Cardiovascular effects of vibration, part 2 Final report, 31 Jul. 1968 - 31 Jul. 1969
Human cardiovascular system reactions to forward-back and transverse vibrations
Roberts, L. B.↗
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Approximation methods for inverse problems involving the vibration of beams with tip bodies
Two cubic spline based approximation schemes for the estimation of structural parameters associated with the transverse vibration of flexible beams with tip appendages are outlined. The identification problem is formulated as a least squares fit to data subject to the system dynamics which are given by a hybrid system of coupled ordinary and partial differential equations. The first approximation scheme is based upon an abstract semigroup formulation of the state equation while a weak/variational form is the basis for the second. Cubic spline based subspaces together with a Rayleigh-Ritz-Galerkin approach were used to construct sequences of easily solved finite dimensional approximating identification problems. Convergence results are briefly discussed and a numerical example demonstrating the feasibility of the schemes and exhibiting their relative performance for purposes of comparison is provided.
Rosen, I. G.↗
On vibration control of tethered satellite systems
The general dynamics of a shuttle supported tethered subsatellite system taking into account the longitudinal and three dimensional transverse vibrations is considered. It is noted that control of inherently unstable dynamics during retrieval of the subsatellite can be carried out by letting the rate of change length depend on the state variables in an appropriate manner. Control laws using linear feedback of inplane state variables and nonlinear feedback of out-of-plane state variables are proposed.
Xu, D. M.↗
An approximate theory for transverse shear deformation and rotatory inertia effects in vibrating beams
Transverse shear deformation and rotary inertia effects in vibrating beams
Egle, D. M.↗
A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies
A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.
Rosen, I. G.↗
Analytical and experimental study of the vibration of bonded beams with a lap joint
A theoretical model to study the flexural vibration of a bonded lap joint system is described in this paper. First, equations of motion at the joint region are derived using a differential element approach. The transverse displacements of the upper and lower beam are considered to be different. The adhesive is assumed to be linearly viscoelastic and the widely used Kelvin-Voight model is used to represent the viscoelastic behavior of the adhesive. The shear force at the interface between the adhesive and the beam is obtained from the simple bending motion equations of the two beams. The resulting equations of motion are combined with the equations of transverse vibration of the beams in the unjointed regions. These are later solved as a boundary value problem to obtain the eigenvalues and eigenvectors of the system. The model can be used to predict the natural frequencies, modal damping ratios, and mode shapes of the system for free vibration. Good agreement between numerical and experimental results was obtained for a system of graphite epoxy beams lap-jointed by an epoxy adhesive.
Rao, M. D.↗
In Search of Multi-Peaked Reflective Spectrum with Optic Fiber Bragg Grating Sensor for Dynamic Strain Measurement
In a typical optic fiber Bragg grating (FBG) strain measurement, unless in an ideal static laboratory environment, the presence of vibration or often disturbance always exists, which often creates spurious multiple peaks in the reflected spectrum, resulting in a non-unique determination of strain value. In this report we attempt to investigate the origin of this phenomenon by physical arguments and simple numerical simulation. We postulate that the fiber gratings execute small amplitude transverse vibrations changing the optical path in which the reflected light traverses slightly and non-uniformly. Ultimately, this causes the multi-peak reflected spectrum.
Tai, Hsiang↗
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↗
New Gear Transmission Error Measurement System Designed
The prime source of vibration and noise in a gear system is the transmission error between the meshing gears. Transmission error is caused by manufacturing inaccuracy, mounting errors, and elastic deflections under load. Gear designers often attempt to compensate for transmission error by modifying gear teeth. This is done traditionally by a rough "rule of thumb" or more recently under the guidance of an analytical code. In order for a designer to have confidence in a code, the code must be validated through experiment. NASA Glenn Research Center contracted with the Design Unit of the University of Newcastle in England for a system to measure the transmission error of spur and helical test gears in the NASA Gear Noise Rig. The new system measures transmission error optically by means of light beams directed by lenses and prisms through gratings mounted on the gear shafts. The amount of light that passes through both gratings is directly proportional to the transmission error of the gears. A photodetector circuit converts the light to an analog electrical signal. To increase accuracy and reduce "noise" due to transverse vibration, there are parallel light paths at the top and bottom of the gears. The two signals are subtracted via differential amplifiers in the electronics package. The output of the system is 40 mV/mm, giving a resolution in the time domain of better than 0.1 mm, and discrimination in the frequency domain of better than 0.01 mm. The new system will be used to validate gear analytical codes and to investigate mechanisms that produce vibration and noise in parallel axis gears.
Oswald, Fred B.↗
Hybrid Double Perovskite Containing Helium: [He 2 ][CaZr]F 6
Perovskites are of great technological and geological importance, in large part, due to their considerable compositional and structural flexibility. However, the formation of perovskites with neutral species on their A-sites is very unusual. The formation, phase transitions and properties of [He 2 ][CaZr]F 6 , which is the first noble gas containing perovskite to be made, are reported. It is likely that a large family of related materials can also be prepared. On compression in neon, the negative thermal expansion (NTE) material CaZrF 6 amorphizes at ~ 0. 5 GPa. However, on compression in helium at room temperature, gas is inserted into the structure to form a perovskite with helium on the A-site. This suppresses the amorphization until > 3 GPa. Volume versus pressure and Raman measurements suggest that filling of the A-site, to give [He 2 ][CaZr]F 6 , is complete at > 1 GPa. The presence of helium on the A-site in this perovskite leads to a reduction in the magnitude of negative thermal expansion when compared to the parent phase CaZrF 6 , likely due to steric impediment of the transverse vibrational motion of fluoride. The helium also leads to considerable stiffening of the structure. At room temperature and ~2.5 GPa, the helium containing hybrid perovskite has a bulk modulus of ~ 47 GPa, whereas CaZrF 6 has a bulk modulus of ~ 40 GPa at ambient. At 15 K, the cubic perovskite [He 2 ][CaZr]F 6 undergoes a structural phase transition, that likely involves a cooperative tilting of framework octahedra to give a lower-symmetry phase, which is tentatively assigned as tetragonal.
36 MATERIALS SCIENCE↗
Helium Incorporation into Scandium Fluoride, a Model Negative Thermal Expansion Material
Scandium trifluoride is a model negative thermal expansion (NTE) material. Its simple structure can be described as an A-site vacant perovskite, and it shows isotropic NTE over a very wide temperature range (up to ~1100 K), due to transverse vibrational motion of the fluoride. Like many framework NTE materials, it undergoes a phase transition at low pressures, adopting a rhombohedral (R3̅c) structure at >0.7 GPa and 300 K in commonly used nonpenetrating pressure media, such as silicone oil. High pressure X-ray diffraction data and gas uptake/release measurements indicate that, on compression in helium above ~200 K, helium is inserted into ScF 3 to form the defect perovskite He x ScF 3 . The incorporation of helium stiffens the structure and changes its phase behavior. At room temperature, complete filling of the structure with helium does not occur until >1.5 GPa. On compression, a cubic perovskite structure is maintained until ~5 GPa. As the pressure was increased to ~9.5 GPa, a further transition occurred at ~7 GPa. The first transition at ~5 GPa is likely to a tetragonal (P4/mbm) perovskite, but the detailed structure of the perovskite phase formed on compression above ~7 GPa is unclear. Cooling down from 300 to 100 K in helium at ~0.4 GPa leads to an approximate composition of He 0.1 ScF 3 . High pressure neutron diffraction measurements, in the temperature range 15–150 K show that the incorporation of helium increases the pressure at which the cubic (Pm3̅m) to rhombohedral (R3̅c) putative quantum structural phase transition occurs from close to 0 GPa to ~0.2 GPa at 0 K.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Orbital-Selective Instabilities and Spin Fluctuations at the Verge of Superconductivity in Interlayer-Expanded Iron Selenide
Understanding electron correlation-driven instabilities and their coupling to structural phases is essential for deciphering multiorbital pairing in unconventional superconductors. We investigate Li x (C 5 H 5 N) y Fe 2 Se 2 (x ∼ 0.6; y ∼ 0.7−0.9), a tetragonal β-FeSe intercalate with a superconducting transition temperature (T c = 39 K) closely tied to an expanded Fe-layer spacing (∼11.4 Å). High-resolution synchrotron Xray diffraction and core-level absorption spectroscopy reveal subtle lattice distortions on cooling without a symmetry-breaking transition. Instead, the material exhibits negative thermal expansion (NTE) in the two-dimensional Fe network below T S ∼ 70 K, and stiffening of local Se−Fe−Se bond dynamics near T c . The spatially incoherent rearrangement of FeSe 4 tetrahedra and the site-local fluctuations, signal reduced electron correlations compared to those of parent β-FeSe (T c = 8 K). Complementary X-ray emission spectroscopy, a fast local probe of Fe 3d valence states, detects persistent local Fe spin moments below T S , unlike quenching in related systems. These findings indicate that decoupling of Fe planes leads to an electronically driven lattice instability. The latter emerges as NTE induced from weak, orbital-selective localization of in-plane Fe 3d states rather than conventional transverse vibrations. Governed by Hund’s coupling, this selectivity permits coexistence of local spin fluctuations with itinerant d-electrons critical for enhancing T c . These results suggest that intercalation-driven d-orbital differentiation moderates electron correlations, providing a pathway to optimize the superconductivity in low-dimensional quantum materials.
36 MATERIALS SCIENCE↗
Entanglement Effect and Angular Momentum Conservation in a Nonseparable Tunneling Treatment
The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for nonseparable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for nonseparable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and E-resolved rate constants over broad ranges of temperatures and energies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Strong Negative Thermal Expansion in a Low-Cost and Facile Oxide of Cu 2 P 2 O 7
Negative thermal expansion (NTE) behaviors have been observed in various types of compounds. The achievement in the merits of promising low-cost and facile NTE oxides remains challenging. In the present work, a simple and low-cost Cu 2 P 2 O 7 has been found to exhibit the strongest NTE among the oxides (alpha(v) similar to -27.69 X 10 -6 K -1 , 5-375 K). The complex NTE mechanism has been investigated by the combined methods of high-resolution synchrotron X-ray diffraction, neutron powder diffraction, X-ray pair distribution function, extended X-ray absorption fine structure spectroscopy, and density functional theory calculations. Interesting, the direct experimental evidence reveals that the coupling twist and rotation of PO 4 and CuO 5 polyhedra are the inherent factors for the NTE nature of Cu 2 P 2 O 7 , which is triggered by the transverse vibrations of oxygen atoms. The present new NTE material of Cu 2 P 2 O 7 also has been verified for the practical application.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A new method of measurement of tension on a moving magnetic tape
The possibility of no-contact measurement of the tension on a moving magnetic tape, assuming the tape is uniform, is discussed. A scheme for calculation of the natural frequency of transverse vibrations of magnetic tape is shown. Mathematical models are developed to show the relationships of the parameters. The method is applicable to the analysis of accurate tape feed mechanisms design.
Kurtinaytis, A. K.↗
A combined integrating and differentiating matrix formulation for boundary value problems on rectangular domains
Integrating and differentiating matrices allow the numerical integration and differential of functions whose values are known at points of a discrete grid. Previous derivations of these matrices were restricted to one dimensional grids or to rectangular grids with uniform spacing in at least one direction. Integrating and differentiating matrices were developed for grids with nonuniform spacing in both directions. The use of these matrices as operators to reformulate boundary value problems on rectangular domains as matrix problems for a finite dimensional solution vector is considered. The method requires nonuniform grids which include near boundary points. An eigenvalue problem for the transverse vibrations of a simply supported rectangular plate is solved to illustrate the method.
Lakin, W. D.↗
Eigenvalues and stability problems of rotors
The essential theoretical results of the application of a developed transfer matrix method to the free transverse vibration of a rotor are shown. Gyroscopic and shear effects, rotary inertia, and external and internal damping as well as the influence of sleeve bearings and rotor supports are taken into consideration. The eigenvalues of the motion equations of the rotor are searched by using a modified determinant method.
Walczyk, Z.↗