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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

An enhanced mode shape identification algorithm

A mode shape identification algorithm is developed which is characterized by a low sensitivity to measurement noise and a high accuracy of mode identification. The algorithm proposed here is also capable of identifying the mode shapes of structures with significant damping. The combined results indicate that mode shape identification is much more dependent on measurement noise than identification of natural frequencies. Accurate detection of modal parameters and mode shapes is demonstrated for modes with damping ratios exceeding 15 percent.

Roemer, Michael J.↗
NASA NTRS1985

Shaft mode shape demonstration

The dynamic response of a rotating machine is directly influenced by its geometric configuration and all aspects of the rotor construction. These determine two significant parameters, mass distribution and stiffness, which yield a spectrum of natural frequencies and mode shapes. The mode shapes can be presented as snapshots of the characteristic amplitude/phase reponse patterns of the shaft, due to the major forcing function of unbalance, at different rotative speeds. To demonstrate the three shaft mode shapes of the rotor rig using the Shaft Mode Demonstrator and oscilloscopes. The synchronous (1X) amplitude and phase of the rotor vibration in the vertical direction from several points along the shaft is displayed on corresponding points of the demonstrator. Unfiltered vibration from vertical and horizontal probe pairs is displayed on the oscilloscopes in orbit format for a dynamic presentation of the mode shape.

Grissom, R.↗
NASA NTRS1994

Mode shape analysis using a commercially available peak store video frame buffer

Time exposure photography, sometimes coupled with strobe illumination, is an accepted method for motion analysis that bypasses frame by frame analysis and resynthesis of data. Garden variety video cameras can now exploit this technique using a unique frame buffer that is a non-integrating memory that compares incoming data with that already stored. The device continuously outputs an analog video signal of the stored contents which can then be redigitized and analyzed using conventional equipment. Historically, photographic time exposures have been used to record the displacement envelope of harmonically oscillating structures to show mode shape. Mode shape analysis is crucial, for example, in aeroelastic testing of wind tunnel models. Aerodynamic, inertial, and elastic forces can couple together leading to catastrophic failure of a poorly designed aircraft. This paper will explore the usefulness of the peak store device as a videometric tool and in particular discuss methods for analyzing a targeted vibrating plate using the 'peak store' in conjunction with calibration methods familiar to the close-range videometry community. Results for the first three normal modes will be presented.

Snow, Walter L.↗
NASA NTRS1958

Analytical and Experimental Determination of the Coupled Natural Frequencies and Mode Shapes of a Dynamic Model of a Single-Rotor Helicopter

A combined analytical and experimental determination is made of the coupled natural frequencies and mode shapes in the longitudinal plane of symmetry for a dynamic model of a single-rotor helicopter. The analytical phase is worked out on the basis of a seven-degree-of-freedom system combining elastic deflections of the rotor blades, rotor shaft, pylon, and fuselage. The calculated coupled frequencies are first compared with calculated uncoupled frequencies to show the general effects of coupling and then with measured coupled frequencies to determine the extent to which the coupled frequencies can be calculated. The coupled mode shapes are also calculated and were observed visually with stroboscopic lights during the tests. A comparison of the coupled and uncoupled natural frequencies shows that significant differences exist between these frequencies for some of the modes. Good agreement is obtained between the measured and calculated values for the coupled natural frequencies and mode shapes. The results show that the coupled natural frequencies and mode shapes can be determined by the analytical procedure presented herein with sufficient accuracy if the mass and stiffness distributions of the various components of the helicopter are known.

Silveira, Milton A.↗
NASA NTRS1975

Effect of axial load on mode shapes and frequencies of beams

An investigation of the effect of axial load on the natural frequencies and mode shapes of uniform beams and of a cantilevered beam with a concentrated mass at the tip is presented. Characteristic equations which yield the frequencies and mode shape functions for the various cases are given. The solutions to these equations are presented by a series of graphs so that frequency as a function of axial load can readily be determined. The effect of axial load on the mode shapes are also depicted by another series of graphs.

Shaker, F. J.↗
NASA NTRS1983

Algorithms for on-line parameter and mode shape estimation

Algorithms are presented for on-line parameter and mode-shape estimation. The approach used is based upon a modal decomposition of the dynamic response of the flexible structure and is designed to make use of the parallel processing features of modern minicomputers. Satisfactory performance of the parallel structure identification technique used can be achieved only when the approximation functions noted correspond to the natural modes of the flexible structure. The work summarized here presents a technique for estimating both mode shapes and modal parameters.

Thau, F. E.↗
NASA NTRS1979

Experimental measurements of the rotating frequencies and mode shapes of a full scale helicopter rotor in a vacuum and correlations with calculated results

This paper presents results of an experimental program conducted to obtain data which can be used for correlations of rotor blade dynamic analyses. Measurements were made of the rotating frequencies and mode shapes of a representative full-scale, two-bladed helicopter rotor in a vacuum. The blades were cantilevered to the hub. Mode shape data were obtained optically using a system of cameras developed specifically for this purpose. Excitation of the rotor was provided by vertical oscillatory motion of the hub. To compare experimental and analytical results, correlations of some experimental measurements with calculations from an existing blade modes computer program based on a Holzer-Myklestad procedure are presented, and the differences between the results are discussed. The experimental and analytical natural frequencies were generally in good agreement as were the principal components of the modal deflections for the flap and lag modes. The torsion mode shape indicated disagreement between the measured and calculated results in regard to the amount of flap and lag motions present in this mode, while the spanwise variations of the measured and calculated torsional components were in agreement.

Lee, B. L.↗
NASA NTRS1960

An Analysis of the Flapwise Bending Frequencies and Mode Shapes of Rotor Blades Having Two Flapping Hinges to Reduce Vibration Levels

This paper presents the analysis of the flapwise natural bending frequencies and mode shapes of rotor blades with two flapping hinges located at arbitrary blade radii. The equations of motion are derived for a blade of variable mass and stiffness distribution. Solutions to the equations (natural frequencies and mode shapes) are presented for a typical blade of constant cross section having a wide range of hinge locations. The results show that the natural frequencies of the blades can be changed appreciably by varying the locations of the blade hinges, and that with two properly located flapping hinges, blade designs are possible which eliminate or greatly reduce conditions of resonance between the blade natural frequencies and the frequencies of the harmonic air loads. The results also show that ratios of natural frequency to rotor speed below a value of 6.0 are essentially constant for variations in rotor speed consistent with helicopter and VTOL applications.

Brooks, George W.↗
NASA NTRS1984

Section 1. Method of determining mode shapes and natural frequencies of the NASA unmodified test structure. Section 2. Continuous beam closed from solution to the NASA-LSS astromast torsional vibration, appendix E

The methods used to determine the lower natural frequencies and their corresponding mode shapes of the NASA-LSS Astromast (Unmodified Test Structure), and the mass integrals associated with the mode shapes are illustrated. The test structure is modeled as a cantilever beam with 91 lumped masses and without the tip mass on the free end of the bram. This uncouples the torsion and bending modes and allows for them to be determined separately. The frequency range was limited to an upper bound of 100 rad/sec (15.92 Hz.). In this range from 0.-100. rad/sec, three bending frequencies and one torsion frequency was found.

Source record↗
NASA NTRS1986

A comparison of several methods for the calculation of vibration mode shape derivatives

Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are reviewed and compared. These methods (finite difference method, Nelson's method, modal method and a modified modal method) are implemented in a general-purpose commercial finite element program and applied to a cantilever beam and a stiffened cylinder with a cutout. A beam tip mass, a beam root height and specific dimensions of the cylinder model comprise the design variables. Data are presented showing the amount of central processor time used to compute the first four eigenvector derivatives for each example problem; errors and rapidity of convergence of the approximate derivative to the exact derivative are taken into account. Nelson's method proved to be most reliable and efficient.

Sutter, T. R.↗
NASA NTRS1975

Digital computer program DF1758 fully coupled natural frequencies and mode shapes of a helicopter rotor blade

The analytical techniques and computer program developed in the fully-coupled rotor vibration study are described. The rotor blade natural frequency and mode shape analysis was implemented in a digital computer program designated DF1758. The program computes collective, cyclic, and scissor modes for a single blade within a specified range of frequency for specified values of rotor RPM and collective angle. The analysis includes effects of blade twist, cg offset from reference axis, and shear center offset from reference axis. Coupled inplane, out-of-plane, and torsional vibrations are considered. Normalized displacements, shear forces and moments may be printed out and Calcomp plots of natural frequencies as a function of rotor RPM may be produced.

Bennett, R. L.↗
NASA NTRS1961

An Investigation of the Natural Frequencies and Mode Shapes of Liquids in Oblate Spheroidal Tanks

An experimental investigation was conducted to gain some understanding of the character of the free vibration modes of liquids In oblate spheroidal tanks applicable in missile and space vehicle systems, Measured natural frequencies were obtained for the lowest three or four, antisymmetric modes of oscillation as a function of the liquid depth for three orientations of each of several such tanks of different size and oblateness. The orientations considered were such that: (a) the equator of the spheroid was horizontal and oscillations were along a diameter of the circular liquid surface; (b) the equator of the spheroid was vertical and the oscillations were along the minor axis of the elliptical liquid surface; and (c) the equator of the spheroid was vertical and the oscillations were along the major axis of the elliptical liquid surface; The frequency data are presented as dimensionless parameters developed for each orientation to permit the application of the experimental results to the prediction of the natural frequencies of tanks of different size and oblateness. Photographs we re made of representative surface wave or mode, shapes for each orientation.

Leonard, H. Wayne↗