Complex treatment of a class of nonconservative stability problems
Continuous one dimensional nonconservative elastic systems under complex forces, examining stability theory
Herrmann, G.↗
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The effect of stable thermal stratification on the stability of viscous parallel flows
Stability theory for thermal stratified viscous parallel flows at Prandtl number of unity, considering atmospheric boundary layer and jet stream mechanisms
Gage, K. S.↗
An adaptive scheme for observing the state of an unknown linear system
A full order adaptive observer is described for observing the states of a single-input single-output observable continuous differential system with unknown parameters. Convergence of the observer states to those of the system is accomplished by directly changing the parameters of the observer using an adaptive law based upon Liapunov stability theory. Observer eigenvalues may be freely chosen. Some restriction is placed upon the system input in that it must be sufficiently rich in frequencies in order to insure convergence.
Carroll, R. L.↗
Heat pipe stability. 1: A preliminary investigation into thermally assisted cavitation
The notion is introduced of thermally assisted cavitation by localized fluctuations in capillary forces. Because cavitation in liquids can be closely approximated by an isothermal process, only momentum and mass balances are used to introduce the notion for liquids under mechanical tension. Brief attention is given to developing a stability theory in terms of the stiffness and compliance coefficients for a working fluid. Interestingly, the particular thermodynamic approach taken can be used to suggest experiments relating working fluid performance to meniscus behavior. A correction to the liquid flow equation is suggested.
Source record↗
Stability of large-scale systems.
The purpose of this paper is to present the results obtained in stability study of large-scale systems based upon the comparison principle and vector Liapunov functions. The exposition is essentially self-contained, with emphasis on recent innovations which utilize explicit information about the system structure. This provides a natural foundation for the stability theory of dynamic systems under structural perturbations.
Siljak, D. D.↗
An adaptive observer for single-input single-output linear systems.
A full order adaptive observer is described for observing the state of a single-input single-output observable continuous differential system with unknown parameters. Convergence of the observer states to those of the system is accomplished by directly changing the parameters of the observer using an adaptive law based upon Lyapunov stability theory. Observer eigenvalues may be freely chosen. Some restriction is placed upon the system input in that it must be sufficiently rich in frequencies in order to insure convergence.
Carroll, R. L.↗
Studies of heat source driven natural convection
Natural convection energy transport in a horizontal layer of internally heated fluid with a zero heat flux lower boundary, and an isothermal upper boundary, has been studied. Quantitative information on the time-mean temperature distribution and the fluctuating component of temperature about the mean temperature in steady turbulent convection are obtained from a small thermocouple inserted into the layer through the upper bounding plate. Data are also presented on the development of temperature at several vertical positions when the layer is subject to both a sudden increase and to a sudden decrease in power input. For changes of power input from zero to a value corresponding to a Rayleigh number much greater than the critical linear stability theory value, a slight hysteresis in temperature profiles near the upper boundary is observed between the heat-up and cool-down modes.
Kulacki, F. A.↗
Deformation and burst of a liquid droplet freely suspended in a linear shear field
A theoretical method is presented for predicting the deformation and the conditions for breakup of a liquid droplet freely suspended in a general linear shear field. This is achieved by expanding the solution to the creeping-flow equations in powers of the deformation parameter epsilon and using linear stability theory to determine the onset of bursting. When compared with numerical solutions and with the available experimental data, the theoretical results are generally found to be of acceptable accuracy although, in some cases, the agreement is only qualitative.
Barthes-Biesel, D.↗
Wind tunnel experiments relating to supersonic and hypersonic boundary layer transition
Hot-wire anemometry is used to study the origin and growth of 'natural' fluctuations in zero pressure gradient boundary layers and the location of transition to turbulence for several Mach numbers between 1.6 and 8.5. The importance to transition of certain physical mechanisms is examined through comparison of the fluctuation growth with the sound-forcing and stability theories of Mack. The mechanisms are shown to assume varying importance in low supersonic, high supersonic and hypersonic regimes. The effect on transition of cone angle of attack, tip heating, and model vibration is mentioned.
Kendall, J. M.↗
External field effects on solidification - Macroscopic and microscopic models
Comparison of theoretical effects of magnetic and gravitational fields on melts of metals and semiconductors provides two kinds of insight into space processing materials problems. First, the task of comparing effects of the two fields yields mathematical models which may be used to estimate material properties and responses to processing under various field conditions. Then, by using these models, microgravity effects can be inferred from magnetic field data already obtained in laboratories on earth. Magnetohydrodynamics (static and oscillating fields) and the Free Volume Model are used to study macroscopic effects, and Sekerka's interface stability theory is used to show how external fields can affect microsegregation. It is demonstrated that the mathematical formalism is essentially the same for describing macroscopic effects of both microgravity and magnetic fields.
Miller, R. I.↗
Application of the comparison principle to analysis of nonlinear systems
A comparison principle based on a Kamke theorem and Lipschitz conditions is presented along with its possible applications and modifications. It is shown that the comparison lemma can be used in the study of such areas as classical stability theory, higher order trajectory derivatives, Liapunov functions, boundary value problems, approximate dynamic systems, linear and nonlinear systems, and bifurcation analysis.
Gunderson, R. W.↗
Design and performance of the University of Michigan 6.6-inch hypersonic wind tunnel
The tunnel described has several design features intended to maintain laminar flow in the boundary layer of its nozzle. Measurements show that transition to turbulence in the nozzle wall boundary layer begins at the throat and is sensitive to surface roughness, heat transfer rate, and longitudinal radius of curvature. The observed dependence of transition on heat transfer rate is the reverse of that predicted by stability theory for infinitesimal disturbances. Tests include boundary layer surveys of a contoured nozzle and a conical nozzle with four interchangeable throats.
Amick, J. L.↗
Discretized partial differential equations - Examples of control systems defined on modules
The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.
Brockett, R. W.↗
Diagonalization and simultaneous symmetrization of the gas-dynamic matrices
The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.
Warming, R. F.↗
Model reference adaptive control, estimation and identification using only input and output signals
Significant recent advances in the application of stability theory to the adaptive control and identification of systems, and adaptive state estimation, are considered. Emphasis is on those methods which utilize only input and output measurements of the system, and do not require derivatives of the output signal.
Carroll, R. L.↗
Acoustics-turbulence interaction
An investigation of the instability frequency was undertaken. Measurements revealed that the hot wire probe induces and sustains stable upstream oscillation of the free shear layer. The characteristics of the free shear layer tone are found to be different from the slit jet wedge edgetone phenomenon. The shear tone induced by a plane wedge in a plane free shear layer was then examined in order to further document the phenomenon. The eigenvalues and eigenfunctions of the tone fundamental show agreement with the spatial stability theory. A comprehensive summary of the results is also included.
Hussain, A. K. M. F.↗
Stability analysis for laminar flow control, part 1
The basic equations for the stability analysis of flow over three dimensional swept wings are developed and numerical methods for their solution are surveyed. The equations for nonlinear stability analysis of three dimensional disturbances in compressible, three dimensional, nonparallel flows are given. Efficient and accurate numerical methods for the solution of the equations of stability theory were surveyed and analyzed.
Benney, D. J.↗
Instability of a compressible circular free jet with consideration of the influence of the jet boundary layer thickness
The instability of a circular jet was investigated by means of the inviscid linearized stability theory. By variation of a jet parameter which takes the ratio of jet radius to boundary layer thickness into account, the influence of axisymmetry on the spatial growth rate and disturbance phase velocity is studied. The influence of Mach number and temperature ratio is discussed. A comparison with measurements shows that the instability of a turbulent jet boundary layer may also be explained by these results.
Michalke, A.↗