LOW FREQUENCY APPROXIMATION OF MUTUAL MODAL RADIA- TION EFFICIENCY OF A VIBRATING RECTANGULAR PLATE

This paper presents some elementary formulations for the mutual modal radiation efficiency of a simply supported rectangular plate embedded into a rigid infinite baffle. The magnitude makes it possible to introduce the intermodal plate's interactions into the total radiation efficiency of the plate vibrating under the influence of an external surface force. The approximate formula has been expressed as a combinations of some trigonometric and special functions. The formula is convenient for some numerical computations of the modal and total radiation efficiency values of the plate

THE TOTAL SOUND POWER OF SOME FORCED VIBRATIONS OF A CLAMPED ANNULAR PLATE IN FLUID

The energetic aspect of sound radiation by a clamped annular plate has been considered. The total sound power, active and reactive, was computed using the impedance approach, which makes possible to correctly design some acoustic systems. The plate was excited by the external pressure of an axisymmetric and time-harmonic distribution on the plate's surface. The Kelvin-Voigt theory of a visco-elastic plate was employed. The results of a modal analysis of an annular plate's in-vacuo motion were used

LOW FREQUENCY APPROXIMATION OF MUTUAL MODAL RADIATION EFFICIENCY OF A VIBRATING RECTANGULAR PLATE

This paper presents some elementary formulations for the mutual modal radiation efficiency of a simply supported rectangular plate embedded into a rigid infinite baffle. The magnitude makes it possible to introduce the intermodal plate's interactions into the total radiation efficiency of the plate vibrating under the influence of an external surface force. The approximate formula has been expressed as a combinations of some trigonometric and special functions. The formula is convenient for some numerical computations of the modal and total radiation efficiency values of the plate

The acoustic power radiated by a circular membrane excited for vibration both by means of the edge and by external surface load

In this paper the acoustic power of the circular membrane, excited both by the edge and external exciting forces uniformly distributed over the whole surface, is examined. Some different amplitudes of exciting factors and some differences between the phases of excitations were considered. It has been assumed that the source of a sound is located in a flat, rigid and infinite baffle and is sourrounded by a lossless and homogeneous fluid medium. The vibrations are axisymmetric and time-harmonic. Employing the Cauchy's theorem of residues and asymptotic formulae for the Bessel functions, the asymptotes for active and reactive power consisting of elementary functions are obtained. The acoustic power radiated by the membrane was shown graphically in terms of the parameters describing both kinds of excitations

Moc bierna dźwięku płyty kołowej w zakresie niskich częstości

An efficient low frequency approximation for the reactive sound power of an elastically supported circular plate has been directly derived from the corresponding high frequency expressions presented earlier. The analysis of the approximation error has shown that the low frequency formulation can be applied if the error of 10% can be accepted. The result is valid for any axisymmetric boundary configuration of the plate. The influence of the boundary configuration on the reactive sound power has been examined.Efektywną aproksymację niskoczęstościową biernej mocy dźwięku płyty kołowej zamocowanej sprężyście wyprowadzono bezpośrednio z odpowiednich wyrażeń wysokoczęstościowych przedstawionych wcześniej. Analiza błędów aproksymacji pokazała, że wzór niskoczęstościowy może być stosowany, jeśli dopuszczalny błąd względny może wynosić do 10%. Otrzymany wynik jest słuszny dla dowolnej osiowosymetrycznej konfiguracji brzegowej płyty. Zbadano wpływ konfiguracji brzegowej na moc bierną

Wyznaczanie akustycznej impedancji własnej płaskich płyt pierścieniowych o różnych konfiguracjach brzegowych z zastosowaniem równań asymptotycznych

This study focuses on the sound radiation of a vibrating flat annular plate. The rigorous theoretical considerations deal with some time-harmonic and axisymmetric vibrations. Three different boundary configurations are considered, i.e. one of the plate's edges is simply supported and the other one is clamped or also is simply supported. The active and reactive self-impedance of the system are presented in their Hankel's representations, valid within the whole frequency spectrum. The expressions obtained are transformed to their elementary forms, valid for the high frequencies. Low fluid loading and low internal friction of the plate are assumed. The obtained results are illustrated with sample plots in the domain of acoustic wave number. Elementary formulae presented can be useful for further theoretical analysis of the total sound power radiated by an excited flat plate in an acoustic fluid as well as for efficient engineering computations.W pracy podjęto zagadnienie promieniowania dźwięku przez drgającą płaską płytę pierścieniową. Ścisłe rozważania teoretyczne dotyczą osiowosymetrycznych drgań harmonicznych. Rozpatrzono trzy różne konfiguracje brzegowe, tj. dla jednej krawędzi płyty swobodnie podpartej, a drugiej utwierdzonej łub swobodnie podpartej. Czynną i bierną impedancję własną układu drgającego przedstawiono w reprezentacji Hankela, słusznej w całym spektrum częstości. Wyrażenia te zostały przekształcone do ich elementarnych postaci, słusznych dla wysokich częstości. Założono, że wpływ powietrza na drgania płyty oraz tłumienie wewnętrzne są znikome. Otrzymane wyniki zilustrowano wybranymi wykresami w funkcji liczby falowej. Przedstawione wzory elementarne mogą być przydatne do dalszej analizy teoretycznej całkowitej mocy promieniowania dźwięku przez płaską płytę pobudzoną do drgań z uwzględnieniem wpływu ośrodka, jak również do szybkich obliczeń inżynierskich

The Acoustic Impedance of a Vibrating Annular Piston Located on a Flat Rigid Baffle Around a Semi-Infinite Circular Rigid Cylinder

The axisymmetric problem of acoustic impedance of a vibrating annular piston embedded into a flat rigid baffle concentrically around a semi-infinite rigid cylindrical circular baffle has been undertaken in this study. The Helmholtz equation has been solved. The Green’s function valid for the zone considered has been used for this purpose. The influence of the semi-infinite cylindrical baffle on the piston’s acoustic impedance has been investigated. The acoustic impedance has been presented in both forms: integral and asymptotic, both valid for the steady harmonic vibrations. Additionally, the acoustic impedances of the piston with and without the cylindrical baffle have been compared to one another. In the case without the cylindrical baffle some earlier results have been used

Acoustic Power Radiated by a System of Two Vibrating Circular Membranes Located at the Boundary of Three-Wall Corner Spatial Region

Two vibrating circular membranes radiate acoustic waves into the region bounded by three infinite baffles arranged perpendicularly to one another. The Neumann boundary value problem has been inves- tigated in the case when both sources are embedded in the same baffle. The analyzed processes are time harmonic. The membranes vibrate asymmetrically. External excitations of different surface distributions and different phases have been applied to the sound sources’ surfaces. The influence of the radiated acoustic waves on the membranes’ vibrations has been included. The acoustic power of the sound sources system has been calculated by using a complete eigenfunctions system

The acoustic radiation impedance of a circular membrane vibrating near the three-wall corner

A flat circular membrane is located near the three- wall corner, limited by the three rigid baffles arranged perpendicularly to each other. The problem of sound radiation has been solved using the spectral form of the Green function for this Neumann boundary value problem together with the complete eigenfunction system of the axisymmetric and asymmetric modes of the membrane is excited by a surface vibrating harmonically with respect to time within the vacuum. The membrane is excited by a surface force. The acoustic attenuation 3399effect has been taken into account as well as the influence of the corner baffles. The resultant sound pressure and the resultant acoustic impedance have been presented as their eigenfunction series. The modal, self and mutual, radiation resistance has been presented in the form of the approximation valid within the low frequency vibration range. The low frequency approximation for the modal radiation reactance has been obtained on the basis of the radiation resistance using the Hilbert transform

The Acoustic Impedance of a Vibrating Annular Piston Located on a Flat Rigid Baffle Around a Semi-Infinite Circular Rigid Cylinder

The axisymmetric problem of acoustic impedance of a vibrating annular piston embedded into a flat rigid baffle concentrically around a semi-infinite rigid cylindrical circular baffle has been undertaken in this study. The Helmholtz equation has been solved. The Green’s function valid for the zone considered has been used for this purpose. The influence of the semi-infinite cylindrical baffle on the piston’s acoustic impedance has been investigated. The acoustic impedance has been presented in both forms: integral and asymptotic, both valid for the steady harmonic vibrations. Additionally, the acoustic impedances of the piston with and without the cylindrical baffle have been compared to one another. In the case without the cylindrical baffle some earlier results have been used