Revisiting the Jones Eigenproblem in Fluid-Structure Interaction

Domínguez, Sebastián; Nigam, Nilima; Sun, Jiguang

doi:10.1137/18m1198235

Cited by 5 publications

(6 citation statements)

References 21 publications

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“…Above, δ(•) is Dirac's delta. Using this fundamental solution, it is possible to express any solution to Equation (13) in terms of density functions φ, and λ that correspond to the Cauchy data of the problem, namely, the pressure restricted to Γ and its normal derivative, respectively. This is known as the Kirchhoff representation formula (see e.g., [18,31,32])…”

Section: Time-dependent Transmission Problemmentioning

confidence: 99%

“…However, the straightforward boundary-field method can not circumvent the drawbacks, because the problem is not uniquely solvable when the frequency of the incident wave coincides with what is known as a "Jones frequency". At such a frequencies, the corresponding homogeneous problem may have traction free solutions (a recent discussion on this can be found in [13]). Moreover, the uniqueness of the solutions to the boundary integral equations may not be guaranteed when the exterior wavenumber coincides with an eigenvalue of the corresponding interior Dirichlet problem (see [14]).…”

Section: Introductionmentioning

confidence: 99%

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Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

Hsiao

Sánchez-Vizuet

2021

Fluids

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In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body that is immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided that an appropriate scaling factor is employed. As usual, based on estimates for solutions in the Laplace-transformed domain, we may obtain properties of corresponding solutions in the time-domain without having to perform the inversion of the Laplace-domain solutions.

show abstract

Section: Time-dependent Transmission Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

Hsiao

Sánchez-Vizuet

2021

Fluids

View full text Add to dashboard Cite

show abstract

“…However, the straightforward boundary-field method can not circumvent the drawbacks, because the problem is not uniquely solvable when the frequency of the incident wave coincides with what is known as a "Jones frequency". At such a frequencies, the corresponding homogeneous problem may have traction free solutions (a recent discussion on this can be found in [10]). Moreover, uniqueness of the solutions to the boundary integral equations may not be guaranteed when the exterior wavenumber coincides with an eigenvalue of the corresponding interior Dirichlet problem (see [20]).…”

Section: Introductionmentioning

confidence: 99%

Time-Dependent Wave-Structure Interaction Revisited: Thermo-piezoelectric Scatterers

Hsiao,

Sánchez-Vizuet

2021

Preprint

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In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided an appropriate scaling factor is employed. As usual, based on estimates for solutions in the Laplace-transformed domain, we may obtain properties of corresponding solutions in the time-domain without having to perform the inversion of the Laplace-domain solutions.

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“…which is the classical Jones eigenvalue problem. The Jones eigenvalue problem arises in studying the fluid-structure interaction [23] and has been extensively in the literature [20,21,29,32]. It is known that under certain conditions of the medium parameters λ, μ, ρ e as well as the domain Ω, there exist Jones eigenvalues [20].…”

mentioning

confidence: 99%

“…The Jones eigenvalue problem arises in studying the fluid-structure interaction [23] and has been extensively in the literature [20,21,29,32]. It is known that under certain conditions of the medium parameters λ, μ, ρ e as well as the domain Ω, there exist Jones eigenvalues [20]. Clearly, Jones eigenvalues to (1.4) are a special subset of the AE transmission eigenvalues to (1.5).…”

mentioning

confidence: 99%

Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications

Diao¹,

Li²,

Liu³

et al. 2022

Preprint

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We are concerned with a coupled-physics spectral problem arising in the coupled propagation of acoustic and elastic waves, which is referred to as the acoustic-elastic transmission eigenvalue problem. There are two major contributions in this work which are new to the literature. First, in a general scenario, we prove the existence of infinitely many acoustic-elastic transmission eigenvalues. Second, we establish a geometric rigidity result of the transmission eigenfunctions by showing that they tend to localize on the boundary of the underlying domain. Moreover, we also consider interesting implications of the obtained results to the effective construction of metamaterials by using bubbly elastic structures and to the inverse problem associated with the fluid-structure interaction.

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Revisiting the Jones Eigenproblem in Fluid-Structure Interaction

Cited by 5 publications

References 21 publications

Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

Time-Dependent Wave-Structure Interaction Revisited: Thermo-Piezoelectric Scatterers

Time-Dependent Wave-Structure Interaction Revisited: Thermo-piezoelectric Scatterers

Spectral properties of an acoustic-elastic transmission eigenvalue problem with applications

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