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NASA NTRS1988

On the problem of modeling for parameter identification in distributed structures

Structures are often characterized by parameters, such as mass and stiffness, that are spatially distributed. Parameter identification of distributed structures is subject to many of the difficulties involved in the modeling problem, and the choice of the model can greatly affect the results of the parameter identification process. Analogously to control spillover in the control of distributed-parameter systems, identification spillover is shown to exist as well and its effect is to degrade the parameter estimates. Moreover, as in modeling by the Rayleigh-Ritz method, it is shown that, for a Rayleigh-Ritz type identification algorithm, an inclusion principle exists in the identification of distributed-parameter systems as well, so that the identified natural frequencies approach the actual natural frequencies monotonically from above.

Norris, Mark A.↗

NASA NTRS1988

A perturbation technique for parameter identification in distributed structures

Meirovitch, L.↗

NASA NTRS1989

On the problem of modeling for parameter identification in distributed structures

Norris, Mark A.↗

NASA NTRS2014

Supersonic Wing Optimization Using SpaRibs

This research investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design a supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The objective is to achieve a more efficient load-bearing mechanism and to passively control the deformation of the structure under the flight loads. Moreover, the use of SpaRibs broadens the design space and allows for natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new optimization MATLAB-based framework referred to as EBF3SSWingOpt. This optimization scheme performs both the sizing and the shaping of the internal structural elements, connecting the optimizer with the analysis software. The shape of the SpaRibs is parametrically defined using the so called Linked Shape method. Each set of SpaRibs is placed in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique; however, mathematical relations link the curvature in an effort to reduce the number of design variables. The internal structure of a High Speed Commercial Transport aircraft concept developed by Boeing is optimized subjected to stress, subsonic flutter and supersonic flutter constraints. The results show that the use of the SpaRibs allows for the reduction of the aircraft's primary structure weight without violating the constraints. A weight reduction of about 15 percent is observed.

Locatelli, David↗

NASA NTRS1985

Electromagnetic resonances of cylinders and aircraft model with resistive wires

Laboratory experiments were done to determine the natural frequencies of the electromagnetic resonances of conducting bodies with attached wires. The bodies include two cylinders and an approximate scale model of the NASA F-106B aircraft. All are three feet in length. Time-domain waveforms of B-dot and D-dot were obtained from a sampling oscilloscope, and Prony analysis was used to extract the natural frequencies. This work is an extension of previous work, but smaller, more resistive wires have been used. The first four natural frequencies of the cylinders (and wires) were determined, and a comparison with calculated results of other investigators show reasonable agreement. Seven natural frequencies were determined for the F-106B model (wire wires), and these have been compared with results obtained by NASA in 1982 during direct lightning strikes to the aircraft. The agreement between the corresponding natural frequencies of the model and the aircraft is fairly good and is better than that obtained in the previous work using wires with less resistance. The frequencies lie between 6.5 MHz and 41 MHz, and all of the normalized damping rates are between 0.14 and 0.27.

Wood, G. W.↗

NASA NTRS1989

An approximation function for frequency constrained structural optimization

The purpose is to examine a function for approximating natural frequency constraints during structural optimization. The nonlinearity of frequencies has posed a barrier to constructing approximations for frequency constraints of high enough quality to facilitate efficient solutions. A new function to represent frequency constraints, called the Rayleigh Quotient Approximation (RQA), is presented. Its ability to represent the actual frequency constraint results in stable convergence with effectively no move limits. The objective of the optimization problem is to minimize structural weight subject to some minimum (or maximum) allowable frequency and perhaps subject to other constraints such as stress, displacement, and gage size, as well. A reason for constraining natural frequencies during design might be to avoid potential resonant frequencies due to machinery or actuators on the structure. Another reason might be to satisy requirements of an aircraft or spacecraft's control law. Whatever the structure supports may be sensitive to a frequency band that must be avoided. Any of these situations or others may require the designer to insure the satisfaction of frequency constraints. A further motivation for considering accurate approximations of natural frequencies is that they are fundamental to dynamic response constraints.

Canfield, R. A.↗

NASA NTRS1995

Vibration Analysis of a Split Path Gearbox

Split path gearboxes can be attractive alternatives to the common planetary designs for rotorcraft, but because they have seen little use, they are relatively high risk designs. To help reduce the risk of fielding a rotorcraft with a split path gearbox, the vibration and dynamic characteristics of such a gearbox were studied. A mathematical model was developed by using the Lagrangian method, and it was applied to study the effect of three design variables on the natural frequencies and vibration energy of the gearbox. The first design variable, shaft angle, had little influence on the natural frequencies. The second variable, mesh phasing, had a strong effect on the levels of vibration energy, with phase angles of 0 deg and 180 deg producing low vibration levels. The third design variable, the stiffness of the shafts connecting the spur gears to the helical pinions, strongly influenced the natural frequencies of some of the vibration modes, including two of the dominant modes. We found that, to achieve the lowest level of vibration energy, the natural frequencies of these two dominant modes should be less than those of the main excitation sources.

Krantz, Timothy L.↗

NASA NTRS1993

Simulation motion effect on single axis compensatory tracking

An experiment that examined how changes in a motion platform drive filter affect pilot-vehicle performance and opinion was conducted on the NASA Ames Vertical Motion Simulator. Pilots controlled a simplified helicopter model in the vertical or the directional axis and tracked a randomly moving target aircraft in the presence of a random disturbance. With both tasks, variations from full motion to fixed-base conditions were made in the high-pass drive filter gain and natural frequency. The results indicate that vertical motion did not affect the open-loop pilot-vehicle target-tracking crossover frequency, but target-tracking phase margins improved with increased filter gain or decreased natural frequency. Vertical disturbance-rejection crossover frequency increased with decreasing filter natural frequency, while disturbance rejection phase margins improved with increasing filter gain. Vertical tracking errors increased significantly when all vertical motion was removed. No significant differences were measured among the directional configurations, which indicates that pure yaw motion cues may not be as important as previously thought in flight simulation.

Schroeder, Jeffery A.↗

NASA NTRS1994

Laminated Thin Shell Structures Subjected to Free Vibration in a Hygrothermal Environment

Parametric studies were performed to assess the effects of various parameters on the free-vibration behavior (natural frequencies) of (+/- theta)(sub 2) angle-ply, fiber composite, thin shell structures in a hygrothermal environment. Knowledge of the natural frequencies of structures is important in considering their response to various kinds of excitation, especially when structures and force systems are complex and when excitations are not periodic. The three dimensional, finite element structural analysis computer code CSTEM was used in the Cray YMP computer environment. The fiber composite shell was assumed to be cylindrical and made from T300 graphite fibers embedded in an intermediate-modulus, high-strength matrix. The following parameters were investigated: the length and the laminate thickness of the shell, the fiber orientation, the fiber volume fraction, the temperature profile through the thickness of the laminate, and laminates with different ply thicknesses. The results indicate that the fiber orientation and the length of the laminated shell had significant effects on the natural frequencies. The fiber volume fraction, the laminate thickness, and the temperature profile through the shell thickness had weak effects on the natural frequencies. Finally, the laminates with different ply thicknesses had an insignificant influence on the behavior of the vibrated laminated shell. Also, a single through-the-thickness, eight-node, three dimensional composite finite element analysis appears to be sufficient for investigating the free-vibration behavior of thin, composite, angle-ply shell structures.

Gotsis, Pascal K.↗

NASA NTRS2001

Structural Damage Detection Using Virtual Passive Controllers

This paper presents novel approaches for structural damage detection which uses the virtual passive controllers attached to structures, where passive controllers are energy dissipative devices and thus guarantee the closed-loop stability. The use of the identified parameters of various closed-loop systems can solve the problem that reliable identified parameters, such as natural frequencies of the open-loop system may not provide enough information for damage detection. Only a small number of sensors are required for the proposed approaches. The identified natural frequencies, which are generally much less sensitive to noise and more reliable than the identified natural frequencies, are used for damage detection. Two damage detection techniques are presented. One technique is based on the structures with direct output feedback controllers while the other technique uses the second-order dynamic feedback controllers. A least-squares technique, which is based on the sensitivity of natural frequencies to damage variables, is used for accurately identifying the damage variables.

Lew, Jiann-Shiun↗

NASA NTRSDate not supplied

Uncertainty Quantification of Inducer Eigenvalues using Conditional Assessment of Models and Modal Test of Simpler Systems

The low pressure fuel pump inducer of the new Space Launch System RS25 core stage engine operates in a highly complex environment that substantially affects its modal characteristics. Some of the more important effects are fluid-added mass resulting from operation within a light liquid (Hydrogen), and the magnification of this effect due to tight tip clearance. Since higher order cavitation has been identified as a significant harmonic driver, knowledge of the natural frequency of potentially excitable modes is critical for safe operation, but this frequency cannot be measured during the severe operational environment. A comprehensive testing and analysis program has therefore been performed over the last four years to identify the nominal value and uncertainty of the frequency by modeling and testing four simpler structures which share some of the characteristics of the operational inducer. This testing was used to assess and adjust modeling techniques and excellent correlation was achieved. Identification of the uncertainty in the inducer frequency itself was still problematic, however. This difficulty led to an investigation of Bayesian uncertainty quantification techniques, and to the application of the relatively simple technique of Multi-Variate Normal conditional distributions to calculate the inducer natural frequency uncertainty. Assumptions on prior distributions of uncertainty of the fluid-added mass and tip clearance effect are initially applied to models of each of the simple structures and the inducer itself, and these uncertainties are propagated to generate natural frequencies using design of experiments. Simple response surfaces are then created from this data in order to calculate a Covariance Matrix relating all of these natural frequencies. Finally, the results from modal test of the simple structures are considered to be observations and used to calculate the conditional variance of the desired inducer frequencies. As this method is less rigorous than more complicated Bayesian methods reported in the literature, a conservative factor is applied to the result, but the resulting uncertainty is still significantly less than originally estimated and will greatly assist certification of the inducer for use in the engine.

Uncertainty Quantification↗

NASA NTRS2001

Free Vibration of Uncertain Unsymmetrically Laminated Beams

Monte Carlo Simulation and Stochastic FEA are used to predict randomness in the free vibration response of thin unsymmetrically laminated beams. For the present study, it is assumed that randomness in the response is only caused by uncertainties in the ply orientations. The ply orientations may become random or uncertain during the manufacturing process. A new 16-dof beam element, based on the first-order shear deformation beam theory, is used to study the stochastic nature of the natural frequencies. Using variational principles, the element stiffness matrix and mass matrix are obtained through analytical integration. Using a random sequence a large data set is generated, containing possible random ply-orientations. This data is assumed to be symmetric. The stochastic-based finite element model for free vibrations predicts the relation between the randomness in fundamental natural frequencies and the randomness in ply-orientation. The sensitivity derivatives are calculated numerically through an exact formulation. The squared fundamental natural frequencies are expressed in terms of deterministic and probabilistic quantities, allowing to determine how sensitive they are to variations in ply angles. The predicted mean-valued fundamental natural frequency squared and the variance of the present model are in good agreement with Monte Carlo Simulation. Results, also, show that variations between plus or minus 5 degrees in ply-angles can affect free vibration response of unsymmetrically and symmetrically laminated beams.

Kapania, Rakesh K.↗

NASA NTRS2001

Modeling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears

Planetary gear noise and vibration are primary concerns in their applications in helicopters, automobiles, aircraft engines, heavy machinery and marine vehicles. Dynamic analysis is essential to the noise and vibration reduction. This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. A lumped-parameter model is built for the dynamic analysis of general planetary gears. The unique properties of the natural frequency spectra and vibration modes are rigorously characterized. These special structures apply for general planetary gears with cyclic symmetry and, in practically important case, systems with diametrically opposed planets. The special vibration properties are useful for subsequent research. Taking advantage of the derived modal properties, the natural frequency and vibration mode sensitivities to design parameters are investigated. The key parameters include mesh stiffnesses, support/bearing stiffnesses, component masses, moments of inertia, and operating speed. The eigen-sensitivities are expressed in simple, closed-form formulae associated with modal strain and kinetic energies. As disorders (e.g., mesh stiffness variation. manufacturing and assembling errors) disturb the cyclic symmetry of planetary gears, their effects on the free vibration properties are quantitatively examined. Well-defined veering rules are derived to identify dramatic changes of natural frequencies and vibration modes under parameter variations. The knowledge of free vibration properties, eigen-sensitivities, and veering rules provide important information to effectively tune the natural frequencies and optimize structural design to minimize noise and vibration. Parametric instabilities excited by mesh stiffness variations are analytically studied for multi-mesh gear systems. The discrepancies of previous studies on parametric instability of two-stage gear chains are clarified using perturbation and numerical methods. The operating conditions causing parametric instabilities are expressed in closed-form suitable for design guidance. Using the well-defined modal properties of planetary gears, the effects of mesh parameters on parametric instability are analytically identified. Simple formulae are obtained to suppress particular instabilities by adjusting contact ratios and mesh phasing.

Parker, Robert G.↗

NASA NTRS2013

Analysis of Handling Qualities Design Criteria for Active Inceptor Force-Feel Characteristics

The force-feel system characteristics of the cyclic inceptors of most helicopters are set based on the characteristics of the mechanical components in the control system (mass, springs, friction dampers, etc.). For these helicopters, the force-feel characteristics typically remain constant over the entire flight envelope, with perhaps a trim release to minimize control forces while maneuvering. With the advent of fly-by-wire control systems and active inceptors in helicopters, the force-feel characteristics are now determined by the closed-loop response of the active inceptor itself as defined by the inertia, force/displacement gradient, damping, breakout force and detent shape configuration parameters in the inceptor control laws. These systems give the flexibility to dynamically prescribe different feel characteristics for different control modes or flight conditions, and the ability to provide tactile cueing to the pilot through the actively controlled side-stick or center-stick cyclic inceptor. For rotorcraft, a few studies have been conducted to assess the effects of cyclic force-feel characteristics on handling qualities in flight. An early study provided valuable insight into the static force-deflection characteristics (force gradient) and the number of axes controlled by the side-stick controller for the U.S. Army's Advanced Digital/Optical Control System (ADOCS) demonstrator aircraft [1]. The first of a series of studies providing insight on the inceptor dynamic force-feel characteristics was conducted on the NASA/Army CH-47B variable-stability helicopter [2]. This work led to a proposed requirement that set boundaries based on the cyclic natural frequency and inertia, with the stipulation of a lower damping ratio limit of 0.3 [3]. A second study was conducted by the Canadian Institute for Aerospace Research using their variable-stability Bell 205A helicopter [4]. This research suggested boundaries for stick dynamics based on natural frequency and damping ratio. While these two studies produced boundaries for acceptable/unacceptable stick dynamics for rotorcraft, they were not able to provide guidance on how variations of the stick dynamics in the acceptable region impact handling qualities. More recently, a ground based simulation study [5] suggested little benefit was to be obtained from variations of the damping ratio for a side-stick controller exhibiting high natural frequencies (greater than 17 rad/s) and damping ratios (greater than 2.0). A flight test campaign was conducted concurrently on the RASCAL JUH-60A in-flight simulator and the ACT/FHS EC-135 in flight simulator [6]. Upon detailed analysis of the pilot evaluations the study identified a clear preference for a high damping ratio and natural frequency of the center stick inceptors. Side stick controllers were found to be less sensitive to the damping. While these studies have compiled a substantial amount of data, in the form of qualitative and quantitative pilot opinion, a fundamental analysis of the effect of the inceptor force-feel system on flight control is found to be lacking. The study of Ref. [6] specifically concluded that a systematic analysis was necessary, since discrepancies with the assigned handling qualities showed that proposed analytical design metrics, or criteria, were not suitable. The overall goal of the present study is to develop a clearer fundamental understanding of the underlying mechanisms associated with the inceptor dynamics that govern the handling qualities using a manageable analytical methodology.

Malpica, Carlos A.↗

NASA NTRS1985

STACBEAM 2

An investigation being conducted by Astro Aerospace Corporation (Astro) for Jet Propulsion Laboratory in which efficient structures for geosynchronous spacecraft solar arrays are being developed is discussed. Recent developments in solar blanket technology, including the introduction of ultrathin (50 micrometer) silicon solar cells with conversion efficiencies approaching 15 percent, have resulted in a significant increase in blanket specific power. System specific power depends not only on blanket mass but also on the masses of the support structure and deployment mechanism. These masses must clearly be reduced, not only to minimize launch weight, but also to increase array natural frequency. The solar array system natural frequency should be kept high in order to reduce the demands on the attitude control system. This goal is approached by decreasing system mass, by increasing structural stiffness, and by partitioning the blanket. As a result of this work, a highly efficient structure for deploying a solar array was developed.

Adams, L. R.↗

NASA NTRS1991

Control strategy for cooperating disparate manipulators: Non-colocated control of disturbances of a flexible arm

The long term objectives for this research are to use a small robot arm to compliment a large robot arm. Disturbances generated by robot tasks were studied. Available equipment made it convenient to study disturbances generated by an abrasive cut off saw mounted on the tip of a large armed robot, and used to cut through rods and pipes in the range of 0.5 in. to 1.5 in. The abrasive process was modeled as a friction operation. The operation of the cut off saw was performed autonomously and under teleoperated control. The behavior was stable in both cases for a P-D joint control algorithm. It was found that broad band excitation during the cutting operation is capable of exciting arm natural frequencies to above the third natural frequency of the arm. The direction of cut changed the modes excited due to the change in coupling coefficients.

Lew, Jae Y.↗

NASA NTRS1990

On dynamic stability boundaries for binary systems

Dynamic stability boundaries are developed for linear two-degree-of-freedom systems with damping and elastic couplings. Special emphasis is placed on the influence of natural frequency proximity and those instabilities which stem from skew-symmetric stiffness properties. These arise in aeroelasticity and flight dynamics systems. Insight is provided into the destabilizing effects of the 'dreaded modal resonance' which results when the two natural frequencies in the modal natural frequency ratio match or nearly match.

Young, M. I.↗

NASA NTRS1972

Blade frequency program for nonuniform helicopter rotors, with automated frequency search

A computer program for determining the natural frequencies and normal modes of a lumped parameter model of a rotating, twisted beam, with nonuniform mass and elastic properties was developed. The program is used to solve the conditions existing in a helicopter rotor where the outboard end of the rotor has zero forces and moments. Three frequency search methods have been implemented. Including an automatic search technique, which allows the program to find up to the fifteen lowest natural frequencies without the necessity for input estimates of these frequencies.

Sadler, S. G.↗