Problem of Non-Stationary Waves in Viscoelastic Orthotropic Strip Solved Using Analytical Method

Adámek, Vítězslav; Valeš, František; Červ, Jan

doi:10.7712/120115.3518.1309

Cited by 1 publication

(4 citation statements)

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“…Each layer has different height and is modelled as linear viscoelastic with special orthotropic properties. This work is a continuation of authors' previous works [7] and [8] in which analogous wave problems for an orthotropic viscoelastic strip and for a strip with two symmetric orthotropic viscoelastic layers were solved, respectively. The structure of the present work is organise in such a way to emphasise the fundamental steps leading to the derivation of Laplace transforms of displacement components for each layer.…”

Section: Introductionmentioning

confidence: 90%

“…When the problem of a single-layered strip is solved (see [7]), the number of these unknowns reduces to four and they can be quite simply derived from four boundary conditions valid at the strip edges. But in the case of a two-layered strip, we receive eight functions which can be determined based on the boundary conditions formulated at the strip edges and at the layer interface.…”

Section: Solving Proceduresmentioning

confidence: 99%

“…The constants c 0,ij,L and c ij,L are analogous to the phase velocities in an elastic orthotropic medium and they are defined in a similar way as in [7].…”

Section: Equations Of Motionmentioning

confidence: 99%

“…The functions a i,L (!, p) and b i,L (!, p) present in (10)(11) follow from the coefficients of biquadratic characteristic equation of the mentioned system of ODEs and they can be expressed for each layer L analogously as in [7].…”

Section: Solving Proceduresmentioning

confidence: 99%

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Propagation of Non-Stationary Waves in Viscoelastic Strip Composed of Orthotropic Layers

Adámek¹,

Valeš²,

Červ³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The analytical solution for transient waves caused by transverse impact on an infinite layered strip with free-free boundaries is presented in this work. The strip is composed of two horizontal layers of different heights. The materials of both layers are assumed to be linear viscoelastic and orthotropic. The case of special orthotropy is assumed for simplicity. The dissipative behaviour of each layer is modelled by the discrete model of standard linear viscoelastic solid in Zener configuration. The solving procedure used in this work follows the methods applied in previously published works dealing with the problems of a viscoelastic orthotropic strip and the symmetric case of a layered strip. The system of four linear partial integro-differential equations describing the non-stationary state of plane stress in the strip is solved by means of integral transform method. Concretely, the Laplace transform in time domain and the Fourier transform in spatial domain are applied. As a results of this procedure, the final formulas for displacement components in both layers are derived in Laplace domain. These transforms contain eight spectra of Fourier integrals which can be found as the solution of the system of eight complex equations arising from boundary conditions of the problem. When the spectra are known, the resulting formulas for the Laplace transforms of displacement components are obtained.The presented new formulation of non-symmetric problem enables to study the wave phenomena in general two-layered solids of strip-like geometry and it is fundamental for solving a problem with arbitrary number of layers.

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Section: Introductionmentioning

confidence: 90%

Section: Solving Proceduresmentioning

confidence: 99%

“…The constants c 0,ij,L and c ij,L are analogous to the phase velocities in an elastic orthotropic medium and they are defined in a similar way as in [7].…”

Section: Equations Of Motionmentioning

confidence: 99%

Section: Solving Proceduresmentioning

confidence: 99%

See 2 more Smart Citations