Coupled twist-bending vibrations of incomplete elastic rings

Ojalvo, I. U.

doi:10.1016/0020-7403(62)90006-1

Cited by 47 publications

(28 citation statements)

References 5 publications

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“…Figure 1. Ring in-plane degrees of freedom [6] The out-of-plane modal solution was presented by Ojalvo [7], who built on the previous work of Archer [5]. Figure 2 depicts a cross section of the mechanical model used by Ojalvo.…”

Section: Effect Of Compression Ring Elastodynamics Behaviour Upon Blomentioning

confidence: 99%

“…Figure 2. Ring out-of-plane (axial) degrees of freedom [7] The transient elastodynamics of compression rings are rarely included in a tribological analysis. Whilst ring flutter and blowby is a widely recognised phenomenon, there has been very little research into improving ring tribological models in an effort to capture these phenomena.…”

Section: Effect Of Compression Ring Elastodynamics Behaviour Upon Blomentioning

confidence: 99%

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Effect of Compression Ring Elastodynamics Behaviour upon Blowby and Power Loss

Baker¹,

Rahmani²,

Karagiannis³

et al. 2014

SAE Technical Paper Series

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Section: Effect Of Compression Ring Elastodynamics Behaviour Upon Blomentioning

confidence: 99%

Section: Effect Of Compression Ring Elastodynamics Behaviour Upon Blomentioning

confidence: 99%

Effect of Compression Ring Elastodynamics Behaviour upon Blowby and Power Loss

Baker¹,

Rahmani²,

Karagiannis³

et al. 2014

SAE Technical Paper Series

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“…The solution is based on the one presented by Ojalvo [11] with a different choice of the form of the assumed solution. Assuming R is constant in Eq.…”

Section: Vibration Of a Constant Radius Curved Beammentioning

confidence: 99%

“…The main distinction of this method compared to [11] is that we do not assume that each of the general solutions are real. The s i are complex and the same is true for any A i e s i .…”

Section: Vibration Of a Constant Radius Curved Beammentioning

confidence: 99%

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Coupled out of plane vibrations of spiral beams for micro-scale applications

Karami

Yardimoglu

Inman

2010

Journal of Sound and Vibration

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a b s t r a c tAn analytical method is proposed to calculate the natural frequencies and the corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equations and the boundary conditions are derived using Hamilton's principle. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the derivative of the radius terms have negligible effect on structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joined together to approximate the slow change of radius along the spiral. The equations of motion are formulated in non-dimensional form and the effect of all the key parameters on natural frequencies is presented. Non-dimensional curves are used to summarize the results for clarity. We also solve the governing equations using Rayleigh's approximate method. The fundamental frequency results of the exact and Rayleigh's method are in close agreement. This to some extent verifies the exact solutions. The results show that the vibration of spirals is mostly torsional which complicates using the spiral beam as a host for a sensor or energy harvesting device.& 2010 Elsevier Ltd. All rights reserved. IntroductionWe are motivated to look at the vibrations of spiral shaped structures as a prelude to sensing and energy harvesting using the piezoelectric effect in micro-electro-mechanical systems (MEMS) devices. Vibrational energy harvesters convert vibrations available in the environment to electrical energy. The energy generated can be used to power sensor nodes [1]. These energy self-sufficient sensors can be placed in remote places to gather data and wirelessly transmit information. A key challenge in designing MEMS energy harvesters is to make them resonate with low frequency ambient vibrations. Spiral geometry has been suggested as a possible option for compact low frequency substrate in energy harvesting devices [2]. However the vibrational analysis of curved beam with varying radius (spirals) is missing in the literature [3]. Hu et al.[3] approximated the spiral by eccentric constant-radius arcs but only derived the governing equations and did not solve them for vibration characteristics. This paper attempts to solve the free vibrations of spiral beams and pave the way to the modeling of spiral MEMS harvesting devices.

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Curved beam finite elements for coupled bending and torsional vibration

Davis

Henshell

Warburton

1972

Earthq Engng Struct Dyn

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Curved beam finite elements are presented for out of plane coupled bending and torsional vibration. The element formulation is based upon the exact differential equations of an infinitesimal element in static equilibrium. The effects of shear deformation and rotary inertia are allowed for in the analysis. The element stiffness and mass matrices can be easily restricted to those of a ‘thin’ beam without the secondary effects. Frequencies obtained using either formulation are shown to converge onto exact values using ‘thick’ or ‘thin’ beam theories.

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Coupled twist-bending vibrations of incomplete elastic rings

Cited by 47 publications

References 5 publications

Effect of Compression Ring Elastodynamics Behaviour upon Blowby and Power Loss

Effect of Compression Ring Elastodynamics Behaviour upon Blowby and Power Loss

Coupled out of plane vibrations of spiral beams for micro-scale applications

Curved beam finite elements for coupled bending and torsional vibration

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