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NASA NTRS1989

Dynamic stability of unidirectional fiber-reinforced viscoelastic composite plates

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a three-dimensional viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi's micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Chandiramani, N. K.↗

NASA NTRS1991

Stability of a non-orthogonal stagnation flow to three dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flow field is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3-D disturbances is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Lasseigne, D. G.↗

NASA NTRS1991

Nonlinear stability and control study of highly maneuverable high performance aircraft

The purpose was to develop and apply new nonlinear system methodologies to the stability analysis and adaptive control of high angle of attack (alpha) aircraft such as the F-18. Considerable progress is documented on nonlinear adaptive control and associated model development, identification, and simulation. The analysis considered linear and nonlinear, longitudinal, high alpha aircraft dynamics with varying degrees of approximation dependent on the purpose. In all cases, angle of attack or pitch rate was controlled primarily by a horizontal stabilizer. In most cases studied, a linear adaptive controller provided sufficient stability. However, it has been demonstrated by simulation of a simplified nonlinear model that certain large rapid maneuvers were not readily stabilized by the investigated linear adaptive control, but were controlled instead by means of a nonlinear time-series based adaptive control.

Mohler, R. R.↗

NASA NTRS1990

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Fay, John F.↗

NASA NTRS1991

Inviscid spatial stability of a compressible mixing layer. III - Effect of thermodynamics

The results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow are reported. The models are: (1) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; (2) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (3) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity temperature relation and arbitrary but constant Prandtl number. The purpose was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the quantitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, it is shown that the stability characteristics are sensitive to the value of the Prandtl number.

Jackson, T. L.↗

NASA NTRS1991

Performance and stability of telemanipulators using bilateral impedance control

A new method of control for telemanipulators called bilateral impedance control is investigated. This new method differs from previous approaches in that interaction forces are used as the communication signals between the master and slave robots. The new control architecture has several advantages: (1) It allows the master robot and the slave robot to be stabilized independently without becoming involved in the overall system dynamics; (2) It permits the system designers to arbitrarily specify desired performance characteristics such as the force and position ratios between the master and slave; (3) The impedance at both ends of the telerobotic system can be modulated to suit the requirements of the task. The main goals of the research are to characterize the performance and stability of the new control architecture. The dynamics of the telerobotic system are described by a bond graph model that illustrates how energy is transformed, stored, and dissipated. Performance can be completely described by a set of three independent parameters. These parameters are fundamentally related to the structure of the H matrix that regulates the communication of force signals within the system. Stability is analyzed with two mathematical techniques: the Small Gain Theorem and the Multivariable Nyquist Criterion. The theoretical predictions for performance and stability are experimentally verified by implementing the new control architecture on a multidegree of freedom telemanipulator.

Moore, Christopher Lane↗

NASA NTRS1992

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

Mohler, R. R.↗

NASA NTRS1992

Effect of model selection on combustor performance and stability predictions using ROCCID

The ROCket Combustor Interactive Design (ROCCID) methodology is an interactive computer program that combines previously developed combustion analysis models to calculate the combustion performance and stability of liquid rocket engines. Test data from 213 kN (48,000 lbf) Liquid Oxygen (LOX)/RP-1 combustor with an O-F-O (oxidizer-fuel-oxidizer) triplet injector were used to characterize the predictive capabilities of the ROCCID analysis models for this injector/propellant configuration. Thirteen combustion performance and stability models were incorporated into ROCCID, and ten of them, which have options for triplet injectors, were examined. Calculations using different combinations of analysis models, with little or no anchoring, were carried out on a test matrix of operating combinations matching those of the test program. Results of the computer analyses were compared to test data, and the ability of the model combinations to correctly predict combustion stability or instability was determined. For the best model combination(s), sensitivity of the calculations to fuel drop size and mixing efficiency was examined. Error in the stability calculations due to uncertainty in the pressure interaction index (N) was examined. The recommended model combinations for this O-F-O triplet LOX/RP-1 configuration are proposed.

Giuliani, James E.↗

NASA NTRS1992

Stability and performance of notch filter control for unbalance response

Many current applications of magnetic bearings for rotating machinery employ notch filters in the feedback control loop to reduce the synchronous forces transmitted through the bearings. The capabilities and limitations of notch filter control are investigated. First, a rigid rotor is examined with some classical root locus techniques. Notch filter control is shown to result in conditional stability whenever complete synchronous attenuation is required. Next, a nondimensional parametric symmetric flexible three mass rotor model is constructed. An examination of this model for several test cases illustrates the limited attenuation possible with notch filters at and near the system critical speeds when the bearing damping is low. The notch filter's alteration of the feedback loop is shown to cause stability problems which limits performance. Poor transient response may also result. A high speed compressor is then examined as a candidate for notch filter control. A collocated 22 mass station model with lead-lag control is used. The analysis confirms the reduction in stability robustness that can occur with notch filter control. It is concluded that other methods of synchronous vibration control yield greater performance without compromising stability.

Knospe, C. R.↗

NASA NTRS1992

Stability of a premixed flame in stagnation-point flow against general disturbances

Previously, the stability of a premixed flame in a stagnation flow was discussed for a restricted class of disturbances that are self-similar to the basic undisturbed flow; thus, flame fronts with corrugations only in the cross stream direction were considered. Here, we consider a more general class of three-dimensional flame front perturbations which also permits corrugations in the streamwise direction. It is shown that, because of the stretch experienced by the flame, the hydrodynamic instability is limited only to disturbances of short wavelength. If in addition diffusion effects have a stabilizing influence, as would be the case of mixtures with Lewis number greater than one, a stretched flame could be absolutely stable. Instabilities occur when the Lewis number is below some critical value less than one. Neutral stability boundaries are presented in terms of the Lewis number, the strain rate, and the appropriate wavenumbers. Beyond the stability threshold, the two-dimensional self-similar modes always grow first. However, if disturbances of long wavelength are excluded, it is possible for the three-dimensional modes to be the least stable one. Accordingly, the pattern that will be observed on the flame front, at the onset of instability, will consist of either ridges in the direction of stretch or the more common three-dimensional cellular structure.

Jackson, Thomas L.↗

NASA NTRS1992

Spacecraft stability and control

The Earth's first artificial satellite, Sputnik 1, slowly tumbled in orbit. The first U.S. satellite, Explorer 1, also tumbled out of control. Today, satellite stability and control has become a higher priority. For a satellite design that is to have a life expectancy of 14 years, appropriate spacecraft flight control systems will be reviewed, stability requirements investigated, and an appropriate flight control system recommended in order to see the design process. Disturbance torques, including aerodynamic, magnetic, gravity gradient, solar, micrometeorite, debris, collision, and internal torques, will be assessed to quantify the disturbance environment so that the required compensating torques can be determined. The control torques, including passive versus active, momentum control, bias momentum, spin stabilization, dual spin, gravity gradient, magnetic, reaction wheels, control moment gyros, inertia augmentation techniques, three-axis control, and reaction control systems (RCSs), will be considered. Conditions for stability will also be considered.

Barret, Chris↗

NASA NTRS1991

Stability and instability of thermocapillary convection in models of float-zone crystal growth

The energy-stability theory has been used to study the stability properties of thermocapillary convection in a half-zone model of the float-zone crystal-growth process. It is concluded that the energy theory provides a sufficient condition for stability to disturbances of arbitrary amplitude. Results of the computation of energy-stability limits are found to be in good agreement with experimentally measured bounds for oscillatory thermocapillary convection.

Neitzel, G. P.↗

NASA NTRS1992

Stability of a nonorthogonal stagnation flow to three-dimensional disturbances

A similarity solution for a low Mach number nonorthogonal flow impinging on a hot or cold plate is presented. For the constant density case, it is known that the stagnation point shifts in the direction of the incoming flow and that this shift increases as the angle of attack decreases. When the effects of density variations are included, a critical plate temperature exists; above this temperature the stagnation point shifts away from the incoming stream as the angle is decreased. This flowfield is believed to have application to the reattachment zone of certain separated flows or to a lifting body at a high angle of attack. Finally, the stability of this nonorthogonal flow to self similar, 3D disturbance is examined. Stability properties of the flow are given as a function of the parameters of this study; ratio of the plate temperature to that of the outer potential flow and angle of attack. In particular, it is shown that the angle of attack can be scaled out by a suitable definition of an equivalent wavenumber and temporal growth rate, and the stability problem for the nonorthogonal case is identical to the stability problem for the orthogonal case.

Lasseigne, D. G.↗

NASA NTRS1992

Analytical aeroelastic stability considerations and conversion loads for an XV-15 tilt-rotor in a wind tunnel simulation

A rotorcraft analysis is conducted to assess tilt-rotor stability and conversion loads for the XV-15 rotor with metal blades within its specified test envelope. A 38-DOF flutter analysis based on the code by Johnson (1988) is developed to simulate a wind-tunnel test in which the rotor torque is constant and thereby study stability. The same analytical model provides the simulated loads including hub loads, blade loads, and oscillatory pitch-link loads with attention given to the nonuniform inflow through the proprotor in the presence of the wing. Tilt-rotor stability during the cruise mode is found to be sensitive to coupling effects in the control system stiffness, and a stability problem is identified in the XV-15 Advanced Technology Blades. The present analysis demonstrates that the tilt-rotor is stable within the specified test envelope of the NASA 40 x 80-ft wind tunnel.

Kottapalli, Sesi↗

NASA NTRS1990

Bearingless rotor aeromechanical stability measurements and correlations using nonlinear aerodynamics

The aeromechanical stability of a 1/8th Froude scaled bearingless rotor model was investigated experimentally in a wind tunnel. Both shaft-fixed and shaft-free conditions were examined to study the aeroelastic stability of a bearingless rotor without the incorporation of auxiliary dampers. This wind tunnel investigation generated a set of stability data for four different advance ratios, and a wide range of collective pitch settings. Theoretical analysis was performed using the newly developed University of Maryland Advanced Rotorcraft Code (UMARC). For analysis, the blade is modeled as an elastic beam undergoing flap bending, lag bending, elastic twist, and axial deformation. Blade response is calculated using a finite element method in time. Nonlinear aerodynamic effects are included by using a semiempirical stall modeling. The linearized periodic rotor perturbation equations in the nonrotating frame are solved for stability roots using Floquet transition matrix theory, as well as constant coefficient approximation. The predicted results are compared with the experimental data.

Wang, James M.↗

NASA NTRS1991

Application of linear stability theory in laminar flow design

The linear stability of fully three-dimensional supersonic boundary layers formed over swept-wing configurations is investigated using a modified version of the linear stability code COSAL. Configurations studied include a highly swept leading-edge model to be utilized for transition studies in the LARC Low-disturbance Mach 3.5 Pilot Tunnel. The model is a representation of the leading edge of a laminar flow control wing for the F-16XL aircraft. In addition, the region over a laminar flow control glove fitted on the midportion of an F-16XL wing was studied. For each configuration, estimates of the location of the onset of transition were computed using linear stability theory and the e exp N method. The effectiveness of suction in stabilizing the boundary layer over the F-16XL wing glove was also investigated.

Iyer, Venkit↗

NASA NTRS1992

Effect of model selection on combustor performance and stability using ROCCID

The ROCket Combustor Interactive Design (ROCCID) methodology is an interactive computer program that combines previously developed combustion analysis models to calculate the combustion performance and stability of liquid rocket engines. Test data from a 213 kN (48,000 lbf) Liquid Oxygen (LOX)/RP-1 combustor with a O-F-O (oxidizer-fuel-oxidizer) triplet injector were used to characterize the predictive capabilities of the ROCCID analysis models for this injector/propellant configuration. Thirteen combustion performance and stability models have been incorporated into ROCCID, and ten of them, which have options for triplet injectors, were examined in this study. Calculations using different combinations of analysis models, with little or no anchoring, were carried out on a test matrix of operating conditions matching those of the test program. Results of the computer analyses were compared to test data, and the ability of the model combinations to correctly predict combustion stability or instability was determined. For the best model combination(s), sensitivity of the calculations to fuel drop size and mixing efficiency was examined. Error in the stability calculations due to uncertainty in the pressure interaction index (N) was examined. The recommended model combinations for this O-F-O triplet LOX/RP-1 configuration are proposed.

Giuliani, James E.↗

NASA NTRS1992

Determination of robust stability margin for second-order systems

Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.

Chuang, C.-H.↗