Moderately large deflection of asymmetrically layered elastic plate

Habip, L. M.

doi:10.1016/0020-7683(67)90070-4

Cited by 7 publications

(6 citation statements)

References 3 publications

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“…The Wi and Vi are functions of frequency and frequencyresponse curves for r.m.s. transverse displacement at mid-span were calculated from equation (42). Results were obtained for the symmetric beams reported on by Kovac, Anderson and Scott [44], and for unsymmetric beams not previously investigated.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Wempner and Baylor [41] also derived equations for the large amplitude motions of elastic sandwich plates with weak cores. Habip [42] used perturbation methods to derive equations for the static deflection of two-layer plates. The first-order terms are Von Karman equations, whereas the second-order terms reflect shear effects.…”

Section: Considerablementioning

confidence: 99%

“…The form of a given by equation (41) is meant to simulate the spatial dependence of the electromagnetic force on the beam. On the assumption that steady-state conditions exist, the response is taken as $X, r) = W(X) T,(f), (42) 3(X, t) = Y(X) T,(r ).…”

Section: Frequency Responsementioning

confidence: 99%

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Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory

Hyer

Anderson

Scott

1976

Journal of Sound and Vibration

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Approximate equations of motion are developed for large amplitude motions of threelayer axially restrained unsymmetrical beams with viscoelastic cores. The external force consists of a constant plus an oscillatory term. The combination of this form of forcing and the large amplitude motions cause the beam to respond at multiples of the forcing frequency. This can lead to difficulties in the complex modulus approach to viscoelasticity. These are overcome here through use of hereditary integrals and their relationships with complex moduli. Theoretical results on the frequency response of clamped, symmetrical beams are compared with earlier experimental work. On the whole, reasonable agreement is found.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Considerablementioning

confidence: 99%

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Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory

Hyer

Anderson

Scott

1976

Journal of Sound and Vibration

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“…Previous attempts (Habip (1967) and Widera (1969)) to obtain an asymptotic theory for the moderately large deflexion of a transversely isotropic plate and an anisotropic plate by assuming partially nonlinear expressions for the E KL are in error.…”

Section: Discussionmentioning

confidence: 99%

“…In this paper, the method of matching asymptotic expansions is used to obtain one such refinement which is believed to be an improvement on several previous results. Previous authors (Habip (1967), Widera (1969) attempted such refinements within the framework of a partially nonlinear theory of elasticity whereas in the present work all terms neglected by these authors have been retained.The forms of the solutions for the displacements and stresses in the interior of the plate are given in equations (3.7) to (3.12) while those for the boundary layer are given in (4.40) to (4.45). On comparing both sets of solutions it will be observed that the order of magnitude of the stresses increases near the edge of the plate.…”

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confidence: 99%

Nonlinear symmetric bending of circular elastic plates

Garfoot

1975

J. Aust. Math. Soc.

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Communicated by V. G. HartIn recent years, there has been considerable interest in the refining of thin plate theories. In this paper, the method of matching asymptotic expansions is used to obtain one such refinement which is believed to be an improvement on several previous results. Previous authors (Habip (1967), Widera (1969) attempted such refinements within the framework of a partially nonlinear theory of elasticity whereas in the present work all terms neglected by these authors have been retained.The forms of the solutions for the displacements and stresses in the interior of the plate are given in equations (3.7) to (3.12) while those for the boundary layer are given in (4.40) to (4.45). On comparing both sets of solutions it will be observed that the order of magnitude of the stresses increases near the edge of the plate. This effect is due to the occurrence of a boundary layer depending on a dimensionless thickness parameter e defined in §1. Schematic diagrams illustrating the change in the order of the stresses appear at the end of the paper.The assumptions made on the magnitude of the deformation are given in §2. Formulation of the problemWe consider a thin isotropic ideally elastic circular plate of radius R o , thickness 2H, with the origin of the Langrangian coordinates at the centre on the middle surface. The plate is initially flat. We shall use cylindrical polar coordinates R, 0, Z. Thusfor the plate.In deformations symmetrical about the origin, the two non-zero displacements are independent of 0 . Thus the material point with coordinates R, 0, Z before the deformation has coordinates R + U(R, Z), 0, Z + W(R, Z) after the defor-481 use, available at https://www.cambridge.org/core/terms. https://doi

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Free and forced nonlinear oscillations of a two-layer composite beam with interface slip

Lenci

Warmiński

2012

Nonlinear Dyn

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Moderately large deflection of asymmetrically layered elastic plate

Cited by 7 publications

References 3 publications

Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory

Non-linear vibrations of three-layer beams with viscoelastic cores I. Theory

Nonlinear symmetric bending of circular elastic plates

Free and forced nonlinear oscillations of a two-layer composite beam with interface slip

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