The influence of boundary conditions on dispersion in an elastic plate

Lutianov, Michael; Rogerson, G. A.

doi:10.1016/j.mechrescom.2009.11.008

Cited by 6 publications

(1 citation statement)

References 20 publications

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“…Recalling that along this path the pre-stretch and the electric displacement field are independent, the dependency of the dispersion relation on a few representative values of the pre-stretch λ is also examined. Of special interest is the identification and evaluation of the fundamental modes, i.e., those modes having finite velocity in the limit of long waves (e.g., Lutianov and Rogerson, 2010).…”

Section: Analysis Of the Dispersion Relationmentioning

confidence: 99%

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

Gal¹,

Gei²,

deBotton³

2012

International Journal of Non-Linear Mechanics

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ABSTRACT. The propagation of waves in soft dielectric elastomer layers is investigated. To this end incremental motions superimposed on homogeneous finite deformations induced by bias electric fields and pre-stretch are determined. First we examine the case of mechanically traction-free layer, which is an extension of the Rayleigh-Lamb problem in the purely elastic case. Two other loading configurations are accounted for too. Subsequently, numerical examples for the dispersion relations are evaluated for a dielectric solid governed by an augmented neo-Hookean strain energy. It is found that the the phase speeds and frequencies strongly depend on the electric excitation and pre-stretch.These findings lend themselves at the possibility of controlling the propagation velocity as well as filtering particular frequencies with suitable choices of the electric bias field.

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Section: Analysis Of the Dispersion Relationmentioning

confidence: 99%

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

Gal¹,

Gei²,

deBotton³

2012

International Journal of Non-Linear Mechanics

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Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear

Erbaş,

Itskov,

Kaplunov

et al. 2024

Z. Angew. Math. Phys.

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A general asymptotic approach involving multimode long-wave approximations is illustrated by a 2D time-harmonic scalar problem for the dynamic antiplane shear of a viscoelastic coating. For the first time, a 1D equation of motion with the coefficients depending on frequency parameters is derived. The associated dispersion relation also seems to be a fresh development approximating its exact counterpart near the vicinities of all the cut-off frequencies. As might be expected, the developed formulation is not valid for short wavelength patterns. At the same time, as it is shown for a $$\delta $$ δ -type loading, it proves to be robust for various scenarios dominated by long-wave response.

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Mechanical analysis on extensional and flexural deformations of a thermo-piezoelectric crystal beam with rectangular cross section

Jin

2016

European Journal of Mechanics - A/Solids

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The influence of boundary conditions on dispersion in an elastic plate

Cited by 6 publications

References 20 publications

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

The Rayleigh–Lamb wave propagation in dielectric elastomer layers subjected to large deformations

Multimode long-wave approximation for a viscoelastic coating subject to antiplane shear

Mechanical analysis on extensional and flexural deformations of a thermo-piezoelectric crystal beam with rectangular cross section

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