A perturbation approach for evaluating natural frequencies of moderately thick elliptic plates

Kaplunov, Julius; Nolde, E.V.; Шорр, Б. Ф.

doi:10.1016/j.jsv.2004.02.046

Cited by 32 publications

(20 citation statements)

References 10 publications

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“…= , "° is compared for V 2(1 + ")PP different nodal diameters "m" and nodal circles "n" in Table 2. It can be observed that the results are quite similar, except for the case of m = 1 and n = 1, however, for this case the comparison of the present method with the circular plate, e = 0, seems to be in accordance in contrast with the results obtained by Kaplunov et al [2005], In Table 3, the parameters [3™ m with no nodal diameter m = 0 and one nodal diameter m = 1 are presented. From these results, the frequencies for different values of eccentricity e can be computed.…”

Section: Natural Frequencies Of Almost Circular Plates In Vacuumsupporting

confidence: 69%

“…Next, the natural frequencies for the plate in vacuum are compared with the methods presented in Kaplunov et al [2005].…”

Section: Natural Frequencies Of Almost Circular Plates In Vacuummentioning

confidence: 99%

“…For the values of | = 1.1, e = 0.181818 and r\ = -£-= 0.05, the frequency parameter defined in Kaplunov et al [2005] as f! = , "° is compared for V 2(1 + ")PP different nodal diameters "m" and nodal circles "n" in Table 2.…”

Section: Natural Frequencies Of Almost Circular Plates In Vacuummentioning

confidence: 99%

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Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

Gascón-Pérez

García-Fogeda

2014

Int. J. Appl. Mechanics

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In this work, the influence of the surrounding fluid on the dynamic characteristics of almost circular plates is investigated. First the natural frequencies and normal modes for the plates in vacuum are calculated by a perturbation procedure. The method is applied for the case of elliptical plates with a low value of eccentricity. The results are compared with other available methods for this type of plates with good agreement. Next, the effect of the fluid is considered. The normal modes of the plate in vacuum are used as a base to express the vibration mode of the coupled plate-fluid system. By applying the Hankel transformation the nondimensional added virtual mass 2 increment (NAVMI) are calculated for elliptical plates. Results of the NAVMI factors and the effect of the fluid on the natural frequencies are given and it is shown that when the eccentricity of the plate is reduced to zero (circular plate) the known results of the natural frequencies for circular plates surrounded by liquid are recovered.

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Section: Natural Frequencies Of Almost Circular Plates In Vacuumsupporting

confidence: 69%

“…Next, the natural frequencies for the plate in vacuum are compared with the methods presented in Kaplunov et al [2005].…”

Section: Natural Frequencies Of Almost Circular Plates In Vacuummentioning

confidence: 99%

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Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

Gascón-Pérez

García-Fogeda

2014

Int. J. Appl. Mechanics

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“…1 and 3. We also mention that the relation (14) has the same form as the dispersion relation for the bending wave on an elastically supported beam, e.g., see Ref. 7.…”

Section: J¼1mentioning

confidence: 89%

The edge wave on an elastically supported Kirchhoff plate

Kaplunov

Приказчиков

Rogerson

et al. 2014

The Journal of the Acoustical Society of America

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This Letter deals with an analysis of bending edge waves propagating along the free edge of a Kirchhoff plate supported by a Winkler foundation. The presence of a foundation leads to a nonzero cut-off frequency for this wave, along with a local minimum of the associated phase velocity. This minimum phase velocity corresponds to a critical speed of an edge moving load and is analogous to that in the classical 1D moving load problem for an elastically supported beam.

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“…Instead it provides an equation for the rotation angle θ = ∂W ∂y , evaluated at the edge y = 0, namely, 27) with the constant Q defined in (5.15). The resulting explicit model for the shear edge force is similar to that obtained in respect of a bending moment.…”

Section: (B) Shear Forcementioning

confidence: 99%

Edge bending wave on a thin elastic plate resting on a Winkler foundation

2016

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This paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate which is supported by a Winkler foundation. A homogeneous wave of arbitrary profile is considered, and represented in terms of a single harmonic function. This serves as the basis for derivation of an explicit asymptotic model, containing an elliptic equation governing the decay away from the edge, together with a parabolic equation at the edge, corresponding to beam-like behaviour. The model extracts the contribution of the edge wave from the overall dynamic response of the plate, providing significant simplification for analysis of the localised near-edge wave field.

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A perturbation approach for evaluating natural frequencies of moderately thick elliptic plates

Cited by 32 publications

References 10 publications

Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

Influence of a Liquid on the Natural Frequencies of Almost Circular Plates

The edge wave on an elastically supported Kirchhoff plate

Edge bending wave on a thin elastic plate resting on a Winkler foundation

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