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NASA NTRS1986

A higher order theory of laminated composite cylindrical shells

A new higher order theory has been proposed for the analysis of composite cylindrical shells. The formulation allows for arbitrary variation of inplane displacements. Governing equations are presented in the form of a hierarchy of sets of partial differential equations. Each set describes the shell behavior to a certain degree of approximation. The natural frequencies of simply-supported isotropic and laminated shells and stresses in a ring loaded composite shell have been determined to various orders of approximation and compared with three dimensional solutions. These numerical studies indicate the improvements achievable in estimating the natural frequencies and the interlaminar shear stresses in laminated composite cylinders.

Krishna Murthy, A. V.↗

NASA NTRS1988

Interaction of feel system and flight control system dynamics on lateral flying qualities

An investigation of feel system and flight control system dynamics on lateral flying qualities was conducted using the variable stability USAF NT-33 aircraft. Experimental variations in feel system natural frequency, force-deflection gradient, control system command architecture type, flight control system filter frequency, and control system delay were made. The experiment data include pilot ratings using the Cooper-Harper (1969) rating scale, pilot comments, and tracking performance statistic. Three test pilots served as evaluators. The data indicate that as the feel system natural frequency is reduced lateral flying qualities degrade. At the slowest feel system frequency, the closed-loop response becomes nonlinear with a 'bobweight' effect apparent in the feel system. Feel system influences were essentially independent of the control system architecture. The flying qualities influence due to the feel system was different than when the identical dynamic systenm was used as a flight control system element.

Bailey, Randall E.↗

NASA NTRS1991

Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Watson, Robert A.↗

NASA NTRS1978

Finite element solution for beams using an element averaging technique

The article investigates the error in the computation of natural frequency through finite element models of the structures when elements of unequal length are chosen and then goes on to suggest an averaging technique for unequal length elements, with different structural properties. Using the element averaging technique, a typical structure has been analysed for its natural frequencies and the results are described.

Bhat, B. R.↗

NASA NTRS1985

Finite difference analysis of torsional vibrations of pretwisted, rotating, cantilever beams with effects of warping

Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.

Subrahmanyam, K. B.↗

NASA NTRS1984

A preliminary look at the effects of coupled lateral modes on aircraft handling qualities

Analytic and six-degree-of-freedom motion base simulator studies have been conducted to better understand how the coupled roll-spiral and coupled roll-aileron actuator modes affect aircraft handling qualities. The results reported herein are preliminary and are subject to change until other aircraft and several more data points can be examined. The results obtained thus far indicate that when the roll-spiral coupled mode is brought about by unusual values of an aircraft's stability and control derivatives, the lateral-directional handling qualities will invariably be degraded. However, when the roll spiral coupling is brought about by a roll-rate command/roll-attitude hold stability and control augmentation system (SCAS), the requirements for satisfactory handling qualities can be correlated to the natural frequency and the damping of the coupled mode. Satisfactory handling qualities were also achieved when the lateral SCAS brought about a coupling of the roll mode with the aileron actuator mode. In this case, the pilot ratings indicate that the handling qualities may be correlated to the natural frequency of the coupled roll-aileron mode.

Ruflin, S. J.↗

NASA NTRS1979

Modal testing with Asher's method using a Fourier analyzer and curve fitting

An unusual application of the method proposed by Asher (1958) for structural dynamic and modal testing is discussed. Asher's method has the capability, using the admittance matrix and multiple-shaker sinusoidal excitation, of separating structural modes having indefinitely close natural frequencies. The present application uses Asher's method in conjunction with a modern Fourier analyzer system but eliminates the necessity of exciting the test structure simultaneously with several shakers. Evaluation of this approach with numerically simulated data demonstrated its effectiveness; the parameters of two modes having almost identical natural frequencies were accurately identified. Laboratory evaluation of this approach was inconclusive because of poor experimental input data.

Gold, R. R.↗

NASA NTRS1985

Measurement of damping of graphite expoxy materials

During this period damping measurements were made on the cylindrical graphite epoxy specimen using the forced-vibration test method. The specimen was carefully mounted directly on the shaker through the supporting ring and the impedance head. This was done to simulate an idealized free-free boundary condition at the two edges. The damping ratio value and the natural frequency (first mode) obtained in this experiment were 0.13% and 508.75 Hz respectively. In order to check the damping induced by the supporting ring, measurements were made with the top half of the ring removed. The specimen then was supported only by the bottom half of the ring (half ring). It was observed that the natural frequency of the specimen (first mode) increased of a value of 552.5 Hz due to the influence of the reduced mass of the supporting ring. But the damping ratio value obtained was the same as that obtained with full supporting ring, namely 0.13%.

Crocker, M. J.↗

NASA NTRS2009

Updating the Finite Element Model of the Aerostructures Test Wing Using Ground Vibration Test Data

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the aerostructures test wing (ATW), which was designed and tested at the National Aeronautics and Space Administration Dryden Flight Research Center (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Lung, Shun-Fat↗

NASA NTRS1992

Free vibrations of delaminated beams

Free vibration of laminated composite beams is studied. The effect of interply delaminations on natural frequencies and mode shapes is evaluated both analytically and experimentally. A generalized vibrational principle is used to formulate the equation of motion and associated boundary conditions for the free vibration of a composite beam with a delamination of arbitrary size and location. The effect of coupling between longitudinal vibration and bending vibration is considered. This coupling effect is shown to significantly affect the calculated natural frequencies and mode shapes of the delaminated beam.

Shen, M.-H. H.↗

NASA NTRS1992

Probabilistic evaluation of fuselage-type composite structures

A methodology is developed to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, ply, laminate and structural levels. This methodology is implemented in the IPACS (Integrated Probabilistic Assessment of Composite Structures) computer code. A fuselage-type composite structure is analyzed to demonstrate the code's capability. The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.

Shiao, Michael C.↗

NASA NTRS1998

Probabilistic Evaluation of Fuselage-Type Composite Structures

A methodology is developed to simulate computationally the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, natural frequencies, displacements, stress/strain, etc., which are the consequences of the random variation (scatter) of the primitive (independent random) variables in the constituent, plv. laminate and structural levels. This methodology is implemented in a computer code integrated probabilistic assessment of composite structures (IPACS). A fuselage-type composite structure is analyzed to demonstrate the code's capability . The probability distribution functions of the buckling loads, natural frequency, displacement, strain and stress are computed. The sensitivity of each primitive (independent random) variable to a given structural response is also identified from the analyses.

Shiao, Michael C.↗

NASA NTRS2009

Updating the Finite Element Model of the Aerostructures Test Wing using Ground Vibration Test Data

Improved and/or accelerated decision making is a crucial step during flutter certification processes. Unfortunately, most finite element structural dynamics models have uncertainties associated with model validity. Tuning the finite element model using measured data to minimize the model uncertainties is a challenging task in the area of structural dynamics. The model tuning process requires not only satisfactory correlations between analytical and experimental results, but also the retention of the mass and stiffness properties of the structures. Minimizing the difference between analytical and experimental results is a type of optimization problem. By utilizing the multidisciplinary design, analysis, and optimization (MDAO) tool in order to optimize the objective function and constraints; the mass properties, the natural frequencies, and the mode shapes can be matched to the target data to retain the mass matrix orthogonality. This approach has been applied to minimize the model uncertainties for the structural dynamics model of the Aerostructures Test Wing (ATW), which was designed and tested at the National Aeronautics and Space Administration (NASA) Dryden Flight Research Center (DFRC) (Edwards, California). This study has shown that natural frequencies and corresponding mode shapes from the updated finite element model have excellent agreement with corresponding measured data.

Lung, Shun-fat↗

NASA NTRS1978

An improved computational procedure for determining helicopter rotor blade natural modes

An existing computer program, used for predicting the natural frequencies and mode shapes of helicopter rotor blades, was refined to improve program accuracy and versatility. The program is based on the Holzer-Myklestad approach adapted for rotating beams. Coupled vertical (out-of-plane), horizontal (in-plane), and torsional mode characteristics were determined for a variety of hub and blade configurations. The resulting program is documented by presenting the recursion equations and techniques for determining natural frequencies and mode shapes, input data requirements, and descriptions of various program outputs. The accuracy of the program is demonstrated by comparing computed results with exact solutions to classical problems and experimental data.

Weller, W. H.↗

NASA NTRS2018

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Brown, Andrew M.↗

NASA NTRS1975

Effect of external disturbances and data rate on the response of an automatic landing system capable of curved trajectories

The effects of steady wind, turbulence, data sample rate, and control-actuator natural frequency on the response of a possible automatic landing system were investigated in a nonstatistical study. The results indicate that the system, which interfaces with the microwave landing system, functions well in winds and turbulence as long as the guidance law contains proper compensation for wind. The system response was satisfactory down to five data samples per second, which makes the system compatible with the microwave landing system. No adverse effects were observed when actuator natural frequency was lowered. For limiting cases, those cases where the roll angle goes to zero just as the airplane touches down, the basic method for computing the turn-algorithm gains proved unsatisfactory and unacceptable landings resulted. Revised computation methods gave turn-algorithm gains that resulted in acceptable landings. The gains provided by the new method also improved the touchdown conditions for acceptable landings over those obtained when the gains were determined by the old method.

Sherman, W. L.↗

NASA NTRS2018

Recent Advances to Estimation of Fixed-Interface Modal Models Using Dynamic Substructuring

In 2010, Allen & Mayes proposed to estimate the fixed-interface modes of a structure by measuring the modes of the structure bolted to a fixture and then applying constraints to the fixture using the transmission simulator method. While the method proved useful, and has indeed been used in studies since that point, a few peculiarities were noted. First, in some cases the estimated fixed-base natural frequencies were observed to converge very slowly to the true values (in simulated experiments) as the number of constraints was increased. To formulate these constraints, prior studies used only the free-interface modes of the fixture or the measured modes of the assembly. This work extends that to consider other sets of constraints, showing improved results. Furthermore, in some prior studies it has been observed that there were errors of more than 10% in the natural frequencies even when the fixture motion was hundreds of times smaller than the motion of the structure of interest (and so it had presumably been removed). This work explores this phenomenon, seeking to use the strain energy in the fixture, to the extent that it can be estimated using a test-analysis model for the fixture, as a metric to predict frequency error. The proposed methods are explored by applying them to simulated measurements from a beam and from the NASA Space Launch System coupled to the Mobile Launcher.

Allen, Mathew S.↗

NASA NTRS1988

Free vibration of rectangular plates with a small initial curvature

The method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem.

Adeniji-Fashola, A. A.↗