Stress analysis of cracks
Elastic stress analyses of cracked bodies represented by stress intensity factor method - fracture mechanics
STRESS ANALYSIS↗
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A robust nonlinear attitude control law for space stations with flexible structural components
In this paper, a nonlinear attitude control law for space stations with flexible structural components is derived using a rigid-body model. This control law, depending on the Cayley-Rodriguez parameters, globally stabilizes the equilibrium of the rigid-body model. The effect of elastic deformations of the flexible structural components on the resulting feedback system dynamics is analyzed. It is found that the system's stability property is highly robust with respect to structural vibrations and inertial variations. The time-domain behavior of the feedback system is studied numerically using a model of a typical space station with flexible solar panels.
Wang, P. K. C.↗
Control-structure interaction in precision pointing servo loops
The control-structure interaction problem is addressed via stability analysis of a generic linear servo loop model. With the plant described by the rigid body mode and a single elastic mode, structural flexibility is categorized into one of three types: (1) appendage, (2) in-the-loop minimum phase, and (3) in-the-loop nonminimum phase. Closing the loop with proportional-derivative (PD) control action and introducing sensor roll-off dynamics in the feedback path, stability conditions are obtained. Trade studies are conducted with modal frequency, modal participation, modal damping, loop bandwidth, and sensor bandwidth treated as free parameters. Results indicate that appendage modes are most likely to produce instability if they are near the sensor rolloff, whereas in-the-loop modes are most dangerous near the loop bandwidth. The main goal of this paper is to provide a fundamental understanding of the control-structure interaction problem so that it may benefit the design of complex spacecraft and pointing system servo loops. In this framework, the JPL Pathfinder gimbal pointer is considered as an example.
Spanos, John T.↗
Dynamic analysis of flexible multibody structures
A system composed of several interconnected elastic components that may experience large angular motion relative to each other during operation is referred to as a flexible multibody structure. Several formulations were proposed for the determination of the dynamic response of controlled flexible multibody structures. In general, these formulations consist of superposing elastic deformations of the component body onto the large rigid body motion of the component. It was shown that this particular methodology for combining linear structural deformations with nonlinear kinematics can lead to erroneous response predictions when either the beam member is very flexible or the rotational speed is high. In addition, previous formulations introduce constraint equations to define the interrelations among system components. This approach increases the number of equations that must be solved, and may result in contraint violation when numerical error accumulates during the integration process. In order to overcome the difficulties, a new approach was suggested. The approach is essentially a finite element formulation which takes advantage of the fact that many multibody structures are joint dominated. The Large Angle Transient Dynamic Analysis (LATDYN) program for clarity of documentation, ease of use, user friendliness, modeling generality, and accuracy of results was evaluated. This required gaining a working familiarity with the code and performing several case studies.
Hernried, Alan G.↗
Mathematical modeling of a class of multibody flexible spacecraft structures
A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.
Kelkar, Atul, G.↗
Dynamic Characteristics of Space Station Freedom Mars and Lunar Evolution Reference Configurations
One concept for a manned mission to Mars uses an evolutionary version of Space Station Freedom (SSF) as a transportation node. The station is modified by the addition of dual keels, an upper and lower boom, additional laboratory and habitation modules, increased power and an assembly platform. With these modifications the station is called the Mars Evolution Reference Configuration (MERC). The mass of the station is 65 percent greater than the mass of SSF and its moments of inertia through the mass center are greater by approximately a factor of four. Over a period of months, several flights from Earth to low-Earth-orbit carry the components of a manned Mars piloted vehicle (MPV) to the MERC where the vehicle is constructed on the assembly platform. After each flight the station is reboosted to an appropriate altitude, such that the orbit decay due to atmospheric drag forces lowers the spacecraft to the proper altitude at the appropriate time for rendezvous with the next assembly flight. When the assembly process is completed, the MPV, which has a mass of approximately 200,000 lbm, is situated on the evolutionary station. The mass increase of the MERC with MPV system over SSF is 112 percent and the moments of inertia about axes through the mass center increase by up to a factor of 12. When the MPV is assembled, inspected and verified, the mission is ready to proceed and the MPV is moved from the station to a staging area and mated with fueled trans-Mars injection stages for the flight to Mars. This presentation describes a finite element model of the MERC formulated to investigate the expected low frequency modes and its variation with the addition of a large payload. A basic reboost procedure using near-continuous firing of reaction control system jets is proposed with off-modulation of the jets used to control flight attitude. The reboost procedure is described with the closed-loop attitude control dictating jet on/off cycling based on feedback signals which contain both the rigid body rotation information and the elastic rotations local to the attitude sensor. The presentation contains a description of the dynamic response at critical points of the station during the reboost and concludes with results of a brief study of the dynamic characteristics of a Lunar transportation node configuration.
Ayers, J. Kirk↗
Attitude control system synthesis for the Hoop/Column antenna using the LQG/LTR method
This paper investigates the application of the linear-quadratic-Gaussian (LQG)/loop transfer recovery (LTR) method to the problem of synthesizing a fine-pointing control system for a large flexible space anenna. The study is based on an antenna, which consists of three rigid-body rotational modes and the first ten elastic modes. A robust compensator design for achieving the required pointing performance in the presence of modeling uncertainties is obtained using the LQG/LTR method. For the Hoop/Column antenna, a satisfactory controller design meeting a desired bandwidth of .1 rad/sec and ensuring stability with unmodelled high frequency modes is obtained using only a collocated pair of 3-axis attitude sensors and torque actuators. This study also indicates that to achieve the desired performance bandwidth of 0.1 rad/sec. and to ensure stability in the presence of higher frequency elastic modes, the design model should include at least the first three flexible modes together with the rigid body modes.
Sundararajan, N.↗
A unique formulation of elastic airplane longitudinal equations of motion
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at early stages of preliminary design. An approximate, but reasonably accurate, set of equations of motion are needed for these early analyses. Such a formulation is developed for the longitudinal dynamics of elastic airplanes. It makes use of only rigid-body aerodynamic stability derivatives in formulating the forces and moments due to elastic motion. Verification of accuracy using data for the B-1 airplane shows very good agreement. Frequencies and damping ratios of the coupled modes corresponding to complex roots of the characteristic equations agree closely with four symmetric elastic modes included.
Swaim, R. L.↗
A unique formulation of elastic airplane longitudinal equations of motion
Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at early stages of preliminary design. An approximate but reasonably accurate set of equations of motion are needed for these early analyses. Such a formulation is developed for the longitudinal dynamics of elastic airplanes. It makes use of only rigid-body aerodynamic stability derivatives in formulating the forces and moments due to elastic motion. Verification of accuracy using data for the B-1 airplane shows very good agreement. Frequencies and damping ratios of the coupled modes corresponding to complex roots of the characteristic equations agree closely with four symmetric elastic modes included.
Swaim, R. L.↗
Aeroelastic Analysis of a Trimmed Generic Hypersonic Vehicle
The aeroelastic equations of motion governing a hypersonic vehicle in free flight are derived. The equations of motion for a translating and rotating flexible body using Lagrange's equations in terms of quasi-coordinates are presented. These equations are simplified for the case of a vehicle with pitch and plunge rigid body degrees of freedom and small elastic displacements. The displacements are approximated by a truncated series of the unrestrained mode shapes, which are obtained using equivalent plate theory. Subsequently, the nonlinear equations of motion are linearized about the trim state, which is obtained using a rigid body trim model and steady hypersonic aerodynamics. The appropriate flutter derivatives are calculated from piston theory. Results describing mode shapes, trim behavior, and aeroelastic stability of a generic hypersonic vehicle are presented.
Nydick, I.↗
An experimental and analytical study of a lifting-body wind-tunnel model exhibiting body-freedom flutter
Flutter analysis of the proposed National Aerospace Plane indicates that in the subsonic to transonic flight regime, the vehicle may be susceptible to an instability known as body-freedom flutter. Body-freedom flutter is a dynamic instability involving a vehicle rigid-body mode coupling with one or more of the vehicle's elastic modes. In the case of the NASP, the body-freedom flutter predicted by analysis involves the short-period mode of the vehicle coupling with the pivot mode of the all-movable wings. A wind-tunnel test was designed to investigate this phenomenon. Parameter studies included variations in wing-actuator stiffness, wing-pivot shaft location along the root chord, and thickness of the fuselage. The wind-tunnel test was conducted in the NASA Langley Transonic Dynamics Tunnel. Flutter boundaries were measured in the wind tunnel for three configurations and a model divergence point was measured on a fourth configuration. At the last flutter point obtained during the test, body-freedom flutter proved to be rather violent. The analysis used in this study incorporated thin-wing theory aerodynamics and did a fairly good job of predicting the flutter boundaries.
Soistmann, David L.↗
Aeromechanical stability of helicopters with composite rotor blades in forward flight
The aeromechanical stability, including air resonance in hover, air resonance in forward flight, and ground resonance, of a helicopter with elastically tailored composite rotor blades is investigated. Five soft-inplane hingeless rotor configurations, featuring elastic pitch-lag, pitch-flap and extension-torsion couplings, are analyzed. Elastic couplings introduced through tailored composite blade spars can have a powerful effect on both air and ground resonance behavior. Elastic pitch-flap couplings (positive and negative) strongly affect body, rotor and dynamic inflow modes. Air resonance stability is diminished by elastic pitch-flap couplings in hover and forward flight. Negative pitch-lag elastic coupling has a stabilizing effect on the regressive lag mode in hover and forward flight. The negative pitch-lag coupling has a detrimental effect on ground resonance stability. Extension-torsion elastic coupling (blade pitch decreases due to tension) decreases regressive lag mode stability in both airborne and ground contact conditions. Increasing thrust levels has a beneficial influence on ground resonance stability for rotors with pitch-flap and extension-torsion coupling and is only marginally effective in improving stability of rotors with pitch-lag coupling.
Smith, Edward C.↗
Air and ground resonance of helicopters with elastically tailored composite rotor blades
The aeromechanical stability, including air resonance in hover, air resonance in forward flight, and ground resonance, of a helicopter with elastically tailored composite rotor blades is investigated. Five soft-inplane hingeless rotor configurations, featuring elastic pitch-lag, pitch-flap and extension-torsion couplings, are analyzed. Elastic couplings introduced through tailored composite blade spars can have a powerful effect on both air and ground resonance behavior. Elastic pitch-flap couplings (positive and negative) strongly affect body, rotor and dynamic inflow modes. Air resonance stability is diminished by elastic pitch-flap couplings in hover and forwrad flight. Negative pitch-lag elastic coupling has a stabilizing effect on the regressive lag mode in hover and forward flight. The negative pitch-lag coupling has a detrimental effect on ground resonance stability. Extension-torsion elastic coupling (blade pitch decreases due to tension) decreases regressive lag mode stability in both airborne and ground contact conditions. Increasing thrust levels has a beneficial influence on ground resonance stability for rotors with pitch-flap and extension-torsion coupling and is only marginally effective in improving stability of rotors with pitch-lag coupling.
Smith, Edward C.↗
Real time analog computer simulation of the elastic space vehicle involving beam cell transmission matrices
Real time analog computer simulation of traveling wave effects, bending modes, rigid body motions, and transfer functions in electronic model of elastic space vehicle
COMPUTER SIMULATION↗
Handling qualities of large flexible control-configured aircraft
The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.
Swaim, R. L.↗
An Exploratory Investigation of Some Types of Aeroelastic Instability of Open and Closed Bodies of Revolution Mounted on Slender Struts
Aeroelastic instability phenomena of isolated open and closed rigid bodies of revolution free to move under elastic restraint have been investigated experimentally at low speeds by means of models suspended at zero angles of attack and yaw on slender flexible struts from a wind tunnel ceiling. Three types of instability were observed - flutter similar to classical bending-torsion flutter, divergence, and an uncoupled oscillatory instability which consists in nonviolent continuous or intermittent small-amplitude oscillations involving only angular deformations. The speeds at which this oscillatory instability starts were found to be as low as about one-third of the speed at flutter or divergence and to depend on the shape of the body, particularly that of the afterbody, and on the relative location of the elastic axis. An attempt has been made to calculate the airspeeds and, in the case of the oscillatory phenomena, the frequencies at which these instabilities occur by using slender-body theory for the aerodynamic forces on the bodies and neglecting the aerodynamic forces on the struts. However, the agreement between the speeds and frequencies calculated in this manner and those actually observed has been found to be generally unsatisfactory; with the exception of the frequencies of the uncoupled oscillations which could be predicted with fair accuracy. The nature of the observed phenomena and of the forces on bodies of revolution suggests that a significant improvement in the accuracy of analytical predictions of these aeroelastic instabilities can be had only by taking into account the effects of boundary-layer separation on the aerodynamic forces.
Clevenson, S. A.↗
Handling Qualities of Large Flexible Aircraft
The effects on handling qualities of elastic modes interaction with the rigid body dynamics of a large flexible aircraft are studied by a mathematical computer simulation. An analytical method to predict the pilot ratings when there is a severe modes interactions is developed. This is done by extending the optimal control model of the human pilot response to include the mode decomposition mechanism into the model. The handling qualities are determined for a longitudinal tracking task using a large flexible aircraft with parametric variations in the undamped natural frequencies of the two lowest frequency, symmetric elastic modes made to induce varying amounts of mode interaction.
Poopaka, S.↗
A variational approach to dynamics of flexible multibody systems
This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.
Wu, Shih-Chin↗