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At least 145 records · Page 8

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NASA NTRS1976

Aeroelastic stability of complete rotors with application to a teetering rotor in forward flight

The derivation of a set of nonlinear coupled flap-lag-torsion equations of motion for moderately large deflections of an elastic, two bladed teetering helicopter rotor in forward flight is concisely outlined. The following degrees of freedom are included in the mathematical model: rigid body flapping, rigid body lead lag, elastic bending in flap and lead-lag blade root torsion and shaft torsion. Quasi-steady aerodynamic loads are considered and the effects of reversed flow are included. The aeroelastic stability of the complete rotor is investigated using a linearized system of equations of motion. The equilibrium position about which the equations are linearized is obtained by considering the trim state of the helicopter, in true or simulated forward flight conditions. The sensitivity of the aeroelastic stability boundaries to interblade structural and mechanical coupling is illustrated by comparing the complete rotor stability boundaries with those obtained from a single blade analysis for a number of hover and forward flight cases.

Shamie, J.↗

NASA NTRS1993

Stress stiffening and approximate equations in flexible multibody dynamics

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to 'oversimplified,' or ruthless, equations through the use of open loop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. The consistent and inconsistent models differ by stress stiffening terms. These are due to zeroth-order stresses effecting virtual work via nonlinear strain-displacement terms. In this paper we examine in detail the nature of these stress stiffening terms and conclude that they are significant only when the associated zeroth-order stresses approach 'buckling' stresses. Finally it is emphasized that when the stress stiffening terms are negligible the ruthlessly linearized equations should be used.

Padilla, Carlos E.↗

NASA NTRS1973

Liapunov stability analysis of hybrid dynamical systems in the neighborhood of nontrivial equilibrium

This paper is concerned with the stability of a hybrid dynamical system in the neighborhood of a nontrivial equilibrium, where the system consists of one rigid part and n elastic members. The body moves in a central-force field with its mass center describing a circular orbit. The nontrivial equilibrium is defined by steady rotation of the system at an angular velocity equal to the orbital velocity, with the elastic members being in deformed state. A Liapunov stability analysis is performed by assuming small perturbations about the nontrivial equilibrium, where the latter is generally defined by nonlinear differential equations. The theory is applied to a gravity-gradient stabilized satellite with flexible appendages.

Meirovitch, L.↗

NASA NTRS1976

Analysis of contact pressures attainable using indentors which are bodies of revolution

The elastic behavior of a conical indentor with a rounded tip pressed against a flat anvil has been analyzed. It is found that when the radius of contact extends beyond the rounded tip, the contact radius increases much more rapidly as the pressure increases than it does for the case of a fully spherical or parabolic tip. Consequently, the pressure achieved for a rounded conical tip for a given applied force is considerably less than for a spherical or parabolic tip.

Ruoff, A. L.↗

NASA NTRS1977

Floating reference frames for flexible spacecraft

Floating reference frames which move with the flexible body under dynamic analysis offer the advantages of a linear vibration analysis in the presence of large system rotations. When the deformations of an elastic continuum are expanded in terms of the free-free modes on an unconstrained system, the rigid body modes are found to be fixed in a reference frame called the Tisserand frame, with respect to which the relative momentum is zero. This result also guarantees the independence of small variations of frame motions and coordinates for all modes with nonzero natural frequencies, a condition which can greatly simplify the formulation of equations of motion. A Modified Tisserand Constraint is introduced in order to define a floating reference frame with similar properties for an elastic body which contains spinning rotors.

Canavin, J. R.↗

NASA NTRS1990

Modeling and model simplification of aeroelastic vehicles

The rigid-body degrees of freedom and elastic degrees of freedom of aeroelastic vehicles are typically treated separately in dynamic analysis. Such a decoupling, however, is not always justified and modeling assumptions that imply decoupling must be used with caution. The frequency separation between the rigid-body and elastic degrees of freedom for advanced aircraft may no longer be sufficient to permit the typical treatment of the vehicle dynamics. Integrated, elastic vehicle models must be developed initially and simplified in a manner appropriate to and consistent with the intended application. This paper summarizes key results from the research aimed at developing and implementing integrated aeroelastic vehicle models for flight controls analysis and design. Three major areas will be addressed: (1) the accurate representation of the dynamics of aeroelastic vehicles, (2) properties of several model simplification methods, and (3) the importance of understanding the physics of the system being modeled and of having a model which exposes the underlying physical causes for critical dynamic characteristics.

Waszak, Martin R.↗

NASA NTRS1992

Modeling and model simplification of aeroelastic vehicles: An overview

The rigid-body degrees of freedom and elastic degrees of freedom of aeroelastic vehicles are typically treated separately in dynamic analysis. Such a decoupling, however, is not always justified and modeling assumptions that imply decoupling must be used with caution. The frequency separation between the rigid-body and elastic degrees of freedom for advanced aircraft may no longer be sufficient to permit the typical treatment of the vehicle dynamics. Integrated, elastic vehicle models must be developed initially and simplified in a manner appropriate to and consistent with the intended application. This paper summarizes key results from past research aimed at developing and implementing integrated aeroelastic vehicle models for flight controls analysis and design. Three major areas will be addressed: (1) the accurate representation of the dynamics of aeroelastic vehicles, (2) properties of several model simplification methods, and (3) the importance of understanding the physics of the system being modeled and of having a model which exposes the underlying physical causes for critical dynamic characteristics.

Waszak, Martin R.↗

NASA NTRS1975

A vector-dyadic development of the equations of motion for N-coupled flexible bodies and point masses

The equations of motion for a system of coupled flexible bodies, rigid bodies, point masses, and symmetric wheels were derived. The equations were cast into a partitioned matrix form in which certain partitions became nontrivial when the effects of flexibility were treated. The equations are shown to contract to the coupled rigid body equations or expand to the coupled flexible body equations all within the same basic framework. Furthermore, the coefficient matrix always has the computationally desirable property of symmetry. Making use of the derived equations, a comparison was made between the equations which described a flexible body model and those which described a rigid body model of the same elastic appendage attached to an arbitrary coupled body system. From the comparison, equivalence relations were developed which defined how the two modeling approaches described identical dynamic effects.

Frisch, H. P.↗

NASA NTRS1973

Equations for the kinetic modeling of supersonically flowing electrically excited lasers

The equations for the kinetic modeling of a supersonically flowing electrically excited laser system are presented. The work focuses on the use of diatomic gases, in particular carbon monoxide mixtures. The equations presented include the vibrational rate equation which describes the vibrational population distribution, the electron, ion and electronic level rate equations, the gasdynamic equations for an ionized gas in the presence of an applied electric field, and the free electron Boltzmann equation including flow and gradient coupling terms. The model developed accounts for vibration-vibration collisions, vibration-translation collisions, electron-molecule inelastic excitation and superelastic de-excitation collisions, charge particle collisions, ionization and three body recombination collisions, elastic collisions, and radiative decay, all of which take place in such a system. A simplified form of the free electron Boltzmann equation is developed and discussed with emphasis placed on its coupling with the supersonic flow. A brief description of a possible solution procedure for the set of coupled equations is then discussed.

Lind, R. C.↗

NASA NTRS1978

Tidal friction in the solid earth

The earth's imperfectly elastic response to body and loading tidal forces is discussed using complex Love numbers and complex mass loading coefficients. Exact analytical expressions were derived relating the energy dissipation within an inhomogeneous, compressible solid earth to the surface values of these complex characteristic numbers, thus relating the global dissipation function Q to the phase shifts in the potential, gravity, tilt, strain and displacement tides. Integration of a global ocean tidal model shows that energy dissipated in the solid earth due to ocean loading is at least 10% of that dissipated in the body tides.

Zschau, J.↗

NASA NTRS1982

Attitude and vibration control of a large flexible space-based antenna

The problem of control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear quadratic Gaussian (LQG) control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Joshi, S. M.↗

NASA NTRS1982

Control systems synthesis for a large flexible space antenna

The problem of control systems synthesis is considered for controlling the rigid-body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian (LQG) control theory. A combination of the two methods, which results in a two-level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Joshi, S. M.↗

NASA NTRS1982

Attitude and vibration control of a large flexible space-based antenna

Control systems synthesis is considered for controlling the rigid body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian control theory. A combination of the two methods, which results in a two level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Joshi, S. M.↗

NASA NTRS1984

Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes.

Meirovitch, L.↗

NASA NTRS1986

On contact problems of elasticity theory

Certain contact problems are reviewed in the two-dimensional theory of elasticity when round bodies touch without friction along most of the boundary and, therefore, Herz' hypothesis on the smallness of the contact area cannot be used. Fundamental equations were derived coinciding externally with the equation in the theory of a finite-span wing with unkown parameter. These equations are solved using Multhopp's well-known technique, and numerical calculations are performed in specific examples.

Kalandiya, A. I.↗

NASA NTRS1986

On the Lagrangian turbulence in continua

Lagrangian turbulence in continua is introduced as a failure of Euclidian metric of a material system of coordinates, and it is shown that the Ricci tensor of such a system of coordinates may be used as a measure of L-turbulence. The conditions which are sufficient, though not necessary, for instability of an initially infinitesimal disturbance of this tensor are determined for fluid, elastic, and viscoelastic bodies. The results are obtained from the linearized equations, and therefore the growth of unstable solutions may be bounded.

Zak, M.↗

NASA NTRS1986

Analysis of crack closure under plane strain conditions

The phenomenon of plasticity-induced crack closure is associated with the development of residual material on the flanks of an advancing fatigue crack. While it is easy to see that this residual material can come from the side faces of a specimen under plane stress conditions, it is difficult to discover the origin of this extra volume of material on the crack flanks when it is assumed that plane deformations occur and plastic flow is incompressible. The purpose of this paper is to determine whether plasticity-induced fatigue crack closure occurs in an elastic-perfectly plastic body under plane strain conditions.

Fleck, N. A.↗

NASA NTRS1988

Analysis of crack closure under plane strain conditions

Fleck, Norman A.↗