Some one-dimensional problems in a theory of mechanically and thermally interacting continuous media
Linearized theory applied to mixture of elastic solid and viscous fluid in one dimensional boundary value problems
Martin, C. J.↗
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On some problems in a theory of thermally and mechanically interacting continuous media
Using a linearized theory of thermally and mechanically interacting mixture of linear elastic solid and viscous fluid, we derive a fundamental relation in an integral form called a reciprocity relation. This reciprocity relation relates the solution of one initial-boundary value problem with a given set of initial and boundary data to the solution of a second initial-boundary value problem corresponding to a different initial and boundary data for a given interacting mixture. From this general integral relation, reciprocity relations are derived for a heat-conducting linear elastic solid, and for a heat-conducting viscous fluid. An initial-boundary value problem is posed and solved for the mixture of linear elastic solid and viscous fluid. With the aid of the Laplace transform and the contour integration, a real integral representation for the displacement of the solid constituent is obtained as one of the principal results of the analysis.
Lee, Y. M.↗
A state-of-the-art review of transportation systems evaluation techniques relevant to air transportation, volume 1
Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.
Haefner, L. E.↗
Linear and nonlinear aspects of snow albedo feedbacks in atmospheric models
Namias' hypothesis, that anomalous snowcover on the eastern side of the North American continent can generate an anomalous east coast low pressure system and an anomalous inland high pressure system, is consistent with the time-averaged anomalous response from a nonlinear, primitive equation channel model with an idealized, flat land-sea arrangement. An attempt to understand and describe this anomalous response in the nonlinear model as a linear response to anomalous diabatic heating was largely unsuccessful, primarily because the anomalous eddy fluxes were also important. This unsuccessful attempt to describe the nonlinear model's time averages by linear theory then motivated several comparisons between linear and nonlinear severely truncated quasi-geostrophic models. It was also found in these models that the eddy fluxes were extremely important for forcing or dissipating the stationary eddies.
Roads, J. O.↗
Mock gravity and the cosmic structure
The process of generating large-scale cosmic structure from the radiation-pressure or 'mock gravity' instability is studied with particular emphasis on the implications of the Berkeley-Nagoya rocket data for the submillimeter background. The linear theory of perturbations in an absorbing medium embedded in an expanding universe of radiation sources is presented. The instability sets up collapse velocities in linear perturbation theory which far exceed those from gravitational instability, so growth continues even after the instability switches off. Perturbation due to this effect is analyzed and related to the growth of large-scale cosmic structures at recent times; large-scale structure is shown to evolve very little from 1 + z about 5 to the present. Nonlinear small-scale effects of the instability are analyzed; it is shown that radiation pressure would compress gas into small, dense pressure-confined clouds with tau much greater than one.
Hogan, Craig J.↗
Quasilinear theory of hydromagnetic waves in collisionless plasma.
Quasi-linear theory of hydromagnetic waves in nonrelativistic collisionless plasma, noting resonant diffusion effect on plasma heating mode
Barnes, A.↗
Meso-beta scale numerical simulation studies of terrain-induced jet streak mass and momentum perturbations
An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 11-12 July 1981 CCOPE case study indicated two episodes of coherent waves. While geostrophic adjustment, shearing instability, and terrain were all implicated separately or in combination as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to define the genesis processes from observations alone. The first part of this paper, 3D Numerical Modeling Studies of Terrain-Induced Mass/Momentum Perturbations, employs a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed gravity wave episode. The meso-beta scale numerical model is used to study various simulations of the role of multiple geostrophic adjustment processes in focusing a region for gravity wave genesis. The second part of this paper, Linear Theory and Theoretical Modeling, investigates the response of non-resting rotating homogeneous and continuously stratified Boussinesq models of the terrestrial atmosphere to temporally impulsive and uniformly propagating three-dimensional localized zonal momentum sources representative of midlatitude jet streaks. The methods of linear perturbation theory applied to the potential vorticity (PV) and wave field equations are used to study the geostrophic adjustment dynamics. The total zonal and meridional wind perturbations are separated into geostrophic and ageostrophic components in order to define and follow the evolution of both the primary and secondary mesocirculations accompanying midlatitude jetogenesis forced by geostrophic adjustment processes. This problem is addressed to help fill the gap in understanding the dynamics and structure of mesoscale inertia-gravity waves forced by geostrophic adjustment processes in simple two-dimensional quiescent current systems and those produced by mesoscale numerical models simulating the orographic and diabatic perturbation of three-dimensional quasi-geostrophically balanced synoptic scale jet streaks associated with complex baroclinic severe storm producing environments.
Lin, Yuh-Lang↗
Lorentz resonances and the vertical structure of dusty rings - Analytical and numerical results
The Schaffer and Burns (1987) linear theory of Lorentz resonances (LRs) in planetary rings is extended in order to accurately compute LR locations and to elucidate the nature of grain trajectories within the LR zones. Using the perturbation theory and energy arguments, it is shown that an increase in the inclination or eccentricity of a grain must be accompanied by a shift in the mean orbital radius of the particle. This shift alters the epicyclic frequencies in such a way that the infinite response of the linear resonance theory is suppressed. Chaotic motion is found for the range of charge-to-mass ratios that cause the vertical and horizontal LRs to overlap.
Schaffer, Les↗
A reciprocal theorem for a mixture of interacting continuous media
Using a linearized theory of interacting continuous media composed of linear elastic solid and linear viscous fluid, a reciprocal theorem is derived which relates the solution of one initial-boundary value problem to another. As an illustration of the reciprocal theorem, we obtain the early time displacement and velocity field of a mixture occupying an infinite region and subjected to an impulsively applied moving point load acting on the solid constituent.
Lee, Y. M.↗
Theoretical and experimental study of twisted and cambered delta wings designed for a Mach number of 3.5
Data are provided for the evaluation of the aerodynamic performance of a series of twisted and cambered delta wings designed for a Mach number of 3.5. Systematic force and pressure data are also presented for comparison with theory. Force tests were made at Mach numbers of 2.3, 3.0, 3.5, 4.0, and 4.6. Design lift coefficients of 0.0 and 0.1 were employed on the 55 deg and 68 deg sweep wings, and design lift coefficients of 0.0, 0.05, and 0.1 were employed on the 76 deg sweep wings. Pressure tests were conducted on the 55 deg and 76 deg sweep flat wings and on the 0.1 design lift coefficient 76 deg sweep wing. The results indicate that for the sweep angles tested, an increase in the zero-lift pitching-moment coefficient is the primary benefit of twist and camber at a Mach number of 3.5. Comparison of the experimental results with results obtained from several lift theories indicates that the Carlson-Middleton linear theory method gave the best overall agreement. The pressure data indicate, however, that there is a cancellation of error at high angle of attack where the lower surface pressures are significantly underpredicted over the inboard region of the wing and where the upper and lower surface pressures are overpredicted over the outboard region of the wing.
Sorrells, R. B., III↗
VTOL controls for shipboard landing
The problem of landing a VTOL aircraft on a small ship in rough seas using an automatic controller is examined. The controller design uses the linear quadratic Gaussian results of modern control theory. Linear time invariant dynamic models are developed for the aircraft, ship, and wave motions. A hover controller commands the aircraft to track position and orientation of the ship deck using only low levels of control power. Commands for this task are generated by the solution of the steady state linear quadratic gaussian regulator problem. Analytical performance and control requirement tradeoffs are obtained. A landing controller commands the aircraft from stationary hover along a smooth, low control effort trajectory, to a touchdown on a predicted crest of ship motion. The design problem is formulated and solved as an approximate finite-time linear quadratic stochastic regulator. Performance and control results are found by Monte Carlo simulations.
Mcmuldroch, C. G.↗
Theoretical prediction of nonlinear propagation effects on noise signatures generated by subsonic or supersonic propeller or rotor-blade tips
The nonlinear propagation equations for sound generated by a constant speed blade tip are presented. Propagation from a subsonic tip is treated as well as the various cases that can occur at supersonic speeds. Some computed examples indicate that the nonlinear theory correlates with experimental results better than linear theory for large amplitude waves. For swept tips that generate a wave with large amplitude leading expansion, the nonlinear theory predicts a cancellation effect that results in a significant reduction of both amplitude and impulse.
Barger, R. L.↗
Identification of asteroid dynamical families
Problems involved in the identification of asteroid dynamical families are discussed, and some methodological guidelines are presented. Asteroid family classifications are reviewed, and differences in the existing classifications are examined with special attention given to the effects of observational selection on the classification of family membership. The paper also discusses various theories of secular perturbations, including the classical linear theory, the theory of Williams (1969), and the higher order/degree theory of Yuasa (1973).
Valsecchi, G. B.↗
Conditional symmetric instability and mesoscale rainbands
The linear theory of conditional symmetric instability (CSI) is re-examined in a rigorous framework. In comparison with symmetric instability a new feature of CSI is that the moist updraught tends to be narrow, as with conditional buoyancy instability (CBI). As the width of the moist updraught varies from its tolerance maximum to infinitesimal, the inviscid growth rate increases from zero to its maximum and the slope of the moist updraught increases from the absolute momentum surface to the moist most unstable surface. The fact that CSI circulations absorb energy from the basic shear and moist thermal field but lose energy to the dry basic thermal field is responsible for the narrow and slant feature of the moist updraught. When a bulk viscosity is accounted for, the most rapidly growing CSI modes bear a qualitative resemblance to some observed rainbands. The stability criterion of viscous CSI also shows a better comparison with observational data than inviscid CSI. The linear CSI theory here predicts that the isolated mode is preferred to other non-isolated (periodic or irregular spacing) modes. The preference of non-isolated modes is speculated to occur in the nonlinear stage.
Xu, Q.↗
The theory of flotation
A brief summary of the fundamentals of the Linear theory of flotation is given. The theory by no means contradicts the previous Laminar theory or even the thermodynamics (Wark-Siedler), rather it is a refinement of the known Hardy-Langmuir-Harkin conceptions for the case when there are not two phases and phase boundaries, but rather three phases and corresponding phase boundary edges. The appearance of such three-phase boundaries (ore, water, air) is characteristic for modern flotation methods.
Ostwald, Wolfgang↗
Nonlinear Large Deflection Theory with Modified Aeroelastic Lifting Line Aerodynamics for a High Aspect Ratio Flexible Wing
This paper investigates the effect of nonlinear large deflection bending on the aerodynamic performance of a high aspect ratio flexible wing. A set of nonlinear static aeroelastic equations are derived for the large bending deflection of a high aspect ratio wing structure. An analysis is conducted to compare the nonlinear bending theory with the linear bending theory. The results show that the nonlinear bending theory is length-preserving whereas the linear bending theory causes a non-physical effect of lengthening the wing structure under the no axial load condition. A modified lifting line theory is developed to compute the lift and drag coefficients of a wing structure undergoing a large bending deflection. The lift and drag coefficients are more accurately estimated by the nonlinear bending theory due to its length-preserving property. The nonlinear bending theory yields lower lift and span efficiency than the linear bending theory. A coupled aerodynamic-nonlinear finite element model is developed to implement the nonlinear bending theory for a Common Research Model (CRM) flexible wing wind tunnel model to be tested in the University of Washington Aeronautical Laboratory (UWAL). The structural stiffness of the model is designed to give about 10% wing tip deflection which is large enough that could cause the nonlinear deflection effect to become significant. The computational results show that the nonlinear bending theory yields slightly less lift than the linear bending theory for this wind tunnel model. As a result, the linear bending theory is deemed adequate for the CRM wind tunnel model.
Aeroelasticity↗
On the structure of artificially generated water wave trains
The structure of an artificially generated sinusoidal water wave train of fixed frequency under the influence of wind is analyzed. Artificially generated waves of 1 Hz are studied at seven wind speeds in the range of 140-400 cm/s. It is observed that the water wave train deformed by wind consists of two components at both the fundamental mode and the harmonics. The amplitude and phase of the wave components are derived, and the dispersion relation and component phase speeds are examined. The data reveal that the amplitude of the forced and free-traveling second harmonics correlate with previous theories, and that the deviation of the measured phase speed from the linear theory is caused by the nonlinearity of the primary wave, the interaction between short gravity waves and the primary wave, and the advection effects of wind drift.
Papadimitrakis, Yiannis A.↗
An approach to CMG steering using feedback linearization
This paper presents an approach for controlling spacecraft equipped with control moment gyroscopes. A technique from feedback linearization theory is used to transform the original nonlinear problem to an equivalent linear form without approximating assumptions. In this form, the spacecraft dynamics appear linearly, and are decoupled from redundancy in the system of gyroscopes. A general approach to distributing control effort among the available actuators is described which includes provisions for redistribution of rotors, explicit bounds in gimbal rates, and guaranteed operation at or near singular configurations. A particular algorithm is developed for systems of double-gimbal devices, and demonstrated in two examples for which existing approaches fail to give adequate performance.
Dzielski, John↗