Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
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David Natroshvili
Abstract
Three-dimensional fluid-solid interaction problems with regard for thermal stresses are considered. An elastic structure is assumed to be a bounded homogeneous isotropic body occupying a domain 
, where the thermoelastic four dimensional field is defined, while in the unbounded exterior domain 
there is defined the scalar (acoustic pressure) field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface ∂Ω±. We show that uniqueness of solutions strongly depends on the geometry of the boundary ∂Ω±. In particular, we prove that for the corresponding homogeneous transmission problem for a ball there exist infinitely many exceptional values of the oscillation parameter (Jones eigenfrequencies). The corresponding eigenvectors (Jones modes) are written explicitly. On the other hand, we show that if the boundary surface ∂Ω± contains two flat, non-parallel sub-manifolds then there are no Jones eigenfrequencies for such domains.
© Heldermann Verlag
Articles in the same Issue
- Quadric Hypersurfaces Containing a Projectively Normal Curve
- Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations
- Some Approximation Properties for Modified Baskakov Type Operators
- On a Boundary Value Problem for 𝑛-th Order Linear Functional Differential Systems
- Functional Differential Inequalities with Unbounded Delay
- On Absolutely Negligible Sets in Uncountable Solvable Groups
- Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium
- Semi-Slant Submanifolds of a Locally Product Manifold
- Boundary Regularity for Capillary Surfaces
- Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
- Arcwise Connected Continua and Whitney Maps
- On the Fourier Multipliers of the Space 𝐿𝑝
- Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
- On the Strong Differentiation of Multiple Integrals along Different Frames
- On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
- Mapping Properties of Integral Operators of Levy Type
Articles in the same Issue
- Quadric Hypersurfaces Containing a Projectively Normal Curve
- Gelfand Pairs and Generalized d'Alembert's and Cauchy's Functional Equations
- Some Approximation Properties for Modified Baskakov Type Operators
- On a Boundary Value Problem for 𝑛-th Order Linear Functional Differential Systems
- Functional Differential Inequalities with Unbounded Delay
- On Absolutely Negligible Sets in Uncountable Solvable Groups
- Disturbance Due to a Time Harmonic Source in Orthotropic Micropolar Viscoelastic Medium
- Semi-Slant Submanifolds of a Locally Product Manifold
- Boundary Regularity for Capillary Surfaces
- Boundedness for Multilinear Singular Integral Operators on Some Hardy and Herz Type Spaces
- Arcwise Connected Continua and Whitney Maps
- On the Fourier Multipliers of the Space 𝐿𝑝
- Some Remarks Concerning Jones Eigenfrequencies and Jones Modes
- On the Strong Differentiation of Multiple Integrals along Different Frames
- On the Asymptotic Behaviour of Solutions of Third Order Delay Differential Equations
- Mapping Properties of Integral Operators of Levy Type
