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At least 37 records · Page 2

Transverse vibrations of shear-deformable beams using a general higher order theory

A general higher order theory is developed to study the static and vibrational behavior of beam structures having an arbitrary cross section that utilizes both out-of-plane shear-dependent warping and in-plane (anticlastic) deformations. The equations of motion are derived via Hamilton's principle, where the full 3D constitutive relations are used. A simplified version of the general higher-order theory is also presented for beams having an arbitrary cross section that includes out-of-plane shear deformation but assumes that stresses within the cross section and in-plane deformations are negligible. This simplified model, which is accurate for long to moderately short wavelengths, offers substantial improvements over existing higher order theories that are limited to beams with thin rectangular cross sections. The current approach will be very useful in the study of thin-wall closed-cell beams such as airfoil-type sections where the magnitude of shear-related cross-sectional warping is significant.

Kosmatka, J. B.↗

A design procedure for active control of beam vibrations

The transverse vibrations of beams is discussed and a methodology for the design of an active damping device is given. The Bernoulli-Euler equation is used to derive a transcendental transfer function, which relates a torque applied at one end of the beam to the rotational position and velocity at that point. The active damping device consists of a wire, a linear actuator and a short torque arm attached to one end of the beam. The action of the actuator varies a tension in the wire and creates a torque which opposes the rotation of the beam and thus damps vibration. A design procedure for such an active damper is given. This procedure shows the relationships and trade-offs between the actuator stroke, power required, stress levels in the wire and beam and the geometry of the beam and wire. It is shown that by consideration of the frequency response at the beam natural frequencies, the aforementioned relationships can be greatly simplified. Similarly, a simple way of estimating the effective damping ratios and eigenvalue locations of actively controlled beams is presented.

Dickerson, S. L.↗

The Effects of Variable Mass and Geometry, Pretwist, Shear Deformation and Rotatory Inertia on the Resonant Frequencies of Intact Long Bones: A Finite Element Model Analysis

The influence of pretwist, nonuniformities in mass and flexural stiffness, rotatory inertia and shear deformation on the natural frequencies of intact bones is evaluated by means of a linear elastic, finite-element model which has been programmed for solution on the digital computer. Theoretical results are compared to the results on the forced vibration of intact canine radii obtained experimentally by Thompson. Surprisingly, inclusion of fairly large pretwist angles (from -14 to 12 deg for one specimen) had little affect on the first three frequencies of transverse vibration in either the cranial or lateral directions. Inclusion of shear deformation reduced the third-mode frequency in the stiffest (lateral) direction by about six percent, otherwise shear deformation played a minor role in determining natural frequencies. Similarly. rotatory inertia had negligible influence up to the third natural frequency. The predominant influence on the first three natural frequencies of transverse vibration could be attributed to the variations in mass and flexural stiffness along the length of the test specimens. Different effective moduli of elasticity are required to yield correct absolute values for the frequencies which correspond to experimental findings. thus implying the presence of some inhomogeneities in material properties around the bone cross-section and/or along its length.

Young, Donald R.↗

Negative and zero thermal expansion in α-(Cu 2-x Znx)V 2 O 7 solid solutions

Negative or zero thermal expansion (NTE or ZTE) of materials is intriguing for controllable thermal expansion. In this work, we report a series of orthorhombic α-Cu 2- x Zn x V 2 O 7 ( x = 0, 0.1, 0.2), in which the volumetric coefficients of thermal expansion are successfully tuned from -10.19 × 10 -6 K -1 to -1.58 × 10 -6 K -1 in the temperature range of 100–475 K by increasing the content of Zn 2+ . It has been revealed that the transverse vibrations of oxygen bonded with vanadium are dominant in the contraction of the bc plane, leading to the overall volume NTE in α-Cu 2 V 2 O 7 . The introduction of Zn 2+ densifies the crystal structure, which is presumed to suppress the space of transverse vibrations and results in the ZTE in α-Cu 1.8 Zn 0.2 V 2 O 7 . This work presents an effective method to realize ZTE in anisotropic framework systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Apparatus and method for determining the mass density of a filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament, inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data, processing the data using a fast-fourier transform analysis, and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

Apparatus and Method for Determining the Mass Density of a Filament

A method and apparatus for determining the mass density of a moving filament is provided. The method includes the steps of providing a filament across two supports, tensioning the filament. inducing a vibration into the filament segment between the supports, reinforcing the vibration using an amplified feedback signal, detecting the vibrational frequency data. processing the data using a fast-fourier transform analysis. and then displaying the frequency. The use of the feedback signal results in a self-tuning resonant loop. Open loop versions may also be used. The apparatus includes a base supporting a fixed support and a transducer which in turn supports a moveable support. The transducer vibrates the moveable support transversely to the direction of travel of the filament, thereby inducing a transverse vibrational mode. The output of the transducer is amplified and used to drive a second amplifier to produce a self-tuning resonant loop. In the open loop version a signal generator is used to drive the transducer through a frequency range, during which the amplitude peak is identified.

Hinkley, Jeffrey A.↗

Effects of Transverse Seat Vibration on Near-Viewing Readability of Alphanumeric Symbology

We measured the impacts on human visual function of a range of vibration levels (0.15, 0.3, 0.5, and 0.7 g) at the frequency and along the axis of the anticipated Ares thrust oscillation. We found statistically significant and equivalent decrements in performance on a reading and a numeric processing task at tested vibration levels above 0.3 g (0-to-peak), but no evidence of after-effects. At the smallest font and highest vibration level tested, the average effect was a 50 percent increase in response time and six-fold increase in errors. Our findings support a preliminary trade space in which currently planned Orion font sizes and text spacing appear to be too small to support accurate and efficient reading at the tested vibration levels above 0.3 g, but not too small to support reading at 0.3 g. This study does not address potential impacts on crew cognitive decision-making or motor control and does not test either the full induced Orion-Ares environment with its sustained Gx-loading or the full complexity of the final Orion seat-helmet-suit interface. A final determination of the Orion-Ares program limit on vibration must take these additional factors into consideration and, thus, may need to be lower than that needed to support effective reading at 1-Gx bias.

Readability↗

Large negative thermal expansion in GdFe(CN) 6 driven by unusual low-frequency modes

Understanding the negative thermal expansion (NTE) mechanism is of great importance. In this work, we consider the new NTE compound GdFe(CN) 6 (αv = -34.2×10 -6 K -1 ) as a case study to investigate the NTE mechanism from the perspective of the lattice vibrational dynamics. The atomic mean-square displacements suggest that the NTE of GdFe(CN) 6 comes from the strong tension effect induced by the transverse vibrations of the atomic –Fe–Ctriple bondN–Gd– linkages, with the largest contribution given by N atoms. Lattice dynamics calculations show that three low-frequency optical modes at about 50 cm -1 show the largest negative Grüneisen parameters thus providing the largest contribution to the NTE. In conclusion, the existence of these unusual low-frequency vibrational modes can be ascribed to the presence of GdN 6 trigonal prisms in the framework structure of GdFe(CN) 6 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Vibration control of flexible beams using an active hinge

The use of an active hinge to attenuate the transverse vibrations of a flexible beam is examined. A slender aluminum beam is suspended vertically, cantilevered at the top. An active hinge is placed at the node of the second vibration mode. The active hinge consists of a torque motor, strain gauge, and tachometer. A control law is implemented using both beam-bending strain and the relative angular velocity measured at this hinge, thereby configuring the hinge to act as an active damper. Results from implementing this control law show little improvement in the first mode damping ratio, 130 percent increase in the second mode damping ratio, and 180 percent increase in the third mode damping ratio. The merits of using a motor with a gearbox are discussed.

Cudney, H. H., Jr.↗

A Galerkin method for the estimation of parameters in hybrid systems governing the vibration of flexible beams with tip bodies

An approximation scheme is developed for the identification of hybrid systems describing the transverse vibrations of flexible beams with attached tip bodies. In particular, problems involving the estimation of functional parameters are considered. The identification problem is formulated as a least squares fit to data subject to the coupled system of partial and ordinary differential equations describing the transverse displacement of the beam and the motion of the tip bodies respectively. A cubic spline-based Galerkin method applied to the state equations in weak form and the discretization of the admissible parameter space yield a sequence of approximating finite dimensional identification problems. It is shown that each of the approximating problems admits a solution and that from the resulting sequence of optimal solutions a convergent subsequence can be extracted, the limit of which is a solution to the original identification problem. The approximating identification problems can be solved using standard techniques and readily available software.

Banks, H. T.↗