Low-Frequency Mode Transition in the Free in-Plane Vibration of Curved Beams

Tarnopolskaya, Tanya; Hoog, Frank de; Fletcher, Neville H.

doi:10.1006/jsvi.1999.2400

Cited by 28 publications

(25 citation statements)

References 13 publications

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“…Then, nonlinearity coefficients (λ) were obtained by using Eqs. (17) and (18). Nonlinearities (λ) of the first mode were given in the cases of two and three springs in Tabs.…”

Section: Case Of Primary Resonancementioning

confidence: 99%

“…Tarnopolskaya et al examined the vibrational behavior of beams with arbitrarily varying curvature and cross-section in the lower region of the spectrum. 18 They examined whether or not the mode transition took place for a particular type of beam curvature and cross-section. Lestari and Hanagud found closed-form exact solutions to the problem of nonlinear vibrations of buckled beams.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

Özkaya¹,

Sarıgül²,

Boyacı³

2016

IJAV

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In this study, nonlinear vibrations of a slightly curved beam of arbitrary rise functions is handled in case it rests on multiple springs. The beam is simply supported on both ends and is restricted in longitudinal directions using the supports. Thus, the equations of motion have nonlinearities due to elongations during vibrations. The method of multiple scales (MMS), a perturbation technique, is used to solve the integro-differential equation analytically. Primary and 3 to 1 internal resonance cases are taken into account during steady-state vibrations. Assuming the rise functions are sinusoidal in numerical analysis, the natural frequencies are calculated exactly for different spring numbers, spring coefficients, and spring locations. Frequency-amplitude graphs and frequency-response graphs are plotted by using amplitude-phase modulation equations.

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“…Then, nonlinearity coefficients (λ) were obtained by using Eqs. (17) and (18). Nonlinearities (λ) of the first mode were given in the cases of two and three springs in Tabs.…”

Section: Case Of Primary Resonancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

Özkaya¹,

Sarıgül²,

Boyacı³

2016

IJAV

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“…In has been shown in [8] that after the sharp increase in eigenvalues and transformation of mode shapes that accompanies an increase in beam curvature and occurs at small values of the beam opening angle, a stage follows where there is virtually no change in mode shape with further increase in beam curvature. This gives us the chance to try to obtain an estimate for the eigenvalues from Raileigh's principle, provided that a reasonable approximation for mode shape is known.…”

Section: Approximations At Small Number Of Helical Turnsmentioning

confidence: 99%

“…We start with flexural modes of a moderately curved planar beam and then follow their development as the non-dimensional curvature of the beam increases to arbitrarily large values. A similar approach has been used in the authors' earlier papers [7,8] for beams with relatively small curvature and revealed many interesting features of mode transition accompanying an increase in beam curvature. Using this approach, it has proved possible to reveal the transformation of modes that occurs with increase in number of helical turns and the association of the modes of a helix with the modes of a curved beam.…”

Section: Introductionmentioning

confidence: 97%

Asymptotic approximations for vibrational modes of helices

Tarnopolskaya¹,

Hoog²

2000

ANZIAMJ

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The free vibrations in the plane normal to the helical axis are studied under the assumption that the helical pitch is small. Asymptotic approximations for eigenvalues and eigenfunctions are derived for both small and large numbers of helical turns. The analytic approximations reveal interesting features of helix vibrations and the connection between the vibrational modes of a helix and the flexural modes of a curved beam. Comparison with numerical calculations shows that the

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“…Chidamparam and Leissa [1995], Tarnopolskaya et al [1996], and Fung [2004] focused on in-plane vibration; and Irie et al [1982] and Howson and Jemah [1999] on out-of-plane vibration. The coupled free-vibration frequencies were also presented as part of an investigation of low-frequency mode transition, also referred to as veering [Tarnopolskaya et al 1999;Chen and Ginsberg 1992].…”

Section: Introductionmentioning

confidence: 99%

Stability studies for curved beams

Chang¹,

Hodges²

2009

J. Mech. Solids Struct.

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The paper presents a concise framework investigating the stability of curved beams. The governing equations used are both geometrically exact and fully intrinsic; that is, they have no displacement and rotation variables, with a maximum degree of nonlinearity equal to two. The equations of motion are linearized about either the reference state or an equilibrium state. A central difference spatial discretization scheme is applied, and the resulting linearized ordinary differential equations are cast as an eigenvalue problem. The scheme is validated by comparing predicted numerical results for prebuckling deformation and buckling loads for high arches under uniform pressure with published analytical solutions. This is a conservative system of forces despite their being modeled as distributed follower forces. The results show that the stretch-bending coupling term must be included in order to accurately calculate the prebuckling curvature and bending moment of high arches. In addition, the lateral-torsional buckling instability of curved beams under tip moments is investigated. Finally, when a curved beam is loaded with nonconservative forces, resulting dynamic instabilities may be found through the current framework.

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Low-Frequency Mode Transition in the Free in-Plane Vibration of Curved Beams

Cited by 28 publications

References 13 publications

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

Nonlinear Transverse Vibrations of a Slightly Curved Beam resting on Multiple Springs

Asymptotic approximations for vibrational modes of helices

Stability studies for curved beams

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