A Hierarchical Functions Set for Predicting Very High Order Plate Bending Modes With Any Boundary Conditions

Beslin, Olivier; Nicolas, Jean

doi:10.1006/jsvi.1996.0797

Cited by 112 publications

(60 citation statements)

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“…A Rayleigh-Ritz approach was used to develop the plate displacement in the baffled case, as well as the pressure jump in the unbaffled case. The plate mode shape function was defined by applying a set of trigonometric functions for arbitrary boundary conditions [35]. As in Laulagnet's model [33], the pressure jump was also expanded in terms of a series of modes.…”

Section: Unbaffled Plate Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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FACULTY OF ENGINEERING, SCIENCE AND MATHEMATICS INSTITUTE OF SOUND AND VIBRATION RESEARCH Doctor of Philosophy SOUND RADIATION FROM PERFORATED PLATES by Azma PutraPerforated plates are quite often used as a means of engineering noise control to reduce the sound radiated by structures. However, there appears to be a lack of representative models to determine the sound radiation from a perforated plate. The aim of this thesis is to develop such a model that can be used to give quantitative guidance corresponding to the design and effectiveness of this noise control measure.Following an assessment of various models for the radiation efficiency of an unbaffled plate, Laulagnet's model is implemented. Results are calculated and compared with those for baffled plates. From this, simple empirical formulae are developed and give a very good agreement with the analytical result. Laulagnet's model is then modified to include the effect of perforation in terms of a continuously distributed surface impedance to represent the holes. This produces a model for the sound radiation from a perforated unbaffled plate. It is found that the radiation efficiency reduces as the perforation ratio increases or as the hole size reduces. An approximate formula for the effect of perforation is proposed which shows a good agreement with the analytical calculation up to half the critical frequency. This could be used for an engineering application to predict the noise reduction due to perforation.The calculation for guided-guided boundary conditions shows that the radiation efficiency of an unbaffled plate is not sensitive to the edge conditions. It is also shown that perforation changes the plate bending stiffness and mass and hence increases the plate vibration.The situation is also considered in which a perforated unbaffled plate is located close to a reflecting rigid surface. This is established by modifying the Green's function in the perforated unbaffled model to include an imaginary source to represent the reflected sound. The result shows that the presence of the rigid surface reduces the radiation efficiency at low frequencies.The limitation of the assumption of a continuous acoustic impedance is investigated using a model of discrete sources. The perforated plate is discretised into elementary sources representing the plate and also the holes. It is found that the uniform surface impedance is only valid if the hole distance is less than an acoustic wavelength for a vibrating rectangular piston and less than half an acoustic wavelength for a rectangular plate in bending vibration. Otherwise, the array of holes is no longer effective to reduce the sound radiation.Experimental validation is conducted using a reciprocity technique. A good agreement is achieved between the measured results and the theoretical calculation for both the unbaffled perforated plate and the perforated plate near a rigid surface.

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Section: Unbaffled Plate Modelsmentioning

confidence: 99%

Sound radiation from perforated plates

Putra

Thompson

2010

Journal of Sound and Vibration

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“…provide a su cient condition satisfying (13). Now, in order to give a simple representation of u on the boundary , it is convenient to group the set of indices e; l; n into a single index.…”

Section: Presentation Of the Finite Element Basismentioning

confidence: 99%

“…The terms u functions could be employed such as high order polynomials (Lagrangian, Legendre or BSpline wavelets) or trigonometric-like bases (see for instance References [13,14], in the domain of structural dynamic analysis), the speciÿc feature of (10) is the physical meaning of such a decomposition. This latter point is discussed at the end of this section.…”

Section: Presentation Of the Finite Element Basismentioning

confidence: 99%

P‐wave and S‐wave decomposition in boundary integral equation for plane elastodynamic problems

Perrey‐Debain¹,

Trevelyan²,

Bettess³

2003

Commun. Numer. Meth. Engng.

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SUMMARYThe method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to ÿnite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in e ciency over conventional boundary element formulations in elastodynamics.

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“…However, the use of beam function will lead to at least a very tedious solution process [38]. The problem with using a complete set of orthogonal polynomials is that the higher-order polynomials tend to become numerically unstable because of the computer round-off errors [38,39]. These numerical difficulties can be avoided by the Fourier series because the Fourier series constitute a complete set and exhibit an excellent numerical stability.…”

Section: Admissible Functionsmentioning

confidence: 99%

A Unified Accurate Solution for Three-dimensional Vibration Analysis of Functionally Graded Plates and Cylindrical Shells with General Boundary Conditions

Jin¹,

Su²,

Ye³

2016

Advances in Functionally Graded Materials and Structures

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Three-dimensional (3-D) vibration analysis of thick functionally graded plates and cylindrical shells with arbitrary boundary conditions is presented in this chapter. The effective material properties of functionally graded structures vary continuously in the thickness direction according to the simple power-law distributions in terms of volume fraction of constituents and are estimated by Voigt's rule of mixture. By using the artificial spring boundary technique, the general boundary conditions can be obtained by setting proper spring stiffness. All displacements of the functionally graded plates and shells are expanded in the form of the linear superposition of standard 3-D cosine series and several supplementary functions, which are introduced to remove potential discontinuity problems with the original displacements along the edge. The Rayleigh-Ritz procedure is used to yield the accurate solutions. The convergence, accuracy and reliability of the current formulation are verified by numerical examples and by comparing the current results with those in published literature. Furthermore, the influence of the geometrical parameters and elastic foundation on the frequencies of rectangular plates and cylindrical shells is investigated.

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A Hierarchical Functions Set for Predicting Very High Order Plate Bending Modes With Any Boundary Conditions

Cited by 112 publications

References 1 publication

Sound radiation from perforated plates

Sound radiation from perforated plates

P‐wave and S‐wave decomposition in boundary integral equation for plane elastodynamic problems

A Unified Accurate Solution for Three-dimensional Vibration Analysis of Functionally Graded Plates and Cylindrical Shells with General Boundary Conditions

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