Computing reflection and transmission coefficients for plate reinforcement beams

Arruda, José Roberto de França; Gautier, François; Donadon, Lazaro Valentim

doi:10.1016/j.jsv.2007.06.052

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…ISM can then be applied to plates with roller boundary conditions, but other kinds of boundaries need further investigation. Coupled structures, such as plate assemblies or stiffened plates [25] can also be investigated by adapting principles of ISM presented in this paper.…”

Section: Resultsmentioning

confidence: 99%

“…for (m ≥ 1, n ≥ 1), which are the same as those in Eq. (25) for L x = L y = L. However, the numerator in Eq. (29) consists in a sum of two terms and therefore is cancelled for m = n, so that ω mm are not singularities of G Ω (i.e.…”

Section: Simply Supported Isosceles Right Triangular Platementioning

confidence: 99%

“…for (m ≥ 1, n ≥ 1), and are the same as those in Eq. (25) for L x = L and L y = √ 3L. As for the case of the isosceles right triangular plate, the circular frequencies ω mn for which the numerator in Eq.…”

Section: Simply Supported Half-equilateral Triangular Platementioning

confidence: 99%

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The image source method for calculating the vibrations of simply supported convex polygonal plates

Cuenca¹,

Gautier²,

Simon³

2009

Journal of Sound and Vibration

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To cite this version:Jacques Cuenca, François Gautier, Laurent Simon. The image source method for calculating the vibrations of simply supported convex polygonal plates. AbstractThe aim of this paper is to show that the Image Source Method (ISM) can be used both for analytically calculating Green's functions of particular simply supported convex polygonal plates and for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates with controllable precision. In the first part of the paper, the method for obtaining the Green's function of a polygonal plate by ISM is developed. Examples for plates of different geometries (rectangle, isosceles right triangle, half-equilateral triangle and equilateral triangle) are given. In the second part of the paper, the pertinence of ISM for predicting medium and high frequency vibrations of arbitrarily shaped simply supported convex polygonal plates is investigated. An approximation based on the exclusion of image sources beyond a certain distance from the receiver is used in order to take advantage of the dissipation of vibrational energy through wave propagation. We investigate the influence of structural damping and truncation distance on the accuracy of such approximation. The computed responses are in good agreement with reference solutions, which are analytically known or obtained by the finite element method.

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Section: Resultsmentioning

confidence: 99%

Section: Simply Supported Isosceles Right Triangular Platementioning

confidence: 99%