Natural Frequencies And Modes For The In-Plane Vibration Of A Triangular Closed Frame

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

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Natural Frequencies and Modes of Beams

The Rayleigh-Ritz Method for Structural Analysis ◽

10.1002/9781118984444.ch9 ◽

2014 ◽

pp. 89-112

Author(s):

Sinniah Ilanko ◽

Luis E. Monterrubio ◽

Yusuke Mochida

Keyword(s):

Natural Frequencies ◽

Natural Frequencies And Modes

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Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

Volume 1D: 16th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc97/vib-4088 ◽

1997 ◽

Author(s):

Mintae Kim ◽

Joonho Moon ◽

Jonathan A. Wickert

Keyword(s):

Mode Shape ◽

Natural Frequencies ◽

Periodic Structures ◽

Spatial Modulation ◽

Vibration Modes ◽

Algebraic Relation ◽

Natural Frequencies And Modes ◽

Axisymmetric Structure ◽

Technical Interest ◽

Model Features

Abstract When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.

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Epicyclic Gear Vibrations

Journal of Engineering for Industry ◽

10.1115/1.3439034 ◽

1976 ◽

Vol 98 (3) ◽

pp. 811-815 ◽

Cited By ~ 56

Author(s):

M. Botman

Keyword(s):

Natural Frequencies ◽

Gear Tooth ◽

Planetary Gear ◽

Periodic Coefficients ◽

Plane Vibration ◽

Epicyclic Gear ◽

Floquet’S Theory ◽

Floquet's Theory

The natural frequenices of in-plane vibration of a single planetary gear stage are analyzed. The gear tooth stiffnesses are approximated as linear springs. The effect of planet pin stiffness on the natural frequencies is evaluated. Rotation of the carrier gives rise to a system with periodic coefficients which is solved by means of Floquet’s theory. The rotation of the carrier appears to suppress the nonaxisymmetric modes which are present in the system with nonrotating carrier.

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