Longitudinal Wave Propagation in a Generalized Thermoelastic Cylinder

Erbay, S.; Uhubi, E. S.

doi:10.1080/01495738608961904

Cited by 97 publications

(39 citation statements)

References 6 publications

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“…Taking the Laplace transform for the both sides of the Eqs. (14)(15)(16)(17)(18)(19), this is defined as follows:…”

Section: The Governing Equationsmentioning

confidence: 99%

“…A method for solving coupled thermoelastic problems by using the state-space approach was developed by Bahar and Hetnarski [5][6][7]. Erbay and Suhubi [19] studied longitudinal wave propagation in an infinite circular cylinder, which is assumed to be made of the generalized thermoelastic material, and thereby obtained the dispersion relation when the surface temperature of the cylinder was kept constant. Generalized thermoelasticity problems for an infinite body with a circular cylindrical hole and for an infinite solid cylinder were solved respectively by Furukawa et al [21].…”

Section: Introductionmentioning

confidence: 99%

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State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Youssef

Al-Harby

2007

Arch Appl Mech

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In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470-475 2005a, IMA J Appl Math, pp 1-8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.

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“…Taking the Laplace transform for the both sides of the Eqs. (14)(15)(16)(17)(18)(19), this is defined as follows:…”

Section: The Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Youssef

Al-Harby

2007

Arch Appl Mech

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“…Erbay and Suhubi [12] studied longitudinal wave propagation in an infinite circular cylinder, which is assumed to be made of the generalized thermoelastic material, and thereby obtained the dispersion relation when the surface temperature of the cylinder is kept constant. GTE problems for an infinite body with a circular cylindrical hole and for an infinite solid cylinder were solved, respectively, by Furukawa et al [13,14].…”

mentioning

confidence: 99%

Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

Youssef

2006

Arch Appl Mech

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This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.

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“…Вопросы распространения гармонических волн в цилиндрических термоупругих телах изучались многими авторами [1][2][3][4][5][6][7][8][9][10]. Распространение про-дольных термоупругих волн обсуждалось в рабо-тах [1; 2].…”

Section: Introductionunclassified

Equations of Dynamics for Prestressed Thermoelastic Cylinder

Sheydakov¹,

Belyankova²,

Sheydakov³

et al. 2018

Sc. South Russ.

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Аннотация. В рамках теории наложения малых деформаций на конечную проведена последователь-ная линеаризация определяющих соотношений нелинейной механики термоупругой сплошной среды. В процессе преобразований была использована материальная система координат Лагранжа, связанная с естественной конфигурацией тела. Предполагалось, что начальное напряженное состояние термо-упругого полуограниченного тела обусловлено как воздействием механических усилий, так и влиянием температуры (преднагрев). В линеаризованных тензорах напряжений Пиолы и Кирхгофа, участвующих в уравнениях движения и граничных условиях, удержаны все члены, которые содержат высшие степени начальной деформации и квадраты температуры. Выражения, определяющие линеаризованный закон состояния преднапряженной среды, а также линеаризованные уравнения, описывающие движение тер-моупругой среды при больших начальных деформациях, представлены в тензорном виде с последу-ющим переходом к компонентному представлению всех соотношений в цилиндрической ортогональ-ной системе координат. Для конкретной формы термоупругого потенциала при однородной начальной деформации приведены окончательные выражения, определяющие линеаризованный закон состояния преднапряженной среды, а также линеаризованные уравнения, описывающие движение термоупругой среды при больших начальных деформациях. Полученные представления позволяют эффективно ис-следовать влияние начальных напряжений и температуры на характеристики динамического процесса в термоупругом цилиндре.Ключевые слова: преднапряженный термоупругий цилиндр, начальная деформация, начальные напряжения, предварительный нагрев, термодинамический потенциал, термоупругие волны. Within the theory of small deformations superposed on a finite one, a step-by-step linearization of the constitutive relations for the nonlinear mechanics of a thermoelastic medium is carried out using a cylindrical coordinate system. In the transformations, the Lagrangian material coordinate system, connected with the natural configuration of the body, is used. It is assumed that the initial stress state of a thermoelastic semibounded body is both due to the action of mechanical forces and the effect of temperature (preheating). In the linearized Piola and Kirchhoff stress tensors involved in the equations of motion and boundary conditions, all terms that contain higher degrees of initial deformation and squares of temperature are retained. The expressions that determine the linearized constitutive law of a prestressed medium, as well as the linearized equations describing the motion of a thermoelastic medium with large initial deformations, are presented in the tensor form with the subsequent transition to the component representation of all relations in a cylindrical orthogonal coordinate system. For the specific form of the thermoelastic potential and for homogeneous initial deformation, the final expressions that determine the linearized constitutive law of the prestressed medium are given, as well as the linearized equations describing the motion of the thermoel...

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Longitudinal Wave Propagation in a Generalized Thermoelastic Cylinder

Cited by 97 publications

References 6 publications

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

Problem of generalized thermoelastic infinite medium with cylindrical cavity subjected to a ramp-type heating and loading

Equations of Dynamics for Prestressed Thermoelastic Cylinder

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