Abstract
This paper presents an analytical investigation on constructing an error sensing strategy of a new type of active MPPA. The proposed active MPPA is composed of MPP, air cavity, and point force-controlled backing panel, which can actively improve the low-frequency sound absorption of the MPPA. Constructing an appropriate error sensing strategy for obtaining an error signal that is highly correlated with the sound absorption coefficient of the active MPPA is a key problem encountered in practical implementation. The theoretical model of the active MPPA is firstly established using the modal analysis approach. Then, the active control performance and surface impedance characteristics in the controlled condition are analyzed in detail. Finally, the error sensing strategy of the active MPPA is constructed by measuring the surface average impedance ratio with an acoustic vector sensor (AVS). Simulation results show that, due to the antisymmetric property of the vibration of the backing panel on the resonant frequency, the surface impedance of the active MPPA after control also has symmetry or antisymmetry properties. Hence, the surface average impedance ratio of the active MPPA can be measured by using the limited number of acoustic vector sensors (sensing pressure and particle velocity). This variable is also highly correlated with the sound absorption coefficient of the active MPPA and thus can be used to construct the cost function (error signal). The active control result obtained by the proposed error sensing strategy is in good agreement with the theoretically optimal result, which validates the feasibility of this approach.
Highlights
E abovementioned works significantly improve the sound absorption of the MPPA in the mid-high-frequency range. ere are many requirements for the MPPA with preferable low-frequency sound absorption, such as designing acoustic liners to reduce fan noise
In order to further broaden the low-frequency absorption bandwidth, passive and active methods are developed. e passive method mainly introduces resonant structure to obtain the improvement of sound absorption in a narrow bandwidth centered on the resonant frequency, such as the MPPA backed by Helmholtz resonators [15], the flexible micro-perforated panel absorber based on polyvinylidene fluoride piezoelectric film [16], the MPPA backed by shunted loudspeaker [17], and the MPPA backed with mechanical impedance plates [18]
If the ideal piston-type source is replaced by a secondary force-controlled elastic plate, the active MPPA will become easier to implement. e piezoelectric excitation or the small shaker placed in the cavity can be used as the control force in practice. e surface impedance of the active MPPA can be adjusted to match the characteristic impedance of the air medium by actively controlling the vibration of the elastic plate
Summary
According to equation (5), the sound pressure on the surface of the MPP in the cavity side (z − D) can be expressed as PD − jωρ0 Luw cos h − Dμuw. Multiplying Ψuw(x, y) on both sides of equation (17), and using the orthogonality of modal shape function, the following expression can be obtained: PDΨuw(x, y)dxdy z0ztuw z0 + σztuw a. Multiplying Ψuw(x, y) on both sides of equation (24) and applying the orthogonality of the modal shape function yield the expression of Ruw: Ruw v1(x, y)Ψuw(x, y)dxdy μuwe− μuwDβuw. Substituting equations (22) and (25) into equation (5), the sound pressure Pr of the reflected wave at the surface of the active MPPA (z − D) can be expressed as
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