The Total Acoustic Power of a Clamped Circular Plate Located at the Boundary of Three-Wall Corner Region

Abstract

The energetic aspect of the sound radiation has been analyzed in the case of the three-wall corner region. This region is the part of space bounded by three baes arranged perpendicularly to one another. The Neumann boundary value problem has been solved assuming that the sound source is the vibrating circular plate embedded in one of the baes of the three-wall corner region. The KelvinVoigt theory of a visco-elastic plate has been used which allows to include internal attenuation existing in the plate material. It has been assumed that the sound source is excited to vibrations by the external pressure asymmetrically distributed on the plate surface. The modal coecients of the acoustic impedance have been obtained in the form of the expressions containing single integrals only. The formula describing the acoustic power of the analyzed sound source has been presented as a fourfold innite series containing the modal coecients of the acoustic impedance. The inuence of some asymmetric excitations on the acoustic power has been analyzed. The possibilities of the modelling some uniform excitations located on the plate fragment of the small area by the point force excitation has been examined. The inuence of the transverse baes on the acoustic power has also been investigated. It has been determined for which frequency the baes inuence on the acoustic power is the greatest.

The Low Frequency Approximation of the Sound Radiation Power of Two Vibrating Circular Pistons Embedded in Two Different Rigid Planes of a~Three-wall Corner

“…Signicant dierences of the acoustic mutual power of radiation in the two-wall corner and in the three-wall corner can be deduced from Eqs. (19) and (22).…”

The Acoustic Pressure Radiated by a Vibrating Circular Plate within the Fraunhofer Zone of the Three-Wall Corner Region

“…They are valid within the Fraunhofer zone. The total acoustics power has been analyzed in the case of the clamped circular plate embedded on the boundary of three-wall corner region [23]. The analysis has been performed for some dierent plate locations and for some selected external excitations.…”

“…Therefore, the main aim of this study is to obtain the asymptotic formulae valid within the Fraunhofer zone to describe the acoustic pressure distribution radiated by the clamped circular plate. Moreover, making use of the results obtained in [23] enables including the acoustic attenuation. The formulae necessary for that purpose have been presented in Appendix for the readers' convenience.…”

“…, E, ν denote Young's modulus and the Poisson ratio, respectively,η is plate's internal attenuation factor [23,24]. The formulae which allow to solve Eq.…”

“…The acoustic pressure (3) can be presented after using Eq. 1as the double series of the modal components [23]…”