Stability of a bar under eccentric follower force.
Uniform cantilevered bar subject to eccentric compressive follower force, considering warping rigidity, bending-torsional flutter and stability
ELASTIC BAR↗
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Results for “BENDING VIBRATION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Vibrating Beam With Spatially Periodic Stiffness
Report presents theoretical analysis of vibrations of simply supported beam, bending stiffness varying about steady value, sinusoidally with position along length. Problem of practical importance because related to vibrations of twisted-pair electric-power transmission lines. Twists promote nonuniform shedding of vortexes and prevents resonant accumulation of vibrational energy from wind.
Townsend, John S.↗
Vibrations of a hollow elastic cylinder bonded to a thin casing of a different material
Exact solutions for vibrations of hollow elastic cylinder bonded to thin casing of different material
ELASTIC CYLINDER↗
Free flight simulated on ground with the Apollo Saturn V space vehicle.
Hydraulic support system for free flight simulation with Saturn V-Apollo vehicle, discussing stability requirements, upper bounds of system design, conversion from nonlinear to linear model, etc
VIBRATION TESTING↗
Multicyclic Controllable Twist Rotor Data Analysis
Rsults provide functional relationship between rotor performance, blade vibratory loads and dual control settings and indicate that multicyclic control produced significant reductions in blade flatwise bending moments and blade root actuator control loads. Higher harmonic terms of servo flap deflection were found to be most pronounced in flatwise bending moment, transmission vertical vibration and pitch link vibratory load equations. The existing test hardware represents a satisfactory configuration for demonstrating MCTR technology and defining a data base for additional wind tunnel testing.
Wei, F. S.↗
Power flow in a beam using a 5-accelerometer probe
A method to determine structure-borne power flow is examined which uses central finite differences to approximate the field variables required to calculate the shear and bending components of flexural vibration. An experimental study using a beam driven by a shaker was performed with the aim of comparing estimates using this proposed five-accelerometer method and the conventional two-accelerometer, free-field method. The advantages and disadvantages of the new method are pointed out.
Downing, J. Micah↗
The Rotational Spectrum of Iodine Dioxide, OIO
The rotational spectra of OIO in its ground vibrational and first excited bending states have been observed for the first time. OIO was formed initially from the products of a microwave discharge in O2 passing over molecular iodine and later with greater yield in a DC discharge through a mixture of O2 and I2 vapor. OIO is an asymmetric prolate rotor (kappa = -0.690) with a (sup 2)B(sub 1) electronic ground state. Over 550 ground state transitions and over 160 transitions of the excited bending state have been included in the fits. The resulting parameters are well determined and will be compared to those recently published for OBrO and OClO. These will be interpreted in terms of the molecular geometry, harmonic force field, and electronic structure.
Miller, Charles E.↗
Two-Stage Passive Vibration Isolator
The design and testing of a structural system were implemented to hold the optics of the planned Space Interferometry Mission (SIM) at positions and orientations characterized by vibrational translation and rotation errors of no more than a few nanometers or a few milliarcseconds, respectively. Much of the effort was devoted to a test bed for verifying the predicted behavior of a vibration- isolation structural subsystem working together with an active control system for positioning and orienting the SIM optics. There was considerable emphasis on the vibration-isolation subsystem, which was passive and comprised two stages. The main sources of vibration were six reaction wheels in an assembly denoted the "backpack." The first vibration-isolation stage consisted of hexapod isolator mounts - one for each reaction wheel - characterized by a natural vibration frequency of 10 Hz. The second stage was a set of three beams, disposed between the backpack and the structure that held the SIM optics, that were flexured such that they transmitted only bending loads, with a natural vibrational frequency and damping of about 5 Hz and 4 percent, respectively. Preliminary test results were presented and characterized as demonstrating the effectiveness of the two-stage vibration-isolation design.
Goullioud, Renaud↗
Viscoelastic Vibration Dampers for Turbomachine Blades
Simple viscoelastic dampers have been invented for use on the root attachments of turbomachine blades. These dampers suppress bending- and torsion-mode blade vibrations, which are excited by unsteady aerodynamic forces during operation. In suppressing vibrations, these dampers reduce fatigue (thereby prolonging blade lifetimes) while reducing noise. These dampers can be installed in new turbomachines or in previously constructed turbomachines, without need for structural modifications. Moreover, because these dampers are not exposed to flows, they do not affect the aerodynamic performances of turbomachines. Figure 1 depicts a basic turbomachine rotor, which includes multiple blades affixed to a hub by means of dovetail root attachments. Prior to mounting of the blades, thin layers of a viscoelastic material are applied to selected areas of the blade roots. Once the blades have been installed in the hub and the rotor is set into rotation, centrifugal force compresses these layers between the mating load-bearing surfaces of the hub and the blade root. The layers of viscoelastic material provide load paths through which the vibration energy of the blade can be dissipated. The viscoelasticity of the material converts mechanical vibration energy into shear strain energy and then from shear strain energy to heat. Of the viscoelastic materials that have been considered thus far for this application, the one of choice is a commercial polyurethane that is available in tape form, coated on one side with an adhesive that facilitates bonding to blade roots. The thickness of the tape can be chosen to suit the specific application. The typical thickness of 0.012 in. (.0.3 mm) is small enough that the tape can fit in the clearance between the mating blade-root and hub surfaces in a typical turbomachine. In an experiment, a blade was mounted in a test fixture designed to simulate the blade-end conditions that prevail in a turbocompressor. Vibrations were excited in the blade by use of an impact hammer, and damping of the vibrations was measured by use of a dynamic signal analyzer. Tests were performed without and with viscoelastic dampers installed in the dovetail root attachment. The results of the measurements, some of which are presented in Figure 2, show that the viscoelastic dampers greatly increased the rate of damping of vibrations. Accordingly, dynamic stresses on rotor blades were significantly reduced, as shown in Figure 2.
Nguyen, Nhan↗
Active control of flexural vibrations in beams
The feasibility of using piezoelectric actuators to control the flexural oscillations of large structures in space is investigated. Flexural oscillations are excited by impulsive loads. The vibratory response can degrade the pointing accuracy of cameras and antennae, and can cause high stresses at structural node points. Piezoelectric actuators have the advantage of exerting localized bending moments. In this way, vibration is controlled without exciting rigid body modes. The actuators are used in collocated sensor/driver pairs to form a feedback control system. The sensor produces a voltage that is proportional to the dynamic stress at the sensor location, and the driver produces a force that is proportional to the voltage applied to it. The analog control system amplifies and phase shifts the sensor signal to produce the voltage signal that is applied to the driver. The feedback control is demonstrated to increase the first mode damping in a cantilever beam by up to 100 percent, depending on the amplifier gain. The damping efficiency of the control system when the piezoelectrics are not optimally positioned at points of high stress in the beam is evaluated.
Gerhold, Carl H.↗
Low Frequency Vibrational Modes of Two-Dimensional Lead-Free Metal Halide Double Perovskites
2D layered double perovskites of (S-MPA) 4 AgBiI 8 (MPA-AgBiI 8 ) and (S-MPA) 4 CuBiI 8 (MPA-CuBiI 8 ) (S-MPA, S-β-methylphenethylammonium) were synthesized with a hydrothermal method. The crystal structure of MPA-AgBiI 8 was determined using single-crystal X-ray diffraction (scXRD). Powder XRD (pXRD) data suggest that the crystal structure of MPA-CuBiI 8 is more complex than that of MPA-AgBiI 8 . UV-Vis electronic absorption spectra of these perovskites reveal a bandgap of 2.03 eV for both. Short exciton lifetime from time-resolved photoluminescence (TRPL) results and low PL intensity of the Cu-based perovskite suggest a high density of trap states within the bandgap. Low frequency Raman spectra of both materials show distinct peaks and a slightly higher frequency for the Cu-based perovskite than the Ag-based perovskite. Density functional theory (DFT) calculations were conducted to simulate the low frequency Raman spectra and help explain the different phonon modes, which are collective vibrations of metal halide bond bending and stretching within the Ag- and Cu-centered octahedra coupled with MPA libration and twisting within the inorganic layer. The DFT theory also quantified octahedral distortions in the two perovskites. Furthermore, this combined experimental and computational study provides new insights into the low frequency vibrations of 2D perovskites.
Halogens↗
Large deflection, large amplitude vibrations and random response of symmetrically laminated rectangular plates
An analytical method is presented for determining large-deflection static bending, large-amplitude free and forced vibrations, and large-amplitude random response of a clamped, symmetrically laminated, rectangular, thin plate subjected to a uniformly distributed transverse loading. Both movable and immovable inplane boundary conditions are considered. Numerical results for bending deflections and strains, frequency ratios, mean-square center deflections and mean-square maximum strains are presented showing the parametric effects of plate length-to-width ratio, orientation of layers, and intensities of applied force for both the linear and nonlinear cases. The analytical results for large-deflection random response are verified through comparison with experimental data.
Gray, C. E., Jr.↗
Topaz, a Potential Volatile-Carrier in Cold Subduction Zone: Constraint from Synchrotron X-ray Diffraction and Raman Spectroscopy at High Temperature and High Pressure
The equation of state and stability of topaz at high-pressure/high-temperature conditions have been investigated by in situ synchrotron X-ray diffraction (XRD) and Raman spectroscopy in this study. No phase transition occurs on topaz over the experimental pressure–temperature ($P-T$) range. The pressure–volume data were fitted by the third-order Birch–Murnaghan equation of state (EoS) with the zero-pressure unit–cell volume V 0 = 343.86 (9) Å 3 , the zero-pressure bulk modulus K 0 = 172 (3) GPa, and its pressure derivative K’ 0 = 1.3 (4), while the obtained K 0 = 155 (2) GPa when fixed K’ 0 = 4. In the pressure range of 0–24.4 GPa, the vibration modes of in-plane bending OH-groups for topaz show non-linear changes with the increase in pressure, while the other vibration modes show linear changes. Moreover, the temperature–volume data were fitted by Fei’s thermal equation with the thermal expansion coefficient α 300 = 1.9 (1) × 10 –5 K –1 at 300 K. Finally, the $P-T$ stability of topaz was studied by a synchrotron-based single-crystal XRD at simultaneously high $P-T$ conditions up to ~10.9 GPa and 700 K, which shows that topaz may maintain a metastable state at depths above 370 km in the upper mantle along the coldest subducting slab geotherm. Thus, topaz may be a potential volatile-carrier in the cold subduction zone. It can carry hydrogen and fluorine elements into the deep upper mantle and further affect the geochemical behavior of the upper mantle.
36 MATERIALS SCIENCE↗
The Failure of Correlation to Describe Out-of-Plane Carbon=Carbon Bending
Carbon-carbon multiply bonded systems are improperly described with standard correlation methods and basis sets. For computations of vibrational modes, the out-of- plane bends can be reported as imaginary at worst or simply too low at best. Utilizing the simplest of aromatic structures (cyclopropenylidene) and various levels of theory, this work diagnoses this known behavior for the first time. A combined 1-particle and n-particle basis set effect conspire to produce these non-physical results. When moving from sp2 to sp3 hybridization in the carbon atoms, the larger number of basis functions overcorrects the energy. This is exacerbated by correlation methods. These allow for occupation of the π and π∗ orbitals in the expanded wave function that combine with the hydrogen s orbitals. As a result, the improperly described space can be further and non-physically stabilized by post-Hartree-Fock correlation. This represents a fundamental problem with at least Hartree-Fock based methods of all flavors in describing carbon. Beyond being a flaw in quantum chemical theory, other repercussions will be present in computations regarding spectroscopy as well as energy and environmental studies where highly-accurate hydrocabon vibrational transitions or thermochemical data are needed.
Fortenberry, Ryan C.↗
An investigation of the vibration characteristics of shrouded-bladed-disk rotor stages
Coupled differential equations of motion are given for application to a rotating, pretwisted and heated beam under the effects of thermal stresses and gas bending loads. The circumferential modes of the multi-blade vibration of a bladed-disk rotor stage were studied. A finite element method was developed for the dynamic and static deformation analysis of the blade. The deformations of a bladed disk and a shrouded-bladed disk were studied by introducing a special bladed-disk element and a special shrouded-blade element. Some features of the vibration of part-span-shrouded, bladed-disk rotor stages are discussed. The static deformation, thermal stress and gas bending effects on the blade vibration were presented previously.
Chen, L.-T.↗
Polyatomic molecule vibrations
Polyatomic molecule vibrations are analyzed as harmonic vibrations along normal coordinates. The energy eigenvalues are found for linear and nonlinear symmetric triatomic molecules for valence bond models of the potential function with arbitrary coupling coefficients; such models can usually be fitted to observed energy levels with reasonably good accuracy. Approximate normal coordinates for the H2O molecule are discussed. Degenerate vibrational modes such as occur in CO2 are analyzed and expressions for Fermi resonance between close-lying states of the same symmetry are developed. The bending modes of linear triatomic molecules are expressed in terms of Laguerre polynomials in cylindrical coordinates as well as in terms of Hermite polynomials in Cartesian coordinates. The effects of large-amplitude bending such as occur in the C3 molecule are analyzed, along with anharmonic effects, which split the usually degenerate bending mode energy levels. Finally, the vibrational frequencies, degeneracies, and symmetry properties of XY3, X2Y2, and XY4 type molecules are discussed.
Source record↗
A theoretical analysis of elastic vibrations of fixed-ended and hinged helicopter blades in hovering and vertical flight
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ROTOR BLADES - FLAPPING↗
Instability of a gravity gradient satellite due to thermal distortion
A nonlinear analytical model and a corresponding computer program were developed to study the influence of solar heating on the anomalous low frequency, orbital instability of the Naval Research Laboratory's gravity gradient satellite 164. The model's formulation was based on a quasi-static approach in which deflections of the satellite's booms were determined in terms of thermally induced bending without consideration of boom vibration. Calculations, which were made for variations in absorptivity, sun angle, thermal lag, and hinge stiffness, demonstrated that, within the confines of a relatively narrow stability criteria, the quasi-static model of NRL 164 not only becomes unstable, but, in a number of cases, responses were computed that closely resembled flight data.
Goldman, R. L.↗