XL.<i>The lowest natural frequency of circular arcs</i>

Hartog, J. P. Den

doi:10.1080/14786440208564480

Cited by 93 publications

(29 citation statements)

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“…His study was confined to in-plane excitations and made use of the classical equations of motion presented earlier by Love (1944). Archer's results showed good agreement with those found earlier by Den Hartog (1928), with similar mode shapes. Ojalvo (1962) stated that treating the in-plane and out-of-plane ring motions as separate problems is a valid assumption, since the two motions are considered as uncoupled.…”

Section: Introductionsupporting

confidence: 82%

“…Though limited to beams with relatively small curvature, equations of motion for a free bar were derived and solved. Den Hartog (1928) extended this approach, using the Rayleigh-Ritz energy method to derive formulae for the first two natural frequencies of an incomplete circular arc, for both hinged and clamped boundary conditions. Lord Rayleigh's method was modified by Brown (1934) in order to find an approximate solution for the in-plane radial vibrations.…”

Section: Introductionmentioning

confidence: 99%

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Influence of In-Plane Dynamics of Thin Compression Rings on Friction in Internal Combustion Engines

Baker

Theodossiades

Rahnejat

et al. 2012

Journal of Engineering for Gas Turbines and Power

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The compression ring-bore conjunction accounts for significant frictional parasitic losses relative to its size. The prerequisite to improving the tribological performance of this contact is a fundamental understanding of ring dynamics within the prevailing transient nature of regime of lubrication.Studies reported thus far take into account ring-bore conformance, based on static fitment of the ring within an out-of-round bore, whose out-of-circularity is affected by manufacturing processes, surface treatment and assembly. The static fitment analyses presume quasi-static equilibrium between ring tension and gas pressure loading with generated conjunctional pressures. This is an implicit assumption of ring rigidity whilst in situ. The current analysis considers the global modal behaviour of the ring as an eigenvalue problem, thus including its dynamic in-plane behaviour in the tribological study of a mixed-hydrodynamic regime of lubrication. The results show that the contact transit time is shorter than that required for the ring to reach steady state condition. Hence, the conjunction is not only subject to transience on account of changing contact kinematics and varied combustion loading, but also subject to perpetual ring transient dynamics. This renders the ring-bore friction a more complex problem than usually assumed in idealised ring fitment analyses. An interesting finding of the analysis is increased ring-bore clearance at and in the vicinity of top dead centre, which reduces the ring sealing effect and suggests a possible increase in blow-by. The current analysis, integrating ring in-plane modal dynamics and mixed regime of lubrication includes salient features which are closer representation of practice, an approach which has not hitherto been reported in literature.

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Section: Introductionsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Influence of In-Plane Dynamics of Thin Compression Rings on Friction in Internal Combustion Engines

Baker

Theodossiades

Rahnejat

et al. 2012

Journal of Engineering for Gas Turbines and Power

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“…For a series of successive quasi-static analyses, it is essential for the converged elastic film shape from the previous analysis to be carried over to the next in order to obtain an estimate of squeeze film velocity, using equation (10). At each piston position, the combustion pressure is obtained from Fig.…”

Section: Solution Proceduresmentioning

confidence: 99%

Tribology of compression ring-to-cylinder contact at reversal

Mishra

Balakrishnan

Rahnejat

2008

Proceedings of the Institution of Mechanical Engineers, Part J:

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Piston ring-pack-to-cylinder contact accounts for one of the major sources of frictional losses in internal combustion engines. The regime of lubrication alters during the piston cycle because of the transient nature of applied load and kinematic contact conditions. Ring geometry, surface topography, and lubricant rheology also play an important role. The aim is to attain full fluid film lubrication, thus reducing friction because of boundary interactions. Therefore, accurate prediction of lubricant film thickness and pressure distribution constitutes the first step in a proper analysis of piston ring-cylinder conjunction. The creation of a gap through elastic deformation is sought in order to inhibit asperity tip interactions. The generated contact pressures in the lubricant film are due to combined entraining motion and squeeze film effect. The integrated pressure distribution balances the elastic force due to ring tension and the applied combustion pressure acting behind the ring. The article highlights a detailed analysis, which forms the basis for its future expansion to include the study of mixed regime of lubrication, which may be prevalent in some real engines.

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“…Lamb [3] investigated the statics of incomplete ring with various boundary conditions and the dynamics of an incomplete free-free ring of small curvature. Den Hartog [4] used the Rayleigh-Ritz method for finding the lowest natural frequency of circular arcs with simply supported or clamped ends, and his work was extended by Volterra and Morell [5] for the vibrations of arches having center lines in the form of cycloids, catenaries, or parabolas. Archer [6] carried out for a mathematical study of the in-plane inextensional vibrations of an incomplete circular ring of small cross section with the basic equations of motion as given in Love [2] and gave a prescribed time-dependent displacement at the other end for the case of clamped ends.…”

Section: Introductionmentioning

confidence: 99%

Extensional Vibration Analysis of Curved Beams Including Rotatory Inertia and Shear Deformation Using DQM

Kang¹,

Park²

2016

Journal of the Korea Academia-Industrial cooperation Society

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One of the most efficient procedures for the solution of partial differential equations is the method of differential quadrature. The differential quadrature method (DQM) has been applied to a large number of cases to overcome the difficulties of complex algorithms of computer programming, as well as the excessive use of storage due to the conditions of complex geometry and loading. The in-plane vibrations of curved beams with extensibility of the arch axis, including the effects of rotatory inertial and shear deformation, are analyzed by the DQM. The fundamental frequencies are calculated for members with various slenderness ratios, shearing flexibilities, boundary conditions, and opening angles. The results are compared with the numerical results obtained by other methods for cases in which they are available. The DQM gives good mathematical precision even when only a limited number of grid points is used, and new results according to diverse variations are also suggested.

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XL.The lowest natural frequency of circular arcs

Cited by 93 publications

References 0 publications

Influence of In-Plane Dynamics of Thin Compression Rings on Friction in Internal Combustion Engines

Influence of In-Plane Dynamics of Thin Compression Rings on Friction in Internal Combustion Engines

Tribology of compression ring-to-cylinder contact at reversal

Extensional Vibration Analysis of Curved Beams Including Rotatory Inertia and Shear Deformation Using DQM

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