Results for “modal model” — Page 6

A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.

Juang, J.-N.↗

NASA NTRS1985

An Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction

A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.

Juang, J. N.↗

NASA NTRS1977

Scaling a discrete structural model to match measured modal frequencies

The structure modification problem, where the computer model of a structure is to be upgraded on the basis of experimental measurements of normal mode frequencies, is approached by the modal energy concept. The modes for correlation with test data are selected on the basis of relative strain energy participation. The resulting procedure can be viewed as an extension of White's (1972) method. Its advantage lies in that both the number and choice of structural parameters to be varied in the modification are arbitrary.

Taylor, J. E.↗

NASA NTRS1993

Dynamic tests on the NASA Langley CSI evolutionary model

A modal analysis study, representing one of the anticipated 'Cooperative Spacecraft Structural Dynamics Experiments on the NASA Langley CSI Evolutionary Model', was carried out as a sub-task under the NASA/DLR collaboration in dynamics and control of large space systems. The CSI evolutionary testbed (CEM) is designed for the development of Controls-Structures Interaction (CSI) technology to improve space science platform pointing. For orbiting space structures like large flexible trusses, new identification challenges arise due to their specific dynamic characteristics (low frequencies and high modal density) on the one hand, and the limited possibilities of exciting such structures and measuring their responses on orbit on the other. The main objective was to investigate the modal identification potential of several different types of forcing functions that could possibly be realized with on-board excitation equipment using a minimum number of exciter locations as well as response locations. These locations were defined in an analytical test prediction process used to study the implications of measuring and analyzing the responses thus produced. It turned out that broadband excitation is needed for a general modal survey, but if only certain modes are of particular interest, combinations of exponentially decaying sine functions provide favorable excitation conditions as they allow to concentrate the available energy on the modes being of special interest. From a practical point-of-view structural nonlinearities as well as noisy measurements make the analysis more difficult, especially in the low frequency range and when the modes are closely spaced.

Troidl, H.↗

NASA NTRS2004

Variable Stiffness Spar Wind-Tunnel Model Development and Testing

The concept of exploiting wing flexibility to improve aerodynamic performance was investigated in the wind tunnel by employing multiple control surfaces and by varying wing structural stiffness via a Variable Stiffness Spar (VSS) mechanism. High design loads compromised the VSS effectiveness because the aerodynamic wind-tunnel model was much stiffer than desired in order to meet the strength requirements. Results from tests of the model include stiffness and modal data, model deformation data, aerodynamic loads, static control surface derivatives, and fuselage standoff pressure data. Effects of the VSS on the stiffness and modal characteristics, lift curve slope, and control surface effectiveness are discussed. The VSS had the most effect on the rolling moment generated by the leading-edge outboard flap at subsonic speeds. The effects of the VSS for the other control surfaces and speed regimes were less. The difficulties encountered and the ability of the VSS to alter the aeroelastic characteristics of the wing emphasize the need for the development of improved design and construction methods for static aeroelastic models. The data collected and presented is valuable in terms of understanding static aeroelastic wind-tunnel model development.

Florance, James R.↗

NASA NTRS1994

Sensitivity of lag-damping correlations to structural and aerodynamic approximations of isolated experimental rotors in forward flight

The predictions of regressive lag-mode damping levels are correlated with the database of an isolated, soft-inplane, three-blade rotor operated untrimmed. The database was generated at the Army Aeroflightdynamics Directorate at Ames. The correlation covers a broad range of data, from near-zero thrust conditions in hover to high-thrust and highly stalled conditions in forward flight with advance ratio as high as 0.55 and shaft angle as high as 20 degrees. In the experimental rotor, the airfoil or blade portion has essentially uniform mass and stiffness distributions, but the root flexure has highly nonuniform mass and stiffness distributions. Accordingly, the structural approximations refer to four models of root-flexure-blade assembly. They range from a rigid flap-lag model to three elastic flap-lag-torsion models, which differ in modeling the root flexure. The three models of root-flexure are: three root springs in which the bending-torsion couplings are fully accounted for; a finite-length beam element with some average mass and stiffness distributions such that the fundamental frequencies match those of the experimental model; and accurate modal representation in which the actual mass and stiffness distributions of the experimental root-flexure-blade assembly are used in calculating the nonrotating mode shapes. The four models of root-flexure-blade assembly are referred to as the rigid flap-lag model, spring model, modified model and modal model. For each of these four models of the root-flexure-blade assembly, the predictions are based on the following five aerodynamic theories: ear theory, which accounts for large angle-of-attack and reverse-flow effects on lift, and has constant drag and pitching moment; quasisteady stall theory, which includes quasisteady stall lift, drag and pitching moment characteristics of the airfoil section, dynamics stall theory, which uses the ONERA dynamic stall models of lift, drag and pitching moment; dynamic wake theory, which is based on a finite-state three-dimensional wake model and includes all wake effects including both shed and trailing vorticity; and dynamics and wake theory, which combines both dynamic stall theory and dynamic wake theory and is a relatively complete aerodynamic representation.

Gaonkar, G. H.↗

NASA NTRS1993

A consistent model reduction of measured modal parameters for reduced-order active control

The problem of synthesizing reduced-order linear models of vibrating structures for the design of fixed-order dynamic feedback control is investigated. The present technique builds on a recently developed procedure for constructing an objective set of mass and stiffness matrices from measured modal parameters that are akin to the Craig-Bampton synthesized ones obtained from finite element models. The constructed mass and stiffness matrices are determined directly from the identification of experimental data, however, rather than through correlation or reconciliation of a finite element model. A model truncation criterion is then applied to the identified minimum-order mass and stiffness model to satisfy certain observability/controllability requirements for the reduced model. Numerical examples illustrate the effectiveness of the proposed technique for synthesizing reduced-order controllers from system realizations of experimental data. The dynamic performance of the resulting closed-loop models is assessed using the known full-order structural dynamics and compared with existing model reduction techniques.

Alvin, K. F.↗

NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

NASA NTRSDate not supplied

Alternate Methods of Model Reduction to Avoid Dynamic Modal Truncation Error

Loads analysis is traditionally performed using dynamically reduced models, which provides the benefit to reduce run time. If the reduced model frequency cutoff is not chosen appropriately, the model will lack the dynamic content required to fully represent the response of the non-reduced model. Standard guidance for reduced model frequency content, provided in NASA-STD-5002, is to solve fixed base modes up to a minimum of 1.5x the model frequency content of interest and to employ static modal truncation methods such as residual vectors, the mode acceleration method, and the residual flexibility method to account for the truncated flexibility of the missing modes. Fixed base modes require the selection of a set of degrees of freedom to be constrained which, if not properly selected, may affect the accuracy of the reduced model by excluding some of the dynamic characteristic of the full model. In this case, the standard NASA guidance would be insufficient, but it may not be readily apparent that a portion of the reduced model response is missing. This error was encountered during an independent verification and validation (IV&V) effort, where it was observed that the resulting dynamic response was lower than the inline analysis. In this specific case, despite following the standard NASA model reduction guidelines in the selection of the frequency cutoff, the inline model still did not fully capture the necessary dynamic content. As part of the IV&V, an alternate reduction methodology was employed using an unconstrained mode acceleration method. The original model initially performed a constrained reduction to twice the frequency content of interest before doing a free-free run, employing the mode acceleration method to account for the truncated modes. In contrast in the IV&V, the unconstrained model reduced directly to the needed frequency content of the free-free run, avoiding any interactions between constraints and dynamic content. To verify the model, the original reduction methodology was used to generate a series of Hurty-Craig-Bampton reductions, each with a higher frequency cutoff than the previous. The results were shown to converge once the frequency cutoff increased past eight times the frequency content of interest. At the same frequency cutoff, the results of the Hurty-Craig-Bampton model converged with the results of the unconstrained mode acceleration model. This comparative study provided confidence that the results of the unconstrained modal acceleration reduced model were correct and that the Hurty-Craig-Bampton needed to increase its frequency cutoff to fully capture the dynamic response.

Erin Simmons↗

NASA NTRS2022

Finite Element Modeling of Rigid-Flex PCB Robotic Structures for Dynamic Environments

Rigid-flex circuit boards are becoming moreprevalent as the limits are pushed on the size, mass, and geometryof electronic systems. A key aspect of designing a rigid-flexprinted circuit boards (PCB) system is an assessment of thedynamic properties of the PCB and predicting system perfor-mance under dynamic loading. Among current modeling method-ologies for rigid-flex PCB, a simplified modeling methodology thatadequately captures the system dynamics does not exist. This arti-cle presents a novel, computationally efficient approach formodeling rigid-flex PCB systems and the calibration of the mate-rial models via modal testing. The resulting simplified model isable to capture system frequencies, mode shapes, and representa-tive force-displacement behavior. The proposed methodology isused to model NASA Jet Propulsion Laboratory’s Pop-Up FlatFolding Explorer Robot (PUFFER) and assess the sensitivity of asystem model to input parameters.

John Bell↗

NASA NTRS1971

Frame modal analysis

Computer model calculates natural frequencies and modal displacements of three-dimensional frame structures, and generates stiffness and mass matrices. Structures may be divided into several substructures prior to calculation of modal characteristics.

Guyan, R. J.↗

NASA NTRS1991

Modal analysis of multistage gear systems coupled with gearbox vibrations

An analytical procedure to simulate vibrations in gear transmission systems is presented. This procedure couples the dynamics of the rotor-bearing gear system with the vibration in the gear box structure. The model synthesis method is used in solving the overall dynamics of the system, and a variable time-stepping integration scheme is used in evaluating the global transient vibration of the system. Locally each gear stage is modeled as a multimass rotor-bearing system using a discrete model. The modal characteristics are calculated using the matrix-transfer technique. The gearbox structure is represented by a finite element models, and modal parameters are solved by using NASTRAN. The rotor-gear stages are coupled through nonlinear compliance in the gear mesh while the gearbox structure is coupled through the bearing supports of the rotor system. Transient and steady state vibrations of the coupled system are examined in both time and frequency domains. A typical three-geared system is used as an example for demonstration of the developed procedure.

Choy, F. K.↗

NASA NTRS1976

Modal structure inferred from static far-field noise directivity

Turbofan noise directivity calculated for two directivity models (equal modal amplitude and equal modal power or energy) was compared with experimental blade passing frequency data from two fans at 60 and 90 percent speeds. Experimental data indicated similar directivity patterns which were well represented by a single average data curve. Calculated points using the equal amplitude model showed over-prediction near the fan axis and near the 90-deg position. Calculated points using the equal power model showed a very good match with the average data lending support to theory of equipartition of modal power from a random source such as the interaction of the rotor with inlet flow distortion. The equal modal power model also gave good agreement with individual data points.

Saule, A. V.↗