Article
Development of a pseudouniform structural quantity for use in active structural acoustic control of simply supported plates: An analytical comparison
Department of Mechanical Engineering, Brigham Young University, Provo, Utah 84602, USA.
The Journal of the Acoustical Society of America (Impact Factor: 1.5). 05/2012; 131(5):383340. DOI: 10.1121/1.3699264 Source: PubMed
ABSTRACT
Active structural acoustic control has been an area of research and development for over two decades with an interest in searching for an "optimal" error quantity. Current error quantities typically require the use of either a large number of transducers distributed across the entire structure, or a distributed shaped sensor, such as polyvinylidene difluoride. The purpose of this paper is to investigate a control objective function for flat, simplysupported plates that is based on transverse and angular velocity components combined into a single composite structural velocity quantity, termed V(comp). Although multiple transducers are used, they are concentrated at a single location to eliminate the need for transducers spanning most or all of the structure. When used as the objective function in an active control situation, squared V(comp) attenuates the acoustic radiation over a large range of frequencies. The control of squared V(comp) is compared to other objective functions including squared velocity, volume velocity, and acoustic energy density. The analysis presented indicates that benefits of this objective function include control of radiation from numerous structural modes, control largely independent of sensor location, and need to measure V(comp) at a single location and not distributed measurements across the entire structure.

 "A recent control metric, termed composite velocity (also referred to as weighted sum of spatial gradients or WSSG) has shown promise in resolving these issues. Composite velocity was developed as a weighted sum of spatial velocity gradients requiring only four sensors to measure, and was found to be relatively insensitive to sensor location (Fisher et al., 2012). Hendricks et al. (2014) extended this research from computer simulations and provided experimental test results for a flat simply supported plate. "
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ABSTRACT: In this paper, the active control of sound transmission through a simply supported softcore sandwich panel is analytically studied. Since, the sound transmission through softcore sandwich panels in the lowfrequency region mainly occurs due to flexural and dilatational modes, and therefore to control these structural modes, volume velocity and weighted sum of spatial gradients (WSSG) are used to drive a piezoceramic actuator (PZT) attached on the exterior side of the bottom face plate. Sound power level and voltage required to drive the PZT are compared for different values of isotropic core loss factor. Numerical studies indicate that both control metrics are capable of attenuating the flexural and the dilatational modes of the sandwich panel, and hence, reduce significant amount of sound power in a wider frequency range. By carefully selecting the modes to calculate the scaling factors, WSSG provides comparable control to volume velocity. However, the necessary voltage required to drive the PZT to minimize the WSSG is less as compared to minimize the volume velocity.  [Show abstract] [Hide abstract]
ABSTRACT: A numerical method is developed for estimating the acoustic power of any baffled planar structure, which is vibrating with arbitrary surface velocity profile. It is well known that this parameter may be calculated with good accuracy using near field data, in terms of an impedance matrix, which is generated by the discretization of the vibrating surface into a number of elementary radiators. Thus, the sound pressure field on the structure surface can be determined by a combination of the matrix and the volume velocity vector. Then, the sound power can be estimated through integration of the acoustic intensity over a closed surface. On the other hand, few works exist in which the calculation is done in the far field from near field data by the use of radiation matrices, possibly because the numerical integration becomes complicated and expensive due to large variations of directivity of the source. In this work a different approach is used, based in the socalled Propagating Matrix, which is useful for calculating the sound pressure of an arbitrary number of points into free space, and it can be employed to estimate the sound power by integrating over a finite number of pressure points over a hemispherical surface surrounding the vibrating structure. Through numerical analysis, the advantages/disadvantages of the current method are investigated, when compared with numerical methods based on near field data. A flexible rectangular baffled panel is considered, where the normal velocity profile is previously calculated using a commercial finite element software. However, the method can easily be extended to any arbitrary shape. Good results are obtained in the low frequency range showing high computational performance of the method. Moreover, strategies are proposed to improve the performance of the method in terms of both computational cost and speed.  [Show abstract] [Hide abstract]
ABSTRACT: A limitation currently facing active structural acoustic control (ASAC) researchers is that an ideal minimization quantity for use in the control algorithms has not been developed. A novel parameter termed the "weighted sum of spatial gradients" (WSSG) was recently developed for use in ASAC and shown to effectively attenuate acoustic radiation from a vibrating flat simply supported plate in computer simulations. This paper extends this research from computer simulations and provides experimental test results. The results presented show that WSSG is a viable control quantity and provides better results than the volume velocity approach. The paper also investigates several of the challenges presented by the use of WSSG. These include determining a method to measure WSSG experimentally, an analysis of the influence of noise on WSSG control results and complications presented when degenerate modes exist. Results are shown and discussed for several experimental configurations.
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