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At least 289 records · Page 16

Application of an enhanced Coordinate Modal Assurance Criterion

This paper presents an extension of the Coordinate Modal Assurance Criterion (COMAC) for spatial comparison of mode shapes. As is the case for the original COMAC, this enhanced COMAC helps identify degrees of freedom differences between test and analysis modes, but also overcomes some of the limitations of the original COMAC. The original COMAC cannot identify errors caused by scaling or polarity mistakes in the test data. Such mistakes are easily made during modal tests and not always easily detected since they do not affect the subjective quality of a frequency response function.

Hunt, David L.↗

Buckling mode localization in elastic plates due to misplacement in the stiffener location

This paper deals with the buckling of the stiffened plate under uni-axial compression. The direct integration of the governing differential equation is performed and the exact solution to the problem is obtained. As examples, a square plate with single stiffener, and a stiffened three-span, continuous plate are investigated, with special attention given to the influence of stiffener misplacement on the buckling load and mode shape of the plate. It is found that a small misplacement of the stiffeners from the nominal configuration may change the buckling mode from a global one to a highly localized one.

Elishakoff, I.↗

Vibrations of twisted rotating blades

The literature dealing with vibrations of turbomachinery blades is voluminous, but the vast majority of it treats the blades as beams. In a previous paper a two-dimensional analytical procedure was developed and demonstrated on simple models of blades having camber. The procedure utilizes shallow shell theory along with the classical Ritz method for solving the vibration problem. Displacement functions are taken as algebraic polynomials. In the present paper the method is demonstrated on blade models having camber. Comparisons are first made with results in the literature for nonrotating twisted plates and various disagreements between results are pointed out. A method for depicting mode shape information is demonstrated, permitting one to examine all three components of displacement. Finally, the analytical procedure is demonstrated on rotating twisted blade modes, both without and with camber.

Leissa, A. W.↗

Improvements to a method for the geometrically nonlinear analysis of compressively loaded stiffened composite panels

The NLPAN computer code uses a finite-strip approach to the analysis of thin-walled prismatic composite structures such as stiffened panels. The code can model in-plane axial loading, transverse pressure loading, and constant through-the-thickness thermal loading, and can account for shape imperfections. The NLPAN code represents an attempt to extend the buckling analysis of the VIPASA computer code into the geometrically nonlinear regime. Buckling mode shapes generated using VIPASA are used in NLPAN as global functions for representing displacements in the nonlinear regime. While the NLPAN analysis is approximate in nature, it is computationally economical in comparison with finite-element analysis, and is thus suitable for use in preliminary design and design optimization. A comprehensive description of the theoretical approach of NLPAN is provided. A discussion of some operational considerations for the NLPAN code is included. NLPAN is applied to several test problems in order to demonstrate new program capabilities, and to assess the accuracy of the code in modeling various types of loading and response. User instructions for the NLPAN computer program are provided, including a detailed description of the input requirements and example input files for two stiffened-panel configurations.

Stoll, Frederick↗

Potential and Limitations of the Modal Characterization of a Spacecraft Bus Structure by Means of Active Structure Elements

Theoretical and experimental studies have been performed to investigate the potential and limitations of the modal characterization of a typical spacecraft bus structure by means of active structure elements. The aim of these studies has been test and advance tools for performing an accurate on-orbit modal identification which may be characterized by the availability of a generally very limited test instrumentation, autonomous excitation capabilities by active structure elements and a zero-g environment. The NASA LARC CSI Evolutionary Testbed provided an excellent object for the experimental part of this study program. The main subjects of investigation were: (1) the selection of optimum excitation and measurement to unambiguously identify modes of interest; (2) the applicability of different types of excitation means with focus on active structure elements; and (3) the assessment of the modal identification potential of different types of excitation functions and modal analysis tools. Conventional as well as dedicated modal analysis tools were applied to determine modal parameters and mode shapes. The results will be presented and discussed based on orthogonality checks as well as on suitable indicators for the quality of the acquired modes with respect to modal purity. In particular, the suitability for modal analysis of the acquired frequency response functions as obtained by excitation with active structure elements will be demonstrated with the help of reciprocity checks. Finally, the results will be summarized in a procedure to perform an on-orbit modal identification, including an indication of limitation to be observed.

Grillenbeck, Anton M.↗

Dynamics of Multistage Gear Transmission with Effects of Gearbox Vibrations

A comprehensive approach is presented in analyzing the dynamic behavior of multistage gear transmission systems with the effects of gearbox induced vibrations and mass imbalances of the rotor. The modal method, with undamped frequencies and planar mode shapes, is used to reduce the degrees of freedom of the gear system for time-transient dynamic analysis. Both the lateral and torsional vibration modes of each rotor-bearing-gear stage as well as the interstage vibrational characteristics are coupled together through localized gear mesh tooth interactions. In addition, gearbox vibrations are also coupled to the rotor-bearing-gear system dynamics through bearing support forces between the rotor and the gearbox. Transient and steady state dynamics of lateral and torsional vibrations of the geared system are examined in both time and frequency domains to develop interpretations of the overall modal dynamic characteristics under various operating conditions. A typical three-stage geared system is used as an example. Effects of mass imbalance and gearbox vibrations on the system dynamic behavior are presented in terms of modal excitation functions for both lateral and torsional vibrations. Operational characteristics and conclusions are drawn from the results presented.

Choy, F. K.↗

An evaluation of higher-order modal methods for calculating transient structural response

The present study evaluates a higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗

Dynamic Analysis of Large In-Space Deployable Membrane Antennas

This paper presents a vibration analysis of an eight-meter diameter membrane reflectarray antenna, which is composed of a thin membrane and a deployable frame. This analysis process has two main steps. In the first step, a two-variable-parameter (2-VP) membrane model is developed to determine the in-plane stress distribution of the membrane due to pre-tensioning, which eventually yields the differential stiffness of the membrane. In the second step, the obtained differential stiffness is incorporated in a dynamic equation governing the transverse vibration of the membrane-frame assembly. This dynamic equation is then solved by a semi-analytical method, called the Distributed Transfer Function Method (DTFM), which produces the natural frequencies and mode shapes of the antenna. The combination of the 2-VP model and the DTFM provides an accurate prediction of the in-plane stress distribution and modes of vibration for the antenna.

vibrations↗

An evaluation of higher-order model methods for calculating transient structural response

A higher-order modal method proposed by Leung for transient structural analysis entitled the force-derivative method is evaluated. This method repeatedly integrates by parts with respect to time the convolution-integral form of the structural response to produce successively better approximations to the contribution of the higher modes which are neglected in the modal summation. Comparisons are made of the force-derivative, the mode-displacement, and the mode-acceleration methods for several numerical example problems for various times, levels of damping, and forcing functions. The example problems include a tip-loaded cantilevered beam and a simply-supported multispan beam. The force-derivative method is shown to converge to an accurate solution in fewer modes than either the mode-displacement or the mode-acceleration methods. In addition, for problems in which there are a large number of closely-spaced frequencies whose mode shapes have a negligible contribution to the response, the force-derivative method is very effective in representing the effect of the important, but otherwise neglected, higher modes.

Camarda, Charles J.↗

Instability of rectangular jets

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.

Tam, Christopher K. W.↗

Temperature Dependent Modal Test/Analysis Correlation of X-34 Fastrac Composite Rocket Nozzle

A unique high temperature modal test and model correlation/update program has been performed on the composite nozzle of the FASTRAC engine for the NASA X34 Reusable Launch Vehicle. The program was required to provide an accurate high temperature model of nozzle for incorporation into the engine system structural dynamics model for loads calculation; this model is significantly different from the ambient case due to the large decrease in composite material properties due to heating. The modal test was enabled by piggybacking onto a hot-fire test of the nozzle at NASA/Marshall and tracking the natural frequencies as they decreased. A series of high fidelity modal tests and finite element model correlation of the nozzle in a free-free configuration was initially performed. This model was then attached to a modal-test verified model of the engine hot-fire test stand and the' ambient system mode shapes identified. A reduced set of accelerometers was then attached to the nozzle, the engine fired full-duration, and the frequency peaks corresponding to the ambient nozzle modes individually isolated and tracked. To update the finite element model of the nozzle to these frequency curves, a multiplicative factor was. applied to the rate of decline of the composite material property versus temperature table. This new property table was used to create high-temperature nozzle models corresponding to 10 second engine operation increments and tied into the engine system model for loads determination.

Brown, Andrew M.↗

Estimation of blade airloads from rotor blade bending moments

This paper presents a method for the estimation of blade airloads, based on the measurements of flap bending moments. In this procedure, the blade rotation in vacuum modes is calculated, and the airloads are expressed as an algebraic sum of the mode shapes, modal amplitudes, mass distribution, and frequency properties. The method was validated by comparing the calculated airload distribution with the original wind tunnel measurements which were made using ten modes and twenty measurement stations. Good agreement between the predicted and the measured airloads was found up to 0.90 R, but the agreement degraded towards the blade tip. The method is shown to be quite robust to the type of experimental problems that could be expected to occur in the testing of full-scale and model-scale rotors.

Bousman, William G.↗

Inner loop flight control for the High-Speed Civil Transport

High-speed aerospace vehicles which employ high strength, light weight, yet deformable materials may exhibit significant interaction between the rigid-body and vibrational dynamics. Preliminary High-Speed Civil Transport (HSCT) configurations are a prime example. Traditionally, separate control systems have been used to augment the rigid-body and vibrational dynamics. In the HSCT arena, the highly coupled motions may not allow this design freedom. The research activity addresses two specific issues associated with the design and development of an integrated flight control system (FCS) for HSCT configurations, which are discussed next. The HSCT is expected to have a short period instability at subsonic speeds. Flight vehicles with this characteristic (i.e., F-16, F-22, X-29, Space Shuttle) are stabilized with what is called a superaugmented pitch rate loop. One concern is 'Will this stability augmentation logic work for a HSCT?' Studies show that an idealized pitch rate design would be acceptable, but is not realistic. Investigations using a contaminated pitch rate design reveal serious hurdles to overcome in the FCS design. Mounting location for the pitch rate sensor is critical. Results indicate a forward location leads to destabilizing pick-up of aeroelastic modes, while aft locations lead to undesirable coupling of the dominate pitch mode with the first aeroelastic mode. Intermediate locations for the sensor may not be acceptable. The source of the problem is the presence of low frequency aeroelastic modes in HSCT configurations, which are not present in vehicles currently using the superaugmented logic. To say the least, a conventional superaugmented pitch rate loop strategy may have undesirable characteristics. An unconventional strategy, which attempts to eliminate the above deficiencies by blending several pitch rate signals, indicates an improvement in the FCS architecture feasibility, but is still lacking in some respects. The HSCT configuration does not have aerodynamic surfaces in the vicinity of the nose (i.e., no canard or vane). A second concern is 'Can the fuselage bending/torsion aeroelastic modes be effectively augmented without sufficient control input near the vehicle nose?' The superaugmented FCS results above may be suggesting the necessity of a secondary feedback loop to achieve an acceptable integrated FCS. Preliminary analysis of HSCT aeroelastic mode shapes indicate the use of existing wing leading edge devices as a second control input may be lacking in control authority for the rigid-body attitude and aeroelastic modes. An effort is underway to incorporate generic wing leading edge devices and canards into a generic HSCT model for the purpose of assessing additional control authority and it's use in candidate FCS designs. A generic HSCT mathematical model was necessary for the studies above. A HSCT category model is available in NASA-CR-172201. This model describes the linear, longitudinal dynamics about the following flight condition: ascent, W = 730,000 lbs, h = 6,500 ft, M = 0.6. The model incorporates the full rigid-body variable set, as well as eighteen aeroelastic modes. Elevator deflection serves as the control input. Modifications to the model include the incorporation of relaxed static stability (i.e., static margin from -7.3% to +10%) and additional control inputs.

Newman, Brett A.↗

Temperature Dependent Modal Test/Analysis Correlation of X-34 Fastrac Composite Rocket Nozzle

A unique high temperature modal test and model correlation/update program has been performed on the composite nozzle of the FASTRAC engine for the NASA X-34 Reusable Launch Vehicle. The program was required to provide an accurate high temperature model of the nozzle for incorporation into the engine system structural dynamics model for loads calculation; this model is significantly different from the ambient case due to the large decrease in composite stiffness properties due to heating. The high-temperature modal test was performed during a hot-fire test of the nozzle. Previously, a series of high fidelity modal tests and finite element model correlation of the nozzle in a free-free configuration had been performed. This model was then attached to a modal-test verified model of the engine hot-fire test stand and the ambient system mode shapes were identified. A reduced set of accelerometers was then attached to the nozzle, the engine fired full-duration, and the frequency peaks corresponding to the ambient nozzle modes individually isolated and tracked as they decreased during the test. To update the finite-element model of the nozzle to these frequency curves, the percentage differences of the anisotropic composite moduli due to temperature variation from ambient, which had been used in the initial modeling and which were obtained by small sample coupon testing, were multiplied by an iteratively determined constant factor. These new properties were used to create high-temperature nozzle models corresponding to 10 second engine operation increments and tied into the engine system model for loads determination.

Brown, Andrew M.↗

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗

Vibration characteristics of hexagonal radial rib and hoop platforms

Experiment and analysis have been used to characterize the modes of vibration of planar radial rib and hoop hexagonal platforms. Finite element analysis correlated very well with experimental results. The sensitivity of mode shapes and frequencies to cable stiffness and initial tension is presented. Threshold values have been identified, above which changes in cable stiffness do not affect the first few platform vibration modes. Primary vibration modes of the radial rib platform involve beam bending. Vibration modes of the hoop platform exhibit both beam bending and frame bending and torsion. Results indicate for low order polygonal structures, the radial rib concept produced a higher fundamental frequency. For high order polygonal structures, the hoop concept has the potential to achieve a higher fundamental frequency than the radial rib concept.

Belvin, W. K.↗

Dynamic Characteristics of Multistory Buildings

In order to evaluate unit stresses or to estimate possible damage in multistory buildings from earthquake or ground motion from underground nuclear explosion it is essential to determine how much of the dynamic response at any level is due to various types of freedom. The effects of shear deformation between floors, joint rotation, over-all flexure, and ground compliance are considered. Joint rotation and over-all flexure are evaluated over a wide range of building characteristics with simply determined indices. Further, a period synthesis concept and a pseudo-stiffness procedure are proposed to enable the determination of periods, mode shapes and stiffnesses with consideration of joint rotation, over-all flexure and ground compliance while performing simple labor-saving analyses for assumed rigid-floor shear buildings. The first three modes of vibration are considered in elastic free vibration. The buildings and models are symmetric in plan without torsional coupling.

42 ENGINEERING↗