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This paper presents a theoretical investigation into the effect of the interaction between a sound field and its boundaries upon the characteristics of the sound field in an enclosure. Recent experimental measurements have shown that the boundaries of the sound field in a reverberation room cannot be correctly described in terms of a locally reactive normal acoustical impedance. Fluid–structural coupling must be taken into account if the mechanism of sound decay in the reverberation room is to be understood. A solution based on modal coupling analysis is obtained for the decay of sound waves in a panel–cavity system. The vibration of the system is resolved into a number of acoustical modes (including fluid and structural vibrations). The reverberation times and the resonance frequencies of different modes are calculated as a function of the modal parameters of the uncoupled panel and cavity. The effect of the panel characteristics on the decay behavior of the cavity sound field is investigated. The interesting phenomena of maximum sound absorption and resonance frequency ‘‘jump’’ are identified and interpreted in terms of the coupling behavior of the panel and cavity modes.

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A technique for controlling noise transmitted into the interior of a cavity involves use of point force actuators on the boundary structures. This paper is an analytical study of the nature of the control mechanism. A rectangular panel-cavity system has been used as a model for this study. The test panel was selected so that the resonance frequencies are well separated. The responses of the structural vibration and the cavity sound field are examined under both controlled and uncontrolled conditions. Results obtained demonstrate that there are two different control mechanisms. If the system response is dominated by panel-controlled modes, sound energy in the cavity is minimized by suppressing the panel modes that radiate into the cavity. if the system response is dominated by cavity-controlled modes, the control force is used to change the panel velocity distribution and thus adjust the radiation of each panel mode. In this latter case, the real part of the sound power radiation into the cavity is minimized, but there may be an increased local reactive intensity field and increased panelvibration level. Co CL oe. h ka•v panel surface area coupling coefficient speed of sound in air speed of longitudinal waves in panel complex force amplitude panel thickness cavity-mode wavenumber = COaN/Co panel-mode wavenumber = c%•v/Co p(r,co) L• ,Ly ,L• length, width, and height of the cavity NR noise reduction level sound pressure in the cavity at location r and angular frequency co (pp*) mean-square cavity sound pressure averaged over space and time total sound pressure on the panel external surface incident sound pressure on the panel external surface complex amplitude of the incident sound pressure reflected sound pressure on the panel external surface sound pressure on the panel external surface due to control forces radiated sound pressure on the panel external surface [P•v ] modal amplitude matrix of the cavity sound pressure [p •xt • generalized total force matrix M1 Ptot Pin PinO Pre Pcon Prad [e;] r T•,M v v(•,o) (vv*) Zimp 7/]aN Po P •(r) q•z (•r) [ •I/con ] (DaN O.) pM primary generalized force matrix secondary generalized force matrix location vector in the sound field modal decay time of the N th cavity mode modal decay time of the M th panel mode volume of the cavity modal amplitude matrix of the panel velocity panel velocity mean-square panel velocity averaged over space and time • internal radiation impedance matrix panel input modal impedance matrix panel average input impedance level elevation and azimuth angles of the incident plane wave loss factor of the Nth cavity mode loss factor of the M th panel mode air density panel density location vector at panel surface the J th cavity-mode shape fucntion uncoupled cavity-mode shape matrix the I th panel-model shape function actuator location matrix uncoupled panel-mode shape matrix angular resonance frequency of the Nth cavity mode angular resonance frequency of the

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