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1

Acoustic Pressure Radiated by a Circular Membrane Into the Quarter-Space

Rdzanek W. P., Szemela K., Pieczonka D.

Archives of Acoustics

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2011

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Vol. 36, No. 1

121-139

EN

The Neumann boundary value problem for the Helmholtz equation within the quarter-space has been considered in this paper. The Green function has been used to find the acoustic pressure amplitude as the approximation valid within the Fraunhoffer’s zone for some time-harmonic steady state processes. The low fluid loading has been assumed and the acoustic attenuation has been neglected. It has also been assumed that the vibration velocity of the acoustic particles is small as compared with the sound velocity in the gaseous medium.

2

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

Rdzanek W. P., Rdzanek W. J., Szemela K.

Hydroacoustics

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2008

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Vol. 11

339-352

EN

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.

3

Czasowooptymalne sterowanie drganiami membrany kołowej

Cupiał P.

Czasopismo Techniczne. Mechanika

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2004

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R. 101, z. 5-M

69--79

PL

W pracy rozważono zagadnienie wyznaczenia minimalnoczasowych sterowań drganiami membrany kołowej w układzie otwartym. Podano rozwiązanie drgań membrany przy wymuszeniu siłą przyłożoną do powierzchni membrany oraz przemieszczeniem brzegu. Opisano sposób wyznaczania sterowań optymalnych stosując tzw. metodę momentów. Podejście zostało zilustrowane wykresami sterowania optymalnego i odpowiedzi układu otrzymanych na drodze symulacji numerycznych.

EN

The paper discusses the problem of the calculations of the open-loop time-optimal controls of a circular membrane. The solutions of the vibration of a membrane excited by a force excitation applied to the membrane surface and kinematic boundary excitation is discussed. An efficient method of calculating the time-optimal controls, the so-called method of l-moments, is discussed. The approach has been illustrated by plots of example time-optimal controls and the response of the system, obtained from numerical simulations.

4

Controllability types of a circular membrane with rotationally symmetric data

Avdonin S., Ivanov S.

Control and Cybernetics

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1999

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Vol. 28, no 3

383-396

EN

Various controllability types are demonstrated for a circular membrane with rotationally symmetric initial data and boundary control depending on time only. We prove that the set of initial states, which can be steered to rest in the critical time interval (equal to the diameter of the membrane) by means of [L^2]-controls is dense in the energy space but contains no eigenmode. We also show that any initial data from a Sobolev space can be transferred to a stationary state. The proof is based on study of exponential families arising in the approach using the method of moments.