Flexural waves on a pinned semi-infinite thin elastic plate

Evans, D. V.; Porter, Robert

doi:10.1016/j.wavemoti.2007.11.006

Cited by 18 publications

(13 citation statements)

References 11 publications

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“…Note that, in the short-circuit limit ξ → 0, the second term inside the brackets at the left-hand side of (3.23) vanishes. Within this limit, the fifth derivative of the velocity potential in (3.23) is multiplied only by the non-dimensional stiffness β and the resulting boundary-value problem is equivalent to that of a submerged elastic plate without power extraction [22][23][24][25], as expected. Indeed, the complex coefficient α 2 ωξ/(i + ωξ) in (3.23) is a dissipative term which models the extraction of energy from the system by means of the resistive circuits of figure 2.…”

Section: Solution Of the Coupled Systemmentioning

confidence: 99%

Hydroelectromechanical modelling of a piezoelectric wave energy converter

Renzi¹

2016

Proc. R. Soc. A.

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We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

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Section: Solution Of the Coupled Systemmentioning

confidence: 99%

Hydroelectromechanical modelling of a piezoelectric wave energy converter

Renzi¹

2016

Proc. R. Soc. A.

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“…Evans and Porter [165] use Green's function to demonstrate existence of edge waves for a semi-infinite plate within the context of plate theory. Specifically, the authors have shown that plane waves incident on a pinned point on the straight edge of an elastic plate can generate edge waves which radiate energy to infinity along the edge.…”

Section: Related Workmentioning

confidence: 99%

Saint-Venant’s Principle in Dynamics of Structures

Karp

Durban

2011

Applied Mechanics Reviews

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Research studies aiming at examination and formulation of a dynamic analog to SaintVenant's principle (DSVP) are critically reviewed. Article concentrates on isotropic homogeneous linear elastic response over a range of structural geometries including waveguides, with either free or constrained lateral surfaces, half space, wedges and cones. Nearly 140 DSVP related references are covered starting with early ideas by Boley. A special chapter is dedicated to available experimental work on end effects and decay rate in dynamically excited structures. Current thinking on possible versions of DSVP is classified into several categories, one of which, the dynamic equivalence, is compatible with much of known experimental data and has been tacitly applied at various engineering situations. That observation provides inspiring ground for renewed interest in both practical and theoretical aspects of DSVP.

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“…From the numerical point of view, some finite element computations with the help of Perfectly Matched Layers can be found in [11]. Let us also mention the studies concerning the so-called platonic crystals [10,16,40,39,15] (by analogy with photonic, phononic or plasmonic crystals). In these works, the authors investigate the propagation of time harmonic waves in waveguides which consist of rigid pins embedded within an elastic Kirchhoff plate.…”

Section: Introductionmentioning

confidence: 99%

On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

Bourgeois

Chesnel

Fliss

2019

Communications in Mathematical Sciences

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We study the propagation of elastic waves in the time-harmonic regime in a waveguide which is unbounded in one direction and bounded in the two other (transverse) directions. We assume that the waveguide is thin in one of these transverse directions, which leads us to consider a Kirchhoff-Love plate model in a locally perturbed 2D strip. For time harmonic scattering problems in unbounded domains, well-posedness does not hold in a classical setting and it is necessary to prescribe the behaviour of the solution at infinity. This is challenging for the model that we consider and constitutes our main contribution. Two types of boundary conditions are considered: either the strip is simply supported or the strip is clamped. The two boundary conditions are treated with two different methods. For the simply supported problem, the analysis is based on a result of Hilbert basis in the transverse section. For the clamped problem, this property does not hold. Instead we adopt the Kondratiev's approach, based on the use of the Fourier transform in the unbounded direction, together with techniques of weighted Sobolev spaces with detached asymptotics. After introducing radiation conditions, the corresponding scattering problems are shown to be well-posed in the Fredholm sense. We also show that the solutions are the physical (outgoing) solutions in the sense of the limiting absorption principle.

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Flexural waves on a pinned semi-infinite thin elastic plate

Cited by 18 publications

References 11 publications

Hydroelectromechanical modelling of a piezoelectric wave energy converter

Hydroelectromechanical modelling of a piezoelectric wave energy converter

Saint-Venant’s Principle in Dynamics of Structures

On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

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