Wave propagation in a transversely isotropic magneto thermo elastic cylindrical panel

Ponnusamy, P.; Selvamani, R.

doi:10.1016/j.euromechsol.2012.11.004

Cited by 20 publications

(5 citation statements)

References 28 publications

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“…is used in Refs. [16,17,20]. Other more significant variations of the above forms that one might better refer to as "Buchwald-type" representations are ubiquitous in the literature (see, for example, Ref.…”

Section: Equations Of Motionmentioning

confidence: 99%

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Solving the Navier-Lame Equation in Cylindrical Coordinates Using the Buchwald Representation: Some Parametric Solutions with Applications

Sakhr¹,

Chronik²

2017

Preprint

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Using a separable Buchwald representation in cylindrical coordinates, we show how under certain conditions the coupled equations of motion governing the Buchwald potentials can be decoupled and then solved using well-known techniques from the theory of PDEs. Under these conditions, we then construct three parametrized families of particular solutions to the Navier-Lamé equation in cylindrical coordinates. In this paper, we specifically construct solutions having 2π-periodic angular parts. These particular solutions can be directly applied to a fundamental set of linear elastic boundary value problems in cylindrical coordinates and are especially suited to problems involving one or more physical parameters. As an illustrative example, we consider the problem of determining the response of a solid elastic cylinder subjected to a time-harmonic surface pressure that varies sinusoidally along its axis, and we demonstrate how the obtained parametric solutions can be used to efficiently construct an exact solution to this problem. We also briefly consider applications to some related forced-relaxation type problems.

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Section: Equations Of Motionmentioning

confidence: 99%

“…The Buchwald representation is also applicable to problems involving isotropic media [13,14]. Application of the Buchwald representation to such problems is however rare [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Solving the Navier-Lame Equation in Cylindrical Coordinates Using the Buchwald Representation: Some Parametric Solutions with Applications

Sakhr¹,

Chronik²

2017

Preprint

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“…Recently, Ponnusamy and Selvamani [21,22] have studied respectively, the three dimensional wave propagation of transversely isotropic magneto thermo elastic and generalized thermo elastic cylindrical panel in the context of the linear theory of thermo elasticity.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a transversely isotropic magneto-electro-elastic solid bar immersed in an inviscid fluid

Selvamani

Ponnusamy²

2016

Journal of the Egyptian Mathematical Society

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Wave propagation in a transversely isotropic magneto-electro-elastic solid bar immersed in an inviscid fluid is discussed within the frame work of linearized three dimensional theory of elasticity. Three displacement potential functions are introduced to uncouple the equations of motion, electric and magnetic induction. The frequency equations that include the interaction between the solid bar and fluid are obtained by the perfect slip boundary conditions using the Bessel functions. The numerical calculations are carried out for the non-dimensional frequency, phase velocity and attenuation coefficient by fixing wave number and are plotted as the dispersion curves. The results reveal that the proposed method is very effective and simple and can be applied to other bar of different cross section by using proper geometric relation.

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“…[5][6][7] and references therein). The Buchwald representation is also applicable to problems involving isotropic media [8,9], but its application to such problems is relatively rare [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Constructing Separable Non-$2π$-Periodic Solutions to the Navier-Lamé Equation in Cylindrical Coordinates Using the Buchwald Representation: Theory and Applications

Sakhr,

Chronik

2019

Preprint

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In a previous paper [Adv. Appl. Math. Mech. 10 (2018), pp. 1025-1056], we used the Buchwald representation to construct several families of separable cylindrical solutions to the Navier-Lamé equation; these solutions had the property of being 2π-periodic in the circumferential coordinate. In this paper, we extend the analysis and obtain the complementary set of separable solutions whose circumferential parts are elementary 2π-aperiodic functions. Collectively, we construct eighteen distinct families of separable solutions; in each case, the circumferential part of the solution is one of three elementary 2π-aperiodic functions. These solutions are useful for solving a wide variety of dynamical problems that involve cylindrical geometries and for which 2π-periodicity in the angular coordinate is incompatible with the given boundary conditions. As illustrative examples, we show how the obtained solutions can be used to solve certain forced-vibration problems involving open cylindrical shells and open solid cylinders where (by virtue of the boundary conditions) 2πperiodicity in the angular coordinate is inappropriate. As an addendum to our prior work, we also include an illustrative example of a certain type of asymmetric problem that can be solved using the particular 2π-periodic subsolutions that ensue when there is no explicit dependence on the circumferential coordinate.

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Wave propagation in a transversely isotropic magneto thermo elastic cylindrical panel

Cited by 20 publications

References 28 publications

Solving the Navier-Lame Equation in Cylindrical Coordinates Using the Buchwald Representation: Some Parametric Solutions with Applications

Solving the Navier-Lame Equation in Cylindrical Coordinates Using the Buchwald Representation: Some Parametric Solutions with Applications

Wave propagation in a transversely isotropic magneto-electro-elastic solid bar immersed in an inviscid fluid

Constructing Separable Non-$2π$-Periodic Solutions to the Navier-Lamé Equation in Cylindrical Coordinates Using the Buchwald Representation: Theory and Applications

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