Refined Solution for Dynamic Axisymmetric Electroelasticity Problem for Rigid Bi-morph Plate

Shlyakhin, D. A.

doi:10.1016/j.proeng.2016.06.717

Cited by 2 publications

(4 citation statements)

References 6 publications

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“…As a result, the cylindrical surface of the structure is docked with the additional function t W 1 used only at one point at the height of the section. Paper [13] shows that in case of a bi-morph plate, this assumption results in a slight change in the tense and deformed state and can be used in the study of thin multi-layer structures.…”

Section: Discussionmentioning

confidence: 99%

“…The task is greatly complicated when multi-layer finite dimension systems with a number of properties that qualitatively distinguish them from traditional structures are investigated [7][8][9][10][11][12][13]. In this case, the mathematical model of the initially boundary problem with account of the connection between movement and temperature, consists of a not self-adjoint system of differential equations of thermoelestic movement [14].…”

Section: Introductionmentioning

confidence: 99%

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Non-stationary axially symmetric goal of thermo-elasticity for a fixed rigid circular multi-layer plate

Shlyakhin

2017

MATEC Web Conf.

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Abstract. This paper considers axially symmetric goal of thermoselasticity for a fixed rigid circular multi-layer isotropic plate with nonstationary heat flows on its front faces. The mathematical model is presented in the form of a not self-adjoint system that includes differential motion equations and a linear equation of the thermal-elastic state in a three-dimensional model. A new closed solution in an unconnected setting is built by the method of finite integral transformation. At the same time, a standardization procedure is conducted at each stage of the solution, which allows to implement an appropriate conversion algorithm. The calculated ratios provide an opportunity to perform a qualitative and quantitative analysis of the associated temperature and mechanical fields and also to examine stress-strain behaviour of the multi-layer systems both under the local thermal shock, which is observed, for example, in the interaction with the laser beam and in the case of uneven unsteady surface heating, which is frequent during the operation of protective construction structures.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-stationary axially symmetric goal of thermo-elasticity for a fixed rigid circular multi-layer plate

Shlyakhin

2017

MATEC Web Conf.

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“…Using the algorithmic procedure of the structural algorithm of FIT method [1][2][3][4], we integrate the first quadrature (6) by parts. As a result, we obtain ( 9 ) (10) (11) Taking into account (8), (10), (11), equations (9) and conditions (7) take the form: …”

Section: ( 8 )mentioning

confidence: 99%

“…One of the main conditions that determines the possibility of such an approach is the self-adjointness of the initial-boundary value problem under consideration. At the same time, as a result of taking into consideration the resistance forces, including internal friction, this important property of the mathematical model is lost, and a direct way of constructing an analytical solution is impossible [1][2][3][4][5][6][7][8]. However, the structural algorithm of FIT method developed by the author [9][10] in combination with the frequency independent Voigt hypothesis [11] by introducing viscous drag forces in the solution process made it possible to obtain a new qualitative solution of the corresponding dynamic problems.…”

Section: Introductionmentioning

confidence: 99%

In the consideration of internal friction forces in nonstationary dynamics problems

Senitsky

Elekina

2017

MATEC Web Conf.

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Abstract. In this paper, the original methodology for taking into consideration internal friction forces is given in the example of nonstationary oscillations of a beam with elastically clamped edges. Bearing in mind the experimentally confirmed fact that the forces of internal friction practically do not affect the forms of structural vibrations, they are introduced into the equation of motion after separation of the spatial variable. This decomposition approach of forming a mathematical model in conjunction with the frequency independent Voigt hypothesis, with a known loss factor, made it possible to represent the solution in the form of spectral decomposition. For this purpose, we used the structural algorithm of the finite integral transform (FIT) method with the definition of the transformation kernel in the solution process. In fact, the proposed method is a method of quasinormal coordinates and represents an effective method of solving dynamic problems for mechanical systems in the presence of internal friction forces.

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Refined Solution for Dynamic Axisymmetric Electroelasticity Problem for Rigid Bi-morph Plate

Cited by 2 publications

References 6 publications

Non-stationary axially symmetric goal of thermo-elasticity for a fixed rigid circular multi-layer plate

Non-stationary axially symmetric goal of thermo-elasticity for a fixed rigid circular multi-layer plate

In the consideration of internal friction forces in nonstationary dynamics problems

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