Asymptotic formulas for the acoustic power output of a clamped annular plate

Rdzanek, Wojciech P.; Engel, Z.

doi:10.1016/s0003-682x(99)00041-9

Cited by 22 publications

(33 citation statements)

References 6 publications

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“…ss, cs or sc, respectively. Several magnitudes valid for a clamped annular plate quoted from Rdzanek and Engel (2000) have been used as denotations in this paper, their subscript contains the letters cc.…”

Section: Analysis Assumptionsmentioning

confidence: 99%

“…The whole computing procedure had been presented in detail earlier for a clamped annular plate (cf. Rdzanek and Engel 2000), and therefore only the asymptotic results obtained have been presented in this paper. During computing the active and reactive self-impedance it was possible to separate their non-oscillating and oscillating parts, denoted with a bar or with a tilde, respectively.…”

Section: Asymptotics For the High Frequenciesmentioning

confidence: 99%

“…The authors focused particularly on the influence of disk rotation on the acoustic field generated. Rdzanek and Engel (2000) presented asymptotic formulae of the self-impedance of a clamped annular plate. Rdzanek (2003) analyzed the sound radiation of clamped-free and free-clamped annular plates embedded in the infinite rigid baffle using the Hankel transform obtaining the asymptotic formulae for the acoustic self-impedance coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

Rdzanek

2014

mech

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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 wavenumber. 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.Keywords: active and reactive self-impedance, sound radiation for the high frequencies, annular flat plate in a rigid baffle WYZNACZANIE AKUSTYCZNEJ IMPEDANCJI WŁASNEJ PŁASKICH PŁYT PIERŚCIENIOWYCH O RÓŻNYCH KONFIGURACJACH BRZEGOWYCH Z ZASTOSOWANIEM RÓWNAŃ ASYMPTOTYCZNYCH 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 lub 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.Słowa kluczowe: czynna i bierna impedancja własna, promieniowanie dźwięku dla wysokich częstości, płaskie płyty pierścieniowe w sztywnej odgrodzie

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Section: Analysis Assumptionsmentioning

confidence: 99%

Section: Asymptotics For the High Frequenciesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

Rdzanek

2014

mech

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“…The authors used the Rayleigh integral formula to examine the effect of rotary inertia and shear deformations on the acoustic sound radiation. In a series of papers, Rdzanek and coworkers used integral formulation techniques and the method of stationary phase to analyze time-harmonic sound radiation from thin circular/annular plates with various edge conditions [11][12][13][14][15]. Rdzanek and Zawieska [16] investigated far-field sound radiation control from a vibrating clamped-guided annular plate under an external pressure, by direct application of a shaker clamped into the internal edge of the plate.…”

Section: Introductionmentioning

confidence: 99%

Vibroacoustic Response of an Annular Sandwich Electrorheological Disc

Hasheminejad

Afsharmanesh

2014

Journal of Low Frequency Noise, Vibration and Active Control

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The steady-state sound radiation characteristics of a rigidly-baffled clampedfree sandwich annular disc with a tunable electrorheological fluid (ERF) core is studied. Hamilton's principle is employed to derive the governing equations of motion for the composite plate along with the associated boundary conditions in general form. The classical Galerkin procedure is subsequently utilized to reduce the structural problem into a linear system of algebraic equations for the unknown displacement coefficients. A modal summation approach based on Rayleigh integral formula along with the proper integral representation of the cylindrical Bessel functions are used to arrive at a useful single integral relation for the far-field modal radiated sound pressure and subsequently determine the radiation power and efficiency. Numerical results reveal the imperative influence of the applied electric field strength (0-3.5kV/mm) on controlling acoustic radiation from the adaptive panel in a wide frequency range. In particular, an effort is made to find the optimal electric field which yields improved sound radiation characteristics for each excitation frequency. Limiting cases are considered and good agreements with the calculations made by using a commercial finite element package as well as with the solutions available in the literature are obtained.

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“…Some analytical formulations for the plate in the form of multiple expansion series have been reached in reference [2]. The active and reactive sound power of a clamped annular plate has been given in reference [5]. An asymptotic}impedance approach was employed to "nd the e!ective damping parameter of a circular plate in reference [16].…”

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confidence: 99%

The Energy Aspect of the Reciprocal Interactions of Pairs of Two Different Vibration Modes of a Clamped Annular Plate

Rdzanek

2002

Journal of Sound and Vibration

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Asymptotic formulas for the acoustic power output of a clamped annular plate

Cited by 22 publications

References 6 publications

Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

Asymptotic Formulae for the Acoustic Self-Impedance of Simply-Supported and Simply Supported-Clamped Annular Plates

Vibroacoustic Response of an Annular Sandwich Electrorheological Disc

The Energy Aspect of the Reciprocal Interactions of Pairs of Two Different Vibration Modes of a Clamped Annular Plate

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