The cantilever beam under tension, bending or flexure at infinity

Gregory, Ruth; Gladwell, I.

doi:10.1007/bf00042208

Cited by 59 publications

(51 citation statements)

References 14 publications

(40 reference statements)

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“…W0 F. In this case, the displacements appearing in (18)-(21) are zero and the tractions at xl = 0 have been calculated numerically by Gregory and Gladwell [6]. The necessary weighted integrals of these tractions were calculated in [6] and are tabulated there and also by Gregory and Wan [7], p. 44. In terms of the notation* used in [7],…”

Section: (:I)mentioning

confidence: 99%

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Boundary conditions at the edge of a thin or thick plate bonded to an elastic support

Gregory

Wan

1994

J Elasticity

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At the clamped edge of a thin plate, the interior transverse deflection W(Xl, x2) of the mid-plane x3 = 0 is required to satisfy the boundary conditions w = Ow/On = 0. But suppose that the plate is not held fixed at the edge but is supported by being bonded to another elastic body; what now are the boundary conditions which should be applied to the interior solution in the plate? For the case in which the plate and its support are in two-dimensional plane strain, we show that the correct boundary conditions for w must always have the formwith exponentially small error as L/h ~ oo, where 2h is the plate thickness and L is the length scale of w in the xl-direction. The four coefficients W s, W E, 0 B, 0 F are computable constants which depend upon the geometry of the support and the elastic properties of the support and the plate, but are independent of the length of the plate and the loading applied to it. The leading terms in these boundary conditions as L/h ~ oo (with all elastic moduli remainingfixed) are the same as those for a thinplate with a clamped edge. However by obtaining asymptotic formulae and general inequalities for O s, W F, we prove that these constants take large values when the support is 'soft' and so may still have a strong influence even when h/L is small. The coefficient W is also shown to become large as the size of the support becomes large but this effect is unlikely to be significant except for very thick plates. When h/L is small, the first order corrected boundary conditions are w=O~ dw 4oB h d2w dxl 3(i :u--) ~Xl 2 ~'-O' which correspond to a hinged edge with a restoring couple proportional to the angular deflection of the plate at the edge.

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Section: (:I)mentioning

confidence: 99%

“…When #/#~ is small, ®B and W E approach their 'rigid support' limits so that we then require h --<< 1 (6) L and ~-7…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions at the edge of a thin or thick plate bonded to an elastic support

Gregory

Wan

1994

J Elasticity

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“…In addition, the partition of energy between different modes above the first cutofffrequency was studied. Using the projection method, Gregory and Gladwell [2,3] studied the free edge reflection problern and extended the frequency range investigated by Torvik [1]. In both cases, the first symmetric mode Lamb wave was used as the incident wave.…”

Section: Introductionmentioning

confidence: 99%

Interaction of Lamb Waves with Defects in a Semi-Infinite Plate

Mal

Chang

Gorman

1997

Review of Progress in Quantitative Nondestructive Evaluation

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“…However, at the end of the semi-strip with y=O for the region x f 2q -1, the rows indicated will be divergent [3,4]. For the determining of stresses in the whole region of the end, it is necessery to attract the methods of the generalized summation of rows.…”

Section: Ixl>1mentioning

confidence: 99%

“…We'll consider the semi-strip with the boundary conditions (1), (3).The semi-strip displacements are represented in the form of rows of the eigenfunctions…”

Section: Ixl>1mentioning

confidence: 99%