Spatial control of far-field structural sound radiation using structural sensors for broadband applications

The focus of the paper is to control the far-field sound radiation from an arbitrary planar structure using multiple structural sensors, particularly for broadband applications. A number of structural velocity sensors are distributed over the structure for sensing the sound radiation at a particular far-field region for control purposes. Spatial control of structural sound radiation is achieved by constructing a frequency-independent spatial filter that reflects the spatially-weighted sound radiation energy. Thus, the signal produced by the spatial filter can be used as an error signal to be minimised by standard active control methods. A numerical case study on the sound radiation of a flat panel structure is performed to investigate the control performance using the developed frequency-independent spatial filter. INTRODUCTION Research in structural sound radiation control has been intensive as reflected by the number of publications in this field, such as (Dimitriadis and Fuller 1992; Clark and Fuller 1991; Burgan et al. 2002). In many practical applications, it is important to be able to control the sound radiation to a particular far-field region, without wasting the control effort in attempting to control the entire far-field region. The work in this paper considers the active control of structural sound radiation with a spatially-weighted objective function that reflects the sound radiation energy at a particular far-field region. In this work, multiple structural sensors are used together with a spatial interpolation function to estimate the sound radiation in the far-field. The effectiveness of multiple structural sensors for vibration or sound radiation control has been demonstrated in various works such as in (Burgan et al. 2002; Meirovitch and Baruh 1982; Pajunen et al. 1994). The primary interest of this work is to consider a practical method which can be used to deal with the spatial control of sound radiation with broadband excitation. SOUND RADIATION ESTIMATION The active control strategy in this work requires the estimation of the far-field sound pressure radiated from a vibrating arbitrary structure. For this purpose, it is important to be able to estimate the vibration profile of the structure first. Sensing the structural vibration The approach used to estimate the vibration profile of a structure depends on the use of multiple structural sensors distributed over the structure. The advantage of this sensing approach is that it can be combined with a spatial interpolation function to estimate the vibration profile of the entire structure, not just at the locations of the sensors. In addition, the method does not require the a-priori information about the system’s dynamic since all the vibration information required directly comes from the structural sensors. The approach here follows the method proposed in (Halim and Cazzolato 2005). Consider an arbitrary structure in Figure 1 where N structural velocity sensors are used at a number of structural locations. In addition, No nodes at the structural boundaries where the vibration level is minimal are also used for the vibration estimation process. A number of nodes can be used to construct an element as shown in Figure 1 using a simple rectangular element, although other geometry can also be utilised. Figure 1 An arbitrary panel structure with N structural sensor nodes and No nodes at the structural boundaries. An element is constructed from several nodes and a spatial interpolation function is used to estimate the normal surface velocity to estimate the far-field sound radiation. Suppose each m element (of M total number of elements) has local coordinates (x,y). A transformation matrix A is used to transform the local coordinates to the global coordinates (x,y) shown in Figure 1. Therefore, the normal surface velocity v(x,y) along the structure can be obtained from the normal velocity measurements from N structural sensors, w (Halim and Cazzolato 2005): w A H (m) (m) (m) ) ,y (x v(x,y)= (1) where H(x,y) is a spatial interpolation matrix. Sensing the far-field sound radiation The estimated velocity profile of the structure can now be used to estimate the far-field sound radiation based on the Rayleigh integral (Wallace 1972; Fuller et al. 1996) assuming an infinite baffle configuration. The far-field complex sound 20-22 November 2006, Christchurch, New Zealand Proceedings of ACOUSTICS 2006 2 Acoustics 2006 pressure p at a distance r can be shown in terms of spherical coordinates shown in Figure 1: ( ) { } φ θ y φ θ x r jk f v(x,y)dR y x r f πr j r p R sin sin cos sin exp ) , , , , , ( 2 ) , , , ( − − − = = ∫ φ θ ω ωρ φ θ ω (2) Where ω is the frequency, R is the region of the structure, ρ is the density of the acoustic medium, and k is the acoustic wave number. Since the normal surface velocity v(x,y) can be estimated from Eq. (1), the far-field sound pressure can be estimated by considering the contributions of all M elements (Halim and Cazzolato 2005b):