Calculating Resonance Frequencies of Perforated Panels

Burgemeister, Kym; Hansen, Colin H.

doi:10.1006/jsvi.1996.0490

Cited by 30 publications

(23 citation statements)

References 6 publications

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“…We apply a standard collocation method to solve the second-kind boundary integral equation (11). The boundary, ∂Ω, is first discretized at collocation points x i , i = 1, .…”

Section: Discretization Of the Integral Equationmentioning

confidence: 99%

“…The specific placement of these perforations permits the manipulation of acoustic and vibrational properties of the plate while economizing on weight and material cost. Homogenization theories have been proposed to replace the natural elastic modulus of the plate with an effective modulus [11,4], however, an averaging approach omits the pronounced localizing effects that clamping has on vibrational modes [23].…”

Section: Introductionmentioning

confidence: 99%

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A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

2017

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We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of these modes in the presence of multiple localized defects for a wide range of two-dimensional geometries. The defects result in eigenfunctions with a weak singularity that is resolved by decomposing the solution as a superposition of Green's functions plus a smooth regular part. This method is applied to a variety of regular and irregular domains and two key phenomena are observed. First, careful placement of clamping points can entirely eliminate particular eigenvalues and suggests a strategy for manipulating the vibrational characteristics of rigid bodies so that undesirable frequencies are removed. Second, clamping of the plate can result in partitioning of the domain so that vibrational modes are largely confined to certain spatial regions. This numerical method gives a precision tool for tuning the vibrational characteristics of thin elastic plates.

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“…We apply a standard collocation method to solve the second-kind boundary integral equation (11). The boundary, ∂Ω, is first discretized at collocation points x i , i = 1, .…”

Section: Discretization Of the Integral Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

2017

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“…It should be noted here that the high peaks shown in the effect of perforation at low frequencies below 1 kHz, for example, at the fundamental frequency of the plate, that is, 250 Hz, are the effects due to the natural frequency shift because of perforation [7], although the level at the fundamental frequency as seen in Figure 8(e) is also increased by roughly 10 dB compared to the level at the fundamental frequency of the solid plate.…”

Section: Effect Of Hole Diameter and Number Of Holes At Fixedmentioning

confidence: 81%

“…According to Burgemeister and Hansen [7], the equation proposed in [6] does not provide correct resonant frequencies when the effective material properties are used. The FEM was then implemented to model the modal response of range of plates with varying perforation geometries, where, from here, the resonant frequencies of the perforated plates were obtained.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Perforation on the Dynamics of a Flexible Panel

Putra

Cheah

Muhammad

et al. 2014

Advances in Acoustics and Vibration

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Introduction of holes into plate-like structures is commonly found as one of the practical noise control measures to reduce sound radiation. However, perforation also reduces the panel stiffness and hence increases its vibration. The discussion on this effect is lacking and hence this paper discusses the dynamics of a perforated panel from the results obtained from Finite Element (FE) model. Different hole geometries and arrangement are simulated to investigate their effect on the plate mobility. In general, it is found that increasing the perforation ratio increases the plate mobility. For a fixed perforation ratio, the mobility increases at high frequency (above 1 kHz) for a smaller hole density in the plate. The plate with holes concentrated at the middle shows the largest increase of vibration around the plate centre compared to those uniformly distributed or away from the middle and concentrated at the plate edges. This is because as the hole separation becomes smaller, the reduction of the global stiffness around the mid area of the plate becomes greater. This also corresponds to the finding here that the mobility is greater at the vicinity of the hole. Different conditions of the plate edges are found to give consistent trend of the effect of perforation.

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“…These equivalent material properties are used in vibration analysis to consider perforated plate as full solid plate. Burgemeister and Hansen [4] showed that, to predict accurately the resonance frequencies of simply supported perforated panel, effective material constants cannot be used in classical equations. They used cubic function fitted from ANSYS results to determine the effective resonance frequency ratio for large range of panel geometries with an error of less than 3%.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

Mali

Singru

2013

Advances in Acoustics and Vibration

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This paper is concerned with a vibration analysis of perforated rectangular plates with rectangular perforation pattern of circular holes. The study is particularly useful in the understanding of the vibration of sound absorbing screens, head plates, end covers, or supports for tube bundles typically including tube sheets and support plates used in the mechanical devices. An energy method is developed to obtain analytical frequencies of the perforated plates with clamped edge, support conditions. Perforated plate is considered as plate with uniformly distributed mass. Holes are considered as concentrated negative masses. The analytical procedure using the Galerkin method is adopted. The deflected surface of the plate is approximated by the cosine series which satisfies the boundary conditions. Finite element method (FEM) results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well for holes of small size.

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Calculating Resonance Frequencies of Perforated Panels

Cited by 30 publications

References 6 publications

A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points

The Effect of Perforation on the Dynamics of a Flexible Panel

Determination of the Fundamental Frequency of Perforated Rectangular Plates: Concentrated Negative Mass Approach for the Perforation

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