Forced Vibration of a Prestretched Two-Layer Slab on a Rigid Foundation

Akbarov, S. D.; Zamanov, A. D.; Suleimanov, T. R.

doi:10.1007/s11029-005-0050-8

Cited by 14 publications

(9 citation statements)

References 11 publications

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“…A systematic analysis of the obtained results was made in a series of monographs [1][2][3]. Reviews of the results obtained before 2002 was made in the paper [4].The later researches in the related field were made in the papers [5][6][7][8][9][10][11][12][13][14][15][16][17] and in many others. It follows from the analysis of the foregoing works and those listed therein that almost all of these investigations were made within the framework of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies (TLTEWISB).…”

Section: Introductionmentioning

confidence: 99%

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

Akbarov

Yildiz

Eröz

2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper, the FEM modelling of the time-harmonic dynamical stress field problem for the pre-stressed plate-strip with finite length resting on a rigid foundation is developed. The mathematical formulation of the considered problem is made by the use of the equations and relations of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stressed Bodies. The proposed modelling is tested on the concrete problems as an example. The numerical results testing the validity of the developed FEM modelling are presented. Moreover, the numerical results attained for the various values of the problem parameters are also presented.

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Section: Introductionmentioning

confidence: 99%

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

Akbarov

Yildiz

Eröz

2011

Applied Mathematical Modelling

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“…Because of the above discussions in [4,15] the investigations carried out in the references [3,6] were developed for systems comprising an infinite bilayered slab and a rigid foundation. It was assumed that the layers of the slab are finite and prestrained (stretched) radially.…”

Section: Time-harmonic Stress-distribution (Frequency-response) Problmentioning

confidence: 99%

“…In [4], it was assumed that e ³ 1, C C 2 were carried out in [15]. Similar investigations for a bilayered slab resting on a rigid foundation in the case where the elasticity relations of the layer are described by the Murnaghan potential were performed using the assumptions and notation from [2].…”

Section: Time-harmonic Stress-distribution (Frequency-response) Problmentioning

confidence: 99%

“…In [58] the investigations carried out in [4,15] were developed for a many-layer slab. It was assumed that the thicknesses of the layers in the natural state are h h 1 2 , ,…, h N (Fig.…”

Section: Time-harmonic Stress-distribution (Frequency-response) Problmentioning

confidence: 99%

“…3). The problem formulation given in [4,15] was generalized to a many-layer slab, and, in this case, Eqs. …”

Section: Time-harmonic Stress-distribution (Frequency-response) Problmentioning

confidence: 99%

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Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review)

Akbarov

2007

Int Appl Mech

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Recent investigations of dynamic problems for bodies with initial stresses are reviewed. These are investigations carried out over the last six years using the piecewise-homogeneous body model and the three-dimensional linearized theory of elastic waves in initially stressed bodies. Emphasis is on the investigations performed by the author and his students. The research studies on the wave propagation and dynamic time-harmonic stress-state problems are reviewed separately. The areas for further investigations are pointed out Keywords: composite, initial stress, residual stress, wave dispersion, layered material, fibrous material, time-harmonic stress field, Lamb's problem 1. Introduction. Elastodynamic problems arise in almost all areas of natural sciences and engineering. As time elapses, these problems increasingly attract the attention from various fundamental and applied areas of science. The intensive development of some fields of the dynamics of deformable bodies was stimulated by the engineering requirements of the key industries. The study of nonlinear elastodynamic problems became urgent in the second half of the 20th century. In this connection, the general nonlinear theory of elastic waves and its various simplified modifications oriented toward problems of natural science and engineering were intensively developed during this time. Many investigations were conducted in this field and the generalized monographs [22,23,42] were published.An interesting and urgent issue, which also applies to the nonlinear dynamic effects in an elastic medium, is elastodynamic problems for initially stressed bodies. It should be noted that initial stresses occur in structural elements during their manufacture and assembly, in the Earth's crust under the action of geostatic and geodynamic forces, in composite materials, etc. Therefore, results of investigations of elastodynamic problems for initially stressed bodies have a wide range of applications.By the theory of elastodynamics for initially stressed bodies is currently meant the linearized theory of elastodynamics for initially stressed bodies constructed using the linearization principle from the general nonlinear theory of elasticity or its simplified modifications.With certain limitations, the linearized equations make it possible to investigate all kinds of dynamic problems for initially stressed bodies. Here it is necessary to distinguish the so-called approximate and exact approaches. The approximate approaches are based on the Bernoulli, Kirchhoff-Love, and Timoshenko hypotheses and other methods of reducing three-dimensional (two-dimensional) problems to two-dimensional (one-dimensional) ones. It is evident that the approximate approaches simplify the mathematical solution procedure. In many cases, however, the results obtained by employing these approaches may be unacceptable in the qualitative and quantitative sense. For example, the applied theories of rods, plates, and shells describe only few propagating waves (modes). Moreover, these approaches fail to d...

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Forced Vibration of Pre-stressed Layered Bodies

Akbarov

2015

Dynamics of Pre-Strained Bi-Material Elastic Systems

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Forced Vibration of a Prestretched Two-Layer Slab on a Rigid Foundation

Cited by 14 publications

References 11 publications

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

FEM modelling of the time-harmonic dynamical stress field problem for a pre-stressed plate-strip resting on a rigid foundation

Recent investigations on dynamic problems for an elastic body with initial (residual) stresses (review)

Forced Vibration of Pre-stressed Layered Bodies

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