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At least 361 records · Page 20

Synthesis and dynamic characteristics of large structures with rotating substructures

The variational equations of motion of large structures with rotating substructures are derived by the substructure synthesis approach, whereby a discretization procedure akin to the Rayleigh-Ritz method is used to represent the elastic motion of every substructure by a suitable set of admissible functions. Using an inclusion principle for gyroscopic systems, the effects on the predicted system dynamic characteristics of truncating the number of admissible functions used for each substructure can be assessed. Criteria for rational selection of admissible functions are presented.

Meirovitch, L.↗

Equations for the design of two-dimensional supersonic nozzles

Equations are presented for obtaining the wall coordinates of two-dimensional supersonic nozzles. The equations are based on the application of the method of characteristics to irrotational flow of perfect gases in channels. Curves and tables are included for obtaining the parameters required by the equations for the wall coordinates. A brief discussion of characteristics as applied to nozzle design is given to assist in understanding and using the nozzle-design method of this report. A sample design is shown.

Pinkel, I Irving↗

Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 1: Structural dynamics analysis

A theoretical investigation of structural vibration characteristics of rotor blades was carried out. Coupled equations of motion for flapwise bending and torsion were formulated for rotor blades with noncollinear elastic and mass axes. The finite element method was applied for a detailed representation of blade structural properties. Coupled structural mass and stiffness coefficients were evaluated. The range of validity of a set of coupled equations of motion linearized with respect to eccentricity between elastic and mass axes was investigated. The sensitivity of blade vibration characteristics to torsion were evaluated by varying blade geometric properties, boundary conditions, and eccentricities between mass and elastic axes.

Bratanow, T.↗

Evaluation of a distributed catchment scale water balance model

The validity of some of the simplifying assumptions in a conceptual water balance model is investigated by comparing simulation results from the conceptual model with simulation results from a three-dimensional physically based numerical model and with field observations. We examine, in particular, assumptions and simplifications related to water table dynamics, vertical soil moisture and pressure head distributions, and subsurface flow contributions to stream discharge. The conceptual model relies on a topographic index to predict saturation excess runoff and on Philip's infiltration equation to predict infiltration excess runoff. The numerical model solves the three-dimensional Richards equation describing flow in variably saturated porous media, and handles seepage face boundaries, infiltration excess and saturation excess runoff production, and soil driven and atmosphere driven surface fluxes. The study catchments (a 7.2 sq km catchment and a 0.64 sq km subcatchment) are located in the North Appalachian ridge and valley region of eastern Pennsylvania. Hydrologic data collected during the MACHYDRO 90 field experiment are used to calibrate the models and to evaluate simulation results. It is found that water table dynamics as predicted by the conceptual model are close to the observations in a shallow water well and therefore, that a linear relationship between a topographic index and the local water table depth is found to be a reasonable assumption for catchment scale modeling. However, the hydraulic equilibrium assumption is not valid for the upper 100 cm layer of the unsaturated zone and a conceptual model that incorporates a root zone is suggested. Furthermore, theoretical subsurface flow characteristics from the conceptual model are found to be different from field observations, numerical simulation results, and theoretical baseflow recession characteristics based on Boussinesq's groundwater equation.

Troch, Peter A.↗

Vibration characteristics of a steadily rotating slender ring

Partial differential equations are derived to describe the structural vibrations of a uniform homogeneous ring which is very flexible because the radius is very large compared with the cross sectional dimensions. Elementary beam theory is used and small deflections are assumed in the derivation. Four sets of structural modes are examined: bending and compression modes in the plane of the ring; bending modes perpendicular to the plane of the ring; and twisting modes about the centroid of the ring cross section. Spatial and temporal characteristics of these modes, presented in terms of vibration frequencies and ratios between vibration amplitudes, are demonstrated in several figures. Given a sufficiently high rotational rate, the dynamics of the ring approach those of a vibrating string. In this case, the velocity of traveling wave in the material of the ring approaches in velocity of the material relative to inertial space, resulting in structural modes which are almost stationary in space.

Lallman, F. J.↗

Sensitivity analysis of torsional vibration characteristics of helicopter rotor blades. Part 2: Aerodynamics and sensitivity analysis

A theoretical investigation of dynamic response characteristics of rotor blades was carried out with special emphasis on torsional degrees-of-freedom. Coupled equations of motion for flapwise bending and torsion were formulated at varying azimuth positions for rotor blades with noncollinear aerodynamic, elastic and mass axes. Both structural and aerodynamic mass, damping and stiffness coefficients were included. The variations of a sample blade at different flight conditions were investigated from these equations. The obtained numerical results were illustrated. The sensitivity of overall blade vibration characteristics to torsional oscillations was also investigated from the equations of motion for the sample blade. The illustrated results show the importance of torsional degrees-of-freedom in rotor blade analysis. Various possibilities of improving the overall response by tuning blade geometric, structural and aerodynamic characteristics are discussed.

Bratanow, T.↗

The method of projected characteristics for the evolution of magnetic arches

A numerical method of solving fully nonlinear MHD equation is described. In particular, the formulation based on the newly developed method of projected characteristics (Nakagawa, 1981) suitable to study the evolution of magnetic arches due to motions of their foot-points is presented. The final formulation is given in the form of difference equations; therefore, the analysis of numerical stability is also presented. Further, the most important derivation of physically self-consistent, time-dependent boundary conditions (i.e. the evolving boundary equations) is given in detail, and some results obtained with such boundary equations are reported.

Nakagawa, Y.↗

The solution of the laminar-boundary-layer equation for the flat plate for velocity and temperature fields for variable physical properties and for the diffusion field at high concentration

In connection with Pohlhausen's solution for the temperature field on the flat plate, a series of formulas were indicated by means of which the velocity and temperature field for variable physical characteristics can be computed by an integral equation and an iteration method based on it. With it, the following cases were solved: On the assumption that the viscosity simply varies with the temperature while the other fluid properties remain constant, the velocity and temperature field on the heated and cooled plate, respectively, was computed at the Prandtl numbers 12.5 and 100 (viscous fluids). A closer study of these two cases resulted in general relations: The calculations for a gas of Pr number 0.7 (air) were conducted on the assumption that all fluid properties vary with the temperature, and the velocities are low enough for the heat of friction to be discounted. The result was a thickening of the boundary layers, but no appreciable modification in shearing stress or heat-transfer coefficient.

BOUNDARY LAYER, LAMINAR - PLATES, FLAT↗

Theory of Characteristics

The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.

Tollmien, W.↗

Modeling taper charge with a non-linear equation

Work aimed at modeling the charge voltage and current characteristics of nickel-cadmium cells subject to taper charge is presented. Work reported at previous NASA Battery Workshops has shown that the voltage of cells subject to constant current charge and discharge can be modeled very accurately with the equation: voltage = A + (B/(C-X)) + De to the -Ex where A, B, D, and E are fit parameters and x is amp-hr of charge removed during discharge or returned during charge. In a constant current regime, x is also equivalent to time on charge or discharge.

Mcdermott, P. P.↗

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗

Analysis of face deformation effects on gas film seal performance

Analyses are presented for compressible fluid flow across shaft face seals with face deformation. The solutions are obtained from an approximate integral analysis. The models, used in this analysis, can predict gas film seal behavior operating at subsonic or choked flow conditions. The flow regime can either be laminar or turbulent. Entrance losses can also be accounted for. When fluid inertia effects are negligible and the sealing faces are slightly deformed, the following results are found for both laminar and turbulent flows: (1) The pressure profiles are independent of fluid properties; and (2) the parallel film leakage equation can be used, provided a characteristic film thickness is used. Pressure profiles are presented for both divergent and convergent seal faces under choked flow conditions.

Zuk, J.↗

Longitudinal impact of cylindrical shells.

The transient response due to longitudinal impact of three aluminum cylindrical shells of different thickness-to-radius ratios is studied both analytically and experimentally. The analyses were obtained from method of characteristics' solutions of two sets of equations: one which includes the transverse shear, radial inertia, and rotary inertial effects; and the other set is from a modified membrane theory. Experimentally, longitudinal and circumferential strains are monitored along the length of each of the shells; the velocity of the impacter ring is also measured. The experimental results of this study indicate that the wave front, after traveling three diameters from the impacted end, propagates at essentially the plate velocity, in agreement with the theory. In addition, the longitudinal and circumferential strain calculated from the two theories are in good agreement with the experimental results.

Mortimer, R. W.↗

On propagation of long waves in curved ducts.

Propagation of waves in curved ducts and pipes belong to the class of motion which is characterized by wave patterns totally different from those known in straight ducts or in unlimited space. The curvilinear boundaries are responsible for the appearance of a continuous standing radial wave which in turn affects the transmitted tangential waves. The purpose of this paper is to solve the problem of propagation of long acoustic waves in slightly and sharply bent ducts. This problem has been only partially analyzed by various authors. In this study two acoustic systems are considered which allow determination of the basic modes of motion and describe the transition and distortion of plane waves as they propagate down the curved channel. A detailed study of the behavior of waves in junctions between straight and curved ducts is also given. Solutions and expressions for principal modes of the wave are obtained by using the linearized equation of motion solved for its characteristic values. This original approach required a novel use of Bessel functions to determine the characteristic values of the steady and the decaying fields of motion.

Rostafinski, W.↗

On propagation of long waves in curved ducts.

A two-dimensional detailed study of the behavior of long waves in curved ducts and in junctions between straight and curved ducts will be given. The mathematical treatment of the problem utilizes the method of separation variables. Solutions and expressions for principal mode of the wave are obtained by using the linearized equation of motion solved for its characteristic values. The unavoidable approximations in the numerical solutions of the cylindrical functions are due to use of series expansion of Bessel functions and from restrictions necessary to solve infinite matrices.

Rostafinski, W.↗

Acoustical theory of turbulence

Fluid functions are expanded in a series of functions constituting a complete and orthogonal system of wave solutions of the linearized Navier-Stokes system. The motion of characteristic waves is described by Hamiltonian equations of ray acoustics. Amplitude of the waves is described with the aid of nonlinear interaction terms. The distribution functions (squares of amplitudes) satisfy Boltzmann-type equations and completely describe the mean turbulence properties.

Kentzer, C. P.↗