Analytical solution for a vibrating rigid sphere with an elastic shell in an infinite linear elastic medium

Klaseboer, Evert; Sun, Qiang

doi:10.1016/j.ijsolstr.2022.111448

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…In this paper, we addressed the fictitious frequency issue for sound-wave phenomena described by a scalar Helmholtz equation. However, such issues also appear in vector wave problems, for example, electromagnetic scattering, which in essence, can be considered as three coupled scalar Helmholtz equations-one for each Cartesian component of the electric field [30][31][32][33][34][35] and possibly even for elastic waves [36]. Our framework demonstrated in this paper can also eliminate the non-unique or non-physical solutions at fictitious frequencies in vector wave problems.…”

Section: Discussionmentioning

confidence: 94%

Non-Singular Burton–Miller Boundary Element Method for Acoustics

Sun

Klaseboer

2023

Fluids

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The problem of non-unique solutions at fictitious frequencies that can appear in the boundary element method for external acoustic phenomena described by the Helmholtz equation is studied. We propose a method to fully desingularise in an analytical way the otherwise hyper-singular Burton–Miller framework, where the original boundary element method and its normal derivative are combined. The method considerably simplifies the use of higher-order elements, for example, quadratic curved surface elements. The concept is validated using the example of scattering on a rigid sphere and a rigid cube, and its robustness and effectiveness for external sound-wave problems are confirmed.

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Section: Discussionmentioning

confidence: 94%

Non-Singular Burton–Miller Boundary Element Method for Acoustics

Sun

Klaseboer

2023

Fluids

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“…The above framework was used recently to find an analytical solution for a vibrating rigid sphere (i.e. moving periodically up and down in an infinite elastic material) [24] and for the same sphere but surrounded by an additional elastic shell [39].…”

Section: Other Physical Systems With Helmholtz Equationsmentioning

confidence: 99%

Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems

Klaseboer¹,

Sun²

2022

Commun. Theor. Phys.

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The famous scientist Hermann von Helmholtz was born 200 years ago. Many complex physical wave phenomena in engineering can effectively be described using one or a set of equations named after him: the Helmholtz equation. Although this has been known for a long time from a theoretical point of view, the actual numerical implementation has often been hindered by divergence free and/or curl free constraints. There is further a need for a numerical method that is accurate, reliable and takes into account radiation conditions at infinity. The classical boundary element method (BEM) satisfies the last condition, yet one has to deal with singularities in the implementation. We review here how a recently developed singularity-free three-dimensional (3D) boundary element framework with superior accuracy can be used to tackle such problems only using one or a few Helmholtz equations with higher order (quadratic) elements which can tackle complex curved shapes. Examples are given for acoustics (a Helmholtz resonator among others) and electromagnetic scattering.

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Waves generated by a vibrating rigid sphere with an elastic shell submerged in a fluid

Sun

Klaseboer

2023

The Journal of the Acoustical Society of America

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An analytical solution for the sound and elastic waves generated by a rigid sphere with a shell made of elastic material submerged in an infinite fluid is introduced. The sphere oscillates up and down at a fixed frequency and generates elastic waves (both longitudinal and transverse) in the shell, which are then transmitted to the fluid. The effects of the acoustic boundary layer are included (thus, no implicit arbitrary “slip” on the surface as in the usual fluid acoustic model is present). An example of a 1 mm radius sphere with an elastic shell is analyzed in detail for several conditions to understand the physical phenomena involved in such a system.

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Analytical solution for a vibrating rigid sphere with an elastic shell in an infinite linear elastic medium

Cited by 3 publications

References 15 publications

Non-Singular Burton–Miller Boundary Element Method for Acoustics

Non-Singular Burton–Miller Boundary Element Method for Acoustics

Helmholtz equation and non-singular boundary elements applied to multi-disciplinary physical problems

Waves generated by a vibrating rigid sphere with an elastic shell submerged in a fluid

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