Recent Developments Concerning Saint-Venant's Principle

Horgan, Cornelius O.; Knowles, Jonathan C.

doi:10.1016/s0065-2156(08)70244-8

Cited by 324 publications

(246 citation statements)

References 102 publications

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“…The standard procedure used in engineering practice to determine the extent of local stresses or edge effects is based on some form of the celebrated Saint Venant principle. A comprehensive surveys of contemporary research concerning Saint Venant principle can be found in [Horgan and Knowles 1983;Horgan 1989;1996].…”

Section: Introductionmentioning

confidence: 99%

“…It is outlined in [Horgan and Knowles 1983] that one would not expect to find unqualified decay estimates of the kind concerning Saint-Venant's principle in problems involving elastic wave propagation, even if the end loads are self-equilibrated at each instant. In this connection, Flavin and Knops [1987] have carried out an analysis of spatial decay for certain damped acoustic and elastodynamic problems in the low frequency range which substantiates the early work of Boley.…”

Section: Introductionmentioning

confidence: 99%

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Spatial evolution of harmonic vibrations in linear elasticity

Chiriţă

Ciarletta

2008

JOMMS

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In the present paper we consider a prismatic cylinder occupied by an anisotropic homogeneous compressible linear elastic material that is subject to zero body force and zero displacement on the lateral boundary. The elasticity tensor is strongly elliptic and the motion is induced by a harmonic time-dependent displacement specified pointwise over the base. We establish some spatial estimates for appropriate cross-sectional measures associated with the harmonic vibrations that describe how the corresponding amplitude evolves with respect to the axial distance at the excited base. The results are established for finite as well as for semi-infinite cylinders (where alternatives results of Phragmén-Lindelöf type are obtained) and the exciting frequencies can take appropriate low and high values. In fact, for the low frequency range the established spatial estimates are of exponential type, while for the high frequency range the spatial estimates are of a certain algebraic type.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spatial evolution of harmonic vibrations in linear elasticity

Chiriţă

Ciarletta

2008

JOMMS

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“…The history and development of these questions was extensively surveyed by Horgan and Knowles [11] in a work periodically updated by Horgan [9,10]. Moreover, the books by Ames and Straughan [1], Flavin and Rionero [6] and Antontsev et al [2] are devoted to such matters.…”

Section: Introductionmentioning

confidence: 99%

Spatial behavior for a fourth-order dispersive equation

Quintanilla

Saccomandi

2006

Quart. Appl. Math.

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Abstract. In this note we investigate the spatial behavior of a linear equation of fourth order which models several mechanical situations when dispersive and dissipative effects are taken into account. In particular, this equation models the extensional vibration of a bar when we assume that external friction, with a rough substrate for example, is present. We show that for such an equation a Phragmén-Lindelöf alternative of exponential type can be obtained. A bound for the amplitude term in terms of boundary data is obtained. Moreover, when friction is absent, we obtain exponential decay results in the case of harmonic vibrations and we prove a polynomial decay estimate for general solutions. Introduction.In recent years much attention has been directed to the study of the damping of end effects in several thermomechanical situations and to the general study of the spatial behavior of solutions of partial differential equations and systems. The history and development of these questions was extensively surveyed by Horgan and Knowles [11] in a work periodically updated by Horgan [9,10]. Moreover, the books by Ames and Straughan [1], Flavin and Rionero [6] and Antontsev et al. [2] are devoted to such matters. The energy method is widely used to study the spatial behavior of solutions of partial differential systems.In this note we investigate the spatial behavior of a linear equation of fourth order which is encountered in several frameworks when we take into account dispersive effects.

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“…A number of spatial decay studies for problems involving various systems of differential equations have appeared in the literatures, e.g., for a survey of SaintVenant type spatial decay results see Hogran and Knowles [6] and Horgan [4,5], and for a decay estimates for the Navier-Stokes equations see Ames and Payne [1], and Horgan and Wheeler [7], and for other type spatial decay results see Quintailla [9] and Ames and Straughan [3]. More recently, Song [10] established exponential decay bounds for a problem in steady magnetohydrodynamical pipe flow.…”

Section: Introductionmentioning

confidence: 99%