Comments on a class of orthogonality relations relevant to fluid-structure interaction

Lawrie, Jane B.

doi:10.1007/s11012-011-9471-8

Cited by 23 publications

(20 citation statements)

References 28 publications

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“…0. It is worth noting that singular behavior similar to that displayed in (8) can be modeled by using a multi-term Galerkin approximation involving Gegenbauer polynomials. [17][18][19] Mode-matching methods are, however, simpler to implement, known to conserve power 12 and, for a velocity field with singularity of Oðr À1=3 Þ as r !…”

Section: The Boundary Value Problemmentioning

confidence: 99%

“…The generalized orthogonality relations for this class of problem are well established 7,8,12,13 and are quoted here as a ð a 0 Yðs m ; yÞYðs n ; yÞdy…”

Section: Mode-matching Solutionmentioning

confidence: 99%

“…In recent years mode-matching methods have been devised to deal with more complicated geometries [3][4][5][6] and problems involving propagation in ducts/channels with high order boundary conditions. [7][8][9][10] Heating, ventilation, and air-conditioning (HVAC) ducting systems are a typical application area for mode-matching techniques. Although these methods generally neglect the effects of break-out, they do provide both physical insight into the underlying scattering processes and benchmark solutions for fully numerical approaches.…”

Section: Introductionmentioning

confidence: 99%

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Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides

Nawaz

Lawrie²

2013

The Journal of the Acoustical Society of America

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The scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides is investigated. The flange is assumed to be rigid on one side and soft on the other; this enables a solution to be formulated using mode-matching. It is shown that both the choice of the edge conditions imposed on the plates at the junction and the choice of incident forcing significantly affect the transmission of energy along the duct. In particular, the edge conditions crucially affect the transmission of structure-borne vibration but have little effect on fluid-borne noise. Given the singular nature of the velocity field at the flange tip, particular attention is paid to the validity of the mode-matching method. It is demonstrated that the velocity field can be accurately reconstructed by incorporating the Lanczos filter into the truncated modal expansions. The mode-matching method is thus confirmed as an viable tool for this class of problem.

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Section: The Boundary Value Problemmentioning

confidence: 99%

“…The generalized orthogonality relations for this class of problem are well established 7,8,12,13 and are quoted here as a ð a 0 Yðs m ; yÞYðs n ; yÞdy…”

Section: Mode-matching Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides

Nawaz

Lawrie²

2013

The Journal of the Acoustical Society of America

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“…These class of problems are non-Sturm Liouville type in nature and the associated eigenvalues are not orthogonal. Lawrie (2012) reviewed various characteristics of the eigensystem associated with wave-structure interaction problems satisfying higher order boundary conditions. Nawaz and Lawrie (2013) investigated the scattering of a fluid structure-coupled wave at a flanged junction between two flexible wave guides using mode-matching method.…”

Section: Introductionmentioning

confidence: 99%

Oblique wave diffraction by a flexible floating structure in the presence of a submerged flexible structure

Mohapatra

Sahoo

2014

Geophysical & Astrophysical Fluid Dynamics

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Expansion formulae associated with the interaction of oblique surface gravity waves with a floating flexible plate in the presence of a submerged horizontal flexible structure are derived using Green's integral theorem in water of finite and infinite water depths. The associated Green's functions are derived using the fundamental solution associated with the reduced wave equation. The integral forms of the Green's functions and the velocity potentials are advantageous over the eigenfunction expansion method in situation when the roots of the dispersion relation coalesce.As an application of the expansion formulae, diffraction of oblique waves by a finite floating elastic plate in the presence of a submerged horizontal flexible membrane is investigated in water of finite depth. The accuracy of the numerical computation is demonstrated by analysing the convergence of the complex amplitude of the reflected waves and the energy relation. Effect of the submerged membrane on the diffraction of surface waves is studied by analysing the reflection and transmission coefficients for various parametric values. Further, the derivation of long wave equation under shallow water approximation is derived in a direct manner in the appendix. The concept and methodology can be easily extended to deal with acoustic wave interaction with flexible structures and related problems of mathematical physics and engineering.

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“…The past decade has seen a dramatic change in this situation. Hybrid modematching methods have been devised to deal with more complicated geometries [4]- [9] and the theory underpinning wave propagation in two-dimensional (2D) ducts with high order boundary conditions has been extensively developed [10,11].…”

Section: Introductionmentioning

confidence: 99%

Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular duct

Lawrie

2013

Wave Motion

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An analytic mode-matching method suitable for the solution of problems involving scattering in three-dimensional waveguides with flexible walls is presented. Prerequisite to the development of such methods is knowledge of closed form analytic expressions for the natural fluid-structure coupled waveforms that propagate in each duct section and the corresponding orthogonality relations. In this article recent theory [Lawrie, Proc. R. Soc. A. 465, 2347Soc. A. 465, -2367Soc. A. 465, (2009] is extended to construct the non-separable eigenfunctions for acoustic propagation in a three-dimensional rectangular duct with four flexible walls.For the special case in which the duct cross-section is square, the symmetrical nature of the eigenfunctions enables the eigenmodes for a right-angled, isosceles triangular duct with flexible hypotenuse to be deduced. The partial orthogonality relation together with other important properties of the triangular modes are discussed. A mode-matching solution to the scattering of a fluid-structure coupled wave at the junction of two identical semi-infinite ducts of triangular cross-section is demonstrated for two different sets of "junction" conditions.

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Comments on a class of orthogonality relations relevant to fluid-structure interaction

Abstract: This article presents an overview of the recent literature and summarises the major theoretical developments pertaining to a class of non-Sturm-Liouville orthogonality relations relevant to fluid-structure interaction.

Cited by 23 publications

References 28 publications

Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides

Scattering of a fluid-structure coupled wave at a flanged junction between two flexible waveguides

Oblique wave diffraction by a flexible floating structure in the presence of a submerged flexible structure

Analytic mode-matching for acoustic scattering in three dimensional waveguides with flexible walls: Application to a triangular duct

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