On Temporal Behaviour of Solutions in Thermoelasticity of Porous Micropolar Bodies

Marín, Marín; Florea, Olivia

doi:10.2478/auom-2014-0014

Cited by 40 publications

(34 citation statements)

References 10 publications

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“…In [15] and [16] are considered systems described by evolution families with exponential growth on the real line. It can also be mentioned the results obtained by M. Marin and O. Florea in [10] as well as K. Sharma and M. Marin in [17].…”

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confidence: 75%

Nonuniform exponential stability for evolution families on the real line

Morariu

Preda

2015

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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The purpose of the present paper is to investigate the problem of nonuniform exponential stability of evolution families on the real line using the input-output technique known in the literature as the Perron method for the study of exponential stability. In this manuscript we describe an evolution family on the real line and we present sufficient conditions for the nonuniform exponential stability of an evolution family on the real line that does not have exponential growth. In 1974 M.G. Krein and J.L. Daleckij in [5, Theorem 4.1, p. 81] shows that if A ∈ B(X) then σ(A) ∩ iR = ∅ if and only if the differential equatioṅ x(t) = Ax(t) + f (t) has an unique solution x ∈ C, for all f ∈ C, where C represents the Banach space of the continuous and bounded functions on R and σ(A) represent the spectrum of the operator A.

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confidence: 75%

Nonuniform exponential stability for evolution families on the real line

Morariu

Preda

2015

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…Basic results regarding these generalized theories of continuous bodies can be found in studies [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 98%

An approach of a heat-flux dependent theory for micropolar porous media

Marín

2015

Meccanica

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This study is dedicated to a micropolar porous body, including voidage time derivative among the independent constitutive variables. We formulate a heat-flux theory in this context taking into account a new set of state variables that includes the heat-flux vector and an evolution equation for it. The mixed initial boundary value problems have the specific feature that the governing system of equations consists of hyperbolic field equations only. Consistency of the theory is supported by a result of uniqueness.

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“…We assume that material properties of the modified FGM axial bar model vary in the radial direction according to the powerlaw distribution. Marin et al [29][30][31] have investigated different kinds of elasticity problem considering dipolar and micropolar bodies. Tornabene et al [32] studied free vibrations of free-form doubly curved shells made of FGMs using higher order equivalent single-layer theories.…”

Section: Introductionmentioning

confidence: 99%

Free vibration and vibrational displacements analysis of thick elastically supported laminated curved panels with power-law distribution functionally graded layers and finite length via 2D GDQ method

Tahouneh

Naei

2015

Jnl of Sandwich Structures & Materials

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This paper deals with free vibration and vibrational displacements analysis of thick laminated curved panels with finite length resting on two-parameter elastic foundations based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including free, simply supported and clamped at the curved edges. The material properties vary continuously through the layers' thickness according to a three-parameter power-low distribution. It is assumed that the inner surfaces of the functionally graded sheets are metal rich, while the outer surfaces of the layers can be metal rich, ceramic rich or made of a mixture of two constituents. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated functionally graded panels are investigated. The obtained results show that the outer functionally Downloaded from graded material layers have significant effect on the vibration behavior of cylindrical panels. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated curved panels.

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On Temporal Behaviour of Solutions in Thermoelasticity of Porous Micropolar Bodies

Cited by 40 publications

References 10 publications

Nonuniform exponential stability for evolution families on the real line

Nonuniform exponential stability for evolution families on the real line

An approach of a heat-flux dependent theory for micropolar porous media

Free vibration and vibrational displacements analysis of thick elastically supported laminated curved panels with power-law distribution functionally graded layers and finite length via 2D GDQ method

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