Localization of eigenforms and limit transformations in problems of the stability of rectangular plates

Баничук, Н. В.; Barsuk, Alexander

doi:10.1016/j.jappmathmech.2008.04.005

Cited by 4 publications

(2 citation statements)

References 1 publication

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“…One of the latest developments in the field has been the localized bending waves in an elastic orthotropic plate; by Mkrtchyan [3] in (2003).The analogy between localized vibrations of plates and plate localized nonstability was established in [4]. Further investigations on the late localized non-stability problems were done, for example [5]- [7]. In the present paper the mathematical model and differential equations is presented.…”

Section: Introductionmentioning

confidence: 99%

Localized buckling of the semi-infinite isotropic plate near elastically fastened edge.

Sharifian¹

2012

Mechanics - Proceedings of National Academy of Sciences of Armenia

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Ռեզա Շարիֆիան Կիսանվերջ իզոտրոպ սալի լոկալիզացված անկայունությունը առաձգականորեն ամրակցված եզրի մոտակայքում Դիտարկված է կիսանվերջ սալ-շերտի լոկալիզացված անկայունությունը, երբ երկու կիսանվերջ ազատ հենված եզրերում կիրառված է հավասարաչափ բաշխված բեռ, իսկ վերջավոր եզրը առաձգականորեն ամրակցված է: Ստացված է խնդրի բնութագրիչ հավասարումը և անալիտիկորեն դուրս են բերված լոկալիզացված անկայունության գոյության պայմանները: Կրիտիկական բեռի համար ստացված են թվային արժեքներ կախված սալի և հենարանի առաձգական գործակիցներից. Реза Шарифиан Локализованная потеря устойчивости полубесконечной изотропной пластинки в окрестности упруго-опертого края Рассмотрена задача о локализованной потере устойчивости полубесконечной пластинки-полосы, нагруженной по полубеслонечным шарнирно опертым краям и упруго опертой по конечному краю. Выведено характеристическое уравнение задачи и аналитически установлены условия существования локализованной неустойчивости. Получены также численные решения для критической нагрузки в зависимости от упругих характеристик пластинки и опоры. Localized buckling of a semi-infinite isotropic plate near elastically fastened edge has been investigated. Mathematical model is of structure is provided and characteristic equation of the problem is derived. The existence conditions of localized buckling are derived analytically. For the cases when localized buckling exists numerical solutions and plots for the critical loads are provided.

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Section: Introductionmentioning

confidence: 99%

Localized buckling of the semi-infinite isotropic plate near elastically fastened edge.

Sharifian¹

2012

Mechanics - Proceedings of National Academy of Sciences of Armenia

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“…So the free edges, even moved far to infinity, affect the critical load and consequently the global state of the plate. It has been found that the maximum deflection occurs in the vicinity of free edges in the buckling problem described by Ishlinskii [2][3][4][5]. This makes the shape of buckling in Ishlinskii type problems very specific that the notion of "localized instability" or "localized buckling" can be used even though it is considered that the plates have finite length.…”

Section: Introductionmentioning

confidence: 99%

Stability of a rectangular plate axially compressed on its two opposite free edges

Sharifian

Belubekyan

2012

Z Angew Math Mech

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The stability of a rectangular plate under two different compressive loading scenarios applied to the free edges of the plate has been investigated. It is assumed that under the applied load the edges have translational and rotational degrees of freedom. In the first case, a conservative external force, that is assumed to have a fixed direction with respect to the deforming body, is applied while in the second case the load is directed to be tangential to the deflected middle surface, the follower force. It is found that for a sufficiently narrow plate the buckling is localized in the neighborhood of free edges as the conservative load is applied. A similar phenomenon is known for the case when a plate is uniformly compressed along hinged edges. In the case of a follower force, the static formulation of the problem leads to the conclusion that localized buckling does not exist. However, depending on the parameters of the problem, the usual (global) buckling is predicted.

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On the dynamic instability of a rectangular plate with one free edge

Gevorgyan

Sahakyan

2018

J. Phys.: Conf. Ser.

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Localization of eigenforms and limit transformations in problems of the stability of rectangular plates

Cited by 4 publications

References 1 publication

Localized buckling of the semi-infinite isotropic plate near elastically fastened edge.

Localized buckling of the semi-infinite isotropic plate near elastically fastened edge.

Stability of a rectangular plate axially compressed on its two opposite free edges

On the dynamic instability of a rectangular plate with one free edge

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