Frequency-independent radiation modes of interior sound radiation: Experimental study and global active control
Introduction
Most recent approaches for the active control of sound radiation of vibrating structures into enclosed spaces are based on structural mode sensing [1], [2]. This requires a priori knowledge of the structural mode shapes which can necessitate a high identification effort. In Hesse et al. [3], the structural vibration is decomposed into a set of interior radiation modes. The interior radiation modes are orthogonal functions that describe vibration modes of the structure, such that the contribution from each one of them to the acoustic potential energy in the enclosed fluid is uncoupled from any other. The interior radiation modes calculated in [3] do not presume the knowledge of structural mode shapes and are independent of frequency, as they are a subset of the cavity modes at the structural interface. Since the radiation modes are orthogonal with respect to the acoustic potential energy, their reduction by active means will lead to a global reduction of the enclosed sound field.
The mechanisms of the active control of the acoustic potential energy are investigated in a series of publications by Snyder et al. [4], [5] using secondary control inputs in the fluid and on the structure. Using an analytical model with vibration control sources, e.g. a point force, the two mechanisms of modal suppression and modal rearrangement can occur. The mechanism of modal suppression consists in the reduction of structural modal amplitudes, which are efficiently coupled to the fluid modes. Modal rearrangement on the other hand, is based on the fact, that one fluid mode is in general coupled to more than one structural mode. If this is the case, the structural modes are rearranged in a way, that the coupling to the cavity mode is less efficient.
Many approaches, regarding experimental realizations of active control of structural sound radiation into enclosed spaces, deal with the reduction of local sound pressures [6], [7], [8] or local energy density [9]. Kim and Brennan investigate the active control of harmonic and random sound transmission into an acoustic enclosure [10], [11]. 11 microphones inside the cavity are used as error sensors and the acoustic potential energy is estimated based on the sum of the squared pressure amplitudes. A structural actuator is shown to be more successful in controlling the structural vibration modes than an acoustic actuator.
The approach of local pressure control does not necessarily result in a global reduction of sound radiation. Although the active control with structural error sensing based on radiation modes is investigated numerically [1], [2], an experimental study using a set of radiation modes and yielding a broadband reduction of the acoustic potential energy is not known to the authors. A reason for the absence of experimental work may be found in the frequency–dependence of the resulting radiation modes, when calculated numerically. These radiation modes have been proven frequency–independent for two considered systems of fluid–structure interaction in [3] using an analytical formulation and are used in this study for experimental investigations.
This paper describes an experimental implementation of the global active control of sound radiation in an acoustic enclosure. The system of fluid–structure interaction consists of a rectangular plate coupled to a cuboid cavity. Section 2 describes the experimental setup. A set of harmonic velocities is measured by means of a scanning laser vibrometer (SLV) and included into an identified plant model. Radiation filters are then evaluated and appended to this plant. The system identification process as well as the control synthesis are described in detail in Section 3. An overview of the achieved global noise suppression as well as the control mechanisms is given in Section 4. Section 5 concludes this study and gives an outlook to future research.
Section snippets
Experimental setup
This section presents the experimental set–up of the plate–cavity system, as well as the measurement equipment and the active elements used. An exterior view of the experimental plate–cavity system is shown in Fig. 1a. The plate is made of 2 mm thick aluminium with the dimensions . The plate edges are fixed in an aluminium frame of 15 mm thickness. A total of 24 accelerometers are distributed equally spaced across the plate. Additionally, a grid of 13×15 highly reflective dots
System identification and controller synthesis
An overview of the methods used for the system identification and the controller design is given in this section. The identification of plant models, their extension with additional velocity outputs as well as radiation filter sensing are presented. Based on the extended plant model with the radiation filter output, the applied feedback control synthesis is described.
Control results
This section presents the control measurement results. The closed loop performance is evaluated in terms of the plate vibration and cavity noise reduction. The acoustic potential energy is estimated from the microphone measurement data according to Eq. (12). A comparison of the estimated acoustic potential energy for the open and closed loop measurements is shown in Fig. 9. Throughout the frequency bandwidth of 0–500 Hz, a reduction of the sound radiation can be observed, with narrowband
Conclusion
The frequency-independent radiation modes of interior sound radiation are studied using an experimental coupled plate–fluid system. Radiation mode sensing is conducted through an extension of structural velocity measurements to the plant model. The estimated acoustic potential energy resulting from radiation mode sensing is compared to microphone measurements and a qualitative agreement is shown. The active control of the radiation filter outputs is then evaluated using a controller. As a
Acknowledgement
This study has been conducted within the project Transferzentrum – MRO und Cabin Upgrade (project nr. LAHH 144), which is funded by the authority for Economy, Transport and Innovation of Freie und Hansestadt Hamburg.
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