Dispersion relations and mode shapes for waves in laminated viscoelastic composites by finite difference methods

Mukherjee, Subrata; Lee, Erastus H.

doi:10.1016/0045-7949(75)90033-4

Cited by 26 publications

(10 citation statements)

References 4 publications

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“…This approach is useful for analyzing steady-state wave fields and comparison with experimental data for finite-sized structures. Another group of meth-ods deals with freely propagating waves possessing complex-valued frequencies, which is relevant for loading conditions of an impulsive nature [45,19,20,48].…”

Section: Introductionmentioning

confidence: 99%

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Krushynska

Kouznetsova

Geers

2016

Journal of the Mechanics and Physics of Solids

131

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Section: Introductionmentioning

confidence: 99%

Visco-elastic effects on wave dispersion in three-phase acoustic metamaterials

Krushynska

Kouznetsova

Geers

2016

Journal of the Mechanics and Physics of Solids

131

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“…Demiray and Eringen [6] developed a two-dimensional lattice dynamics model to study harmonic wave propagation in a fibrous material, in which they assumed that the viscoelastic matrix carries the shear and the fibers carry the tensile forces. Mukherjee and Lee [7,8] used finite difference and variational methods to examine one-dimensional wave propagation in a viscoelastic laminated composite. Sutherland [9] presented some experimental studies on dispersion in fiber reinforced viscoelastic materials.…”

Section: Introductionmentioning

confidence: 99%

“…Dimensionless half cell and its finite element mesh configuration for the fiber reinforced, viscoelastic medium. The dashed curve indicates the matrix-fiber interface.. un = un, eiqa, vm = vm> eiqa, lln = vnf eiqa for the number pairs (m, m') = (I, ll),(2,12),(3,13),(4,14),(5,15), (n, n') = (6,16),(7,17),(8, lg),(9,19),(10,20). (21)Equations (20) guarantee the satisfaction of the first two conditions in equations (15).…”

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confidence: 99%

Harmonic wave propagation in an infinite viscoelastic medium with a periodic array of cylindrical elastic fibers

Scott

Yang

1980

Journal of Sound and Vibration

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The work involves the propagation of plane harmonic waves in an infinite isotropic medium in which a doubly periodic array of cylindrical fibers is embedded. The direction of propagation is perpendicular to the fibers and the matrix material is taken to be viscoelastic in shear, modeled through hereditary integrals. A finite element method based on Galerkin's technique is employed, which leads to a non-linear eigenvalue problem. An iterative scheme is used to obtain two modes of dispersion, for both real and imaginary wave numbers, for a specific composite.

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“…We assume, as in [8] that the matrix is a standard linear solid and the filament is elastic, so that…”

Section: S Z K~(x)mentioning

confidence: 99%

“…This leads to dissipation as well as dispersion. Free wave propagation in an infinite laminated viscoelastic composite was studied by the present authors in [8] using Floquet theory and finite difference methods. In the viscoelastic case, forced steady wave propagation leads to real frequencies and complvx wave numbers (attenuating waves) while free waves with no applied tractions have complex frequenies and real wave numbers (damped waves) [8].…”

Section: Introductionmentioning

confidence: 99%