of investigation has been enlarged to include the tip speed ratios of 0.6 and 0.7. To analyze the complex aeroelastic phenomena a new analytical technique has been utilized to represent the mathematical model of the rotor. This technique, based on transfer matrices and transfer functions, appears very simple and it is believed that this analysis is applicable to many kinds of investigations involving large numbers of variables.
The problem of identifying linear dynamical systems is studied by considering structural and deterministic properties of linear systems that have an impact on stochastic identification algorithms. In particular considered is parametrization of linear systems so that there is a unique solution and all systems in appropriate class can be represented. It is assumed that a parametrization of system matrices has been established from a priori knowledge of the system, and the question is considered of when the unknown parameters of this system can be identified from input/output observations. It is assumed that the transfer function can be asymptotically identified, and the conditions are derived for the local, global and partial identifiability of the parametrization. Then it is shown that, with the right formulation, identifiability in the presence of feedback can be treated in the same way. Similarly the identifiability of parametrizations of systems driven by unobserved white noise is considered using the results from the theory of spectral factorization.
Linear, quadratic, and cubic isoparametric hexahedral solid elements have been added to the element library of NASTRAN. These elements are available for static, dynamic, buckling, and heat-transfer analyses. Because the isoparametric element matrices are generated by direct numerical integration over the volume of the element, variations in material properties, temperatures, and stresses within the elements are represented in the computations. In order to compare the accuracy of the new elements, three similar models of a slender cantilever were developed, one for each element. All elements performed well. As expected, however, the linear element model yielded excellent results only when shear behavior predominated. In contrast, the results obtained from the quadratic and cubic element models were excellent in both shear and bending.
The NASTRAN computer program is capable of executing on three different types of computers: (1) the CDC 6000 series, (2) the IBM 360-370 series, and (3) the Univac 1100 series. A typical activity requiring transfer of data between dissimilar computers is the analysis of a large structure such as the space shuttle by substructuring. Models of portions of the vehicle which have been analyzed by subcontractors using their computers must be integrated into a model of the complete structure by the prime contractor on his computer. Presently the transfer of NASTRAN matrices or tables between two different types of computers is accomplished by punched cards or a magnetic tape containing card images. These methods of data transfer do not satisfy the requirements for intercomputer data transfer associated with a substructuring activity. To provide a more satisfactory transfer of data, two new programs, RDUSER and WRTUSER, were created.
The technology and methods developed at the Plum Brook Reactor to analyze 1000 samples per year and report data on as many as 56 elements are described. The manpower for the complete analysis of 20 to 24 samples per week required only 3 to 3.5 hours per sample. The solutions to problems encountered in sample preparation, irradiation, and counting are discussed. The automation of data reduction is described. Typical data on various sample matrices are presented.
Based upon extensive contacts with vendors, a broad array of non-flammable polymeric specie, and additives generally noted to have flame retarding properties, were considered. The following polymeric matrices were examined: modified silicone and fluorosilicone RTV's polyesters, epoxies, urethanes, and epoxy-urethanes. Optimization of formulations to obtain a suitable balance between the various properties and flammability resistance led to the final selection of a silicone RTV/additive-loaded compound which meets almost all program requirements. The very low valued properties found are within a realistic level of design toleration. Complete formulation, processing, and test data is provided for this compound, EPOCAST 87517-A/B, and the other formulations prepared by the project. Details of those test methods are presented along with procedures utilized in the program. In addition, a description of the special flammability facility previously designed and then modified for this program is also presented.
It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.
The application of the maximum likelihood method to estimate the aerodynamic parameters of elastic flight vehicles in a symmetric flight condition is discussed. In this application, particular attention is directed toward the center of mass, elastic deformation, and sensor equations of motion. It is shown that the two major computational problems to be overcome are the inversion of large-sized matrices and the time-wise integration of a large number of linear, ordinary, differential equations.
Design of multivariable systems is considered and design procedures are formulated in the light of the most recent work on model matching. The word model matching is used exclusively to mean matching the input-output behavior of two systems. The term is used in the frequency domain to indicate the comparison of two transfer matrices containing transfer functions as elements. Design methods where non-interaction is not used as a criteria were studied. Two design methods are considered. The first method of design is based solely upon the specification of generalized error coefficients for each individual transfer function of the overall system transfer matrix. The second design method is called the pole fixing method because all the system poles are fixed at preassigned positions. The zeros of terms either above or below the diagonal are partially fixed via steady state error coefficients. The advantages and disadvantages of each method are discussed and an example is worked to demonstrate their uses. The special cases of triangular decoupling and minimum constraints are discussed.
The computer solution of matrix equations is often difficult to accomplish due to an ill-conditioned matrix or high noise levels. Two methods of solution are compared for matrices of various degrees of ill-conditioning and for various noise levels in the right hand side vector. One method employs the usual Gaussian elimination. The other solves the equation by an optimization technique and employs a function minimization subroutine.