Showing papers by "Earl H. Dowell published in 1984"

Flutter Analysis Using Nonlinear Aerodynamic Forces

Abstract: The nonlinear effects of transonic aerodynamic forces on the flutter boundary of a typical section airfoil are studied. The flutter speed dependence on amplitude is obtained by utilizing a novel variation of the describing function method which takes into account the first fundamental harmonic of the nonlinear oscillatory motion. By using an aerodynamic describing function, traditional flutter analysis methods may still be used while including the effects of aerodynamic nonlinearities. Results from such a flutter analysis are compared with those of brute force time-marching solutions. The aerodynamic forces are computed by the LTRAN2 aerodynamic code for an NACA 64A006 airfoil at Mx = 0.86.

Doublet-Point Method for Supersonic Unsteady Lifting Surfaces.

Abstract: A method to predict unsteady aerodynamic forces on lifting surfaces in supersonic flow is presented. The wing is divided into small segments in which the lift force is expressed by a single-point doublet of the acceleration potential. This is the same concept as the doublet-point method developed by the authors for subsonic flows. In order to avoid sensitiveness to the Mach number, the upwash due to the point doublet is calculated by averaging over small areas. The integration is done analyticaly so that it requires no numerical quadrature. Pressure distributions are directly obtained as the unknowns of the algebraic equation. The results are compared with those obtained by other methods for various wing geometries, including the AGARD wing-tail configuration.

Observation and Evolution of Chaos for an Autonomous System

Abstract: Time histories, phase plane portraits, power spectra, and Poincare maps are used as descriptors to observe the evolution of chaos in an autonomous system. Although the motions of such a system can be quite complex, these descriptors prove helpful in detecting the essential structure of the motion. Here the principal interest is in phase plane portraits and Poincare maps, their methods of construction, and physical interpretation. The system chosen for study has been previously discussed in the literature, i.e., the flutter of a buckled elastic plate in a flowing fluid.

Asymptotic modal analysis and statistical energy analysis of dynamical systems

Abstract: The well known text by Lyon on Statistical Energy Analysis (SEA) [R. H. Lyon, Statistical Energy Analysis of Dynamical Systems: Theory and Applications (MIT Press, Cambridge, MA, 1975)] is the standard reference on the subject. As originally conceived SEA was based upon several plausible hypotheses. Various authors have considered the underlying basis for SEA and thereby advanced our understanding of it. In the present paper, the relationship between classical modal analysis (CMA) and SEA is studied. It is shown how the results of SEA may be obtained as an asymptotic limit of CMA. The present work only considers the response of a single general linear structure under a random or sinusoidal load. However future plans will consider (a) the structural acoustic response of an enclosure bounded by a flexible wall and excited by external forces and (b) two (or more) coupled structural systems. Here the emphasis is on (1) a new derivation of the SEA results from CMA for a single structure under a random load, (2) the generalization of the usual SEA result to show that, asymptotically, all points on the structure have the same response. In the literature this is sometimes invoked as an assumption. Here the result is derived as part of the asymptotic limit of CMA. (3) A numeriCal example which displays the manner in which the asymptotic limit is approached for random loading and (4) an extension of the usual SEA result for sinusoidal loading. In view of the above, the present results might be called more appropriately Asymptotic Modal Analysis (AMA) rather than SEA.

Chaotic oscillations in mechanical systems

Abstract: Abstract Chaotic oscillations have now been observed in nonlinear mechanical systems using analytical, numerical, and experimental methods. Nevertheless, a more fundamental understanding of why and when such oscillations occur is of great importance. This goal will be pursued here by considering the relationship between chaos induced by forced oscillations versus self-excited oscillations, the relationship of indeterminancy of the final equilibrium state in the initial value problem to chaos in the sustained oscillation problem, comparison of theory to physical experiment, necessary and sufficient conditions for chaos to occur, and the question of convergence of systems of modal ordinary differential equations that derive from partial differential equations.