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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Characteristic Elastic Systems of Time-Limited Optimal Maneuvers

Optimizing an elastic system and its active control is discussed. Maneuvers from an initial state to a final state in a finite time interval are considered. An active generalized control force that accomplishes the desired maneuver of a prespecified system is optimal if it minimizes a given quadratic cost function. By also varying a set of design parameters, the elastic system can be determined so as to further minimize the cost function. Here, the elastic system that minimizes the actual control cost is compared with the system that minimizes the ratio of actual cost to the cost of optimally maneuvering a rigid system of the same inertial properties. It is shown that an elastic system corresponding to an extremum of the ratio is actually a characteristic of the time-limited maneuver. Because both the spatial domain and the time interval are fixed, a characteristic elastic system is tuned to the specified temporal boundary conditions. The implication for rest-to-rest, spinup, and spin reversal maneuvers of spacecraft is that the optimal control for a characteristic elastic spacecraft is identical to the optimal control for the same spacecraft as if it were rigid.

Hale, A. L.↗
NASA NTRS1972

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

Poole, L. R.↗
NASA NTRS1973

Part 1: The stability of equilibrium shapes of elastic systems

The stability of equilibrium shapes of elastic systems is examined. Stability loss in the case of similar equilibrium shapes, the disappearance of stable equilibrium shapes, and the disappearance of any forms of equilibrium are discussed. The error made by Euler in analyzing stability loss is pointed out, and Mises' truss is used as an example of stability loss in the case of similar equilibrium shapes.

Panovko, Y. G.↗
NASA NTRS1971

Stability of circulatory elastic systems in the presence of magnetic damping.

The effect of a type of magnetic damping on the stability of equilibrium of some circulatory elastic systems is examined. A simple system with two degrees of freedom is considered first, and a destabilization is found to be caused by the magnetic field. The nature of the destabilization, however, is not identical to that caused by internal viscous damping. The differences and similarities between the two effects are discussed, and the results are also compared with those of linear external viscous damping. A continuous cantilever bar subjected to a follower force at its free end is then examined. It is found that the critical load is independent of the strength of the magnetic field, and is considerably lower than the corresponding critical load in the absence of a magnetic field. Finally, the continuous cantilever is treated approximately by Galerkin's procedure and also by using a two-degree-of-freedom model of the cantilever; the results obtained are qualitatively the same.

Smith, T. E.↗
NASA NTRS1973

Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.

An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

Walker, J. A.↗
NASA NTRS1989

Bending rate damping in elastic systems

Preliminary results of an investigation of the bending rate damping model for elastic structures are presented. A model for which the internal damping term is physically plausible and which can accomodate cantilevered boundary conditions is discussed. The model formulation and mathematical foundations are given, and numerical results are discussed.

Banks, H. T.↗
NASA NTRS1973

Part 2: Oscillations of elastic systems

Problems of oscillations of linear systems are discussed, including systems with a fractional number of degrees of freedom as well as free oscillations of a cantilever in the field of centrifugal forces. Four methods of solving the problem of the action of periodic instantaneous impulses are presented. The Tacoma catastrophe is analyzed and used as an example of aeroelastic oscillations. Problems of nonlinear system oscillations include the vibration maintenance of rotation, the Sommerfeld effect, and self-oscillations of a quasi-system with dry friction.

Source record↗
NASA NTRS1982

Optimal control of distributed parameter elastic systems

This paper presents an analytical solution to the Riccati equation for self-adjoint systems such as beams, plates, strings and membranes moving in space, and shows how the optimal control law can be implemented using the given solution. It is then shown that there always exists a self-adjoint operator describing the distribution of potential energy if the state space is appropriately augmented. A beam-like gravity-stabilized satellite moving in a circular orbit around the earth is used to illustrate the main results in this paper.

Juang, J.-N.↗
NASA NTRS1983

Simultaneous control and optimization for elastic systems

Studies are conducted to determine the dynamic response of beams and plates to loads which are extreme within a certain class of admissible loads. Two approaches to this problem are suggested. In approach one, Pontryagin's maximality principle is regarded as an additional constraint. The optimality of design is then determined by standard numerical techniques. The "adjoint variable approach' to sensitivity of structural design is applied for a given inhomogeneous term. The inhomogeneous term is an extremal element of admissible load vectors, which constitute a closed subspace of a Sobolev space. Again, the maximality principle is invoked. While only beam and plate theory problems are used as examples, generalizations are easy to perceive.

Komkov, V.↗
NASA NTRS1981

Optimal control and controller location for distributed parameter elastic systems

A class of systems governed by second order partial differential equations and driven by controllers located at points r sub i, i = 1, ..., k, is considered. A cost functional quadratic in the time derivative of the state and the control is associated with the system. The optimal controller locations are defined as the ones which minimize the maximum of the cost over all possible initial states. An analytical solution to the associated Riccati equation is presented providing a convenient expression for determining the optimal locations.

Hamidi, M.↗
NASA NTRS1990

Application of the operator spline technique to nonlinear estimation and control of moving elastic systems

A bilinear model of the vibrational dynamics of a deformable maneuvering body is described. Estimates of the deformation state are generated through a low dimensional operator spline interpolator of bilinear systems combined with a feedback linearized based observer. Upper bounds on error estimates are also generated through the operator spline, and potential application to shaping control purposes is highlighted.

Karray, Fakhreddine↗