Development of a pseudo-uniform 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):3833-40. DOI: 10.1121/1.3699264
Source: PubMed


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, simply-supported 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.

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    • "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. "

    Journal of Vibration and Control 10/2015; DOI:10.1177/1077546315616523 · 4.36 Impact Factor
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    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 so-called 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.
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    ABSTRACT: The weighted sum of spatial gradients (WSSG) control minimization parameter is developed for use in active structural acoustic control (ASAC) on a clamped flat rectangular plate. The WSSG minimization parameter is measured using four accelerometers grouped closely together on the test structure. In previous work, WSSG was developed on a simply supported flat rectangular plate and showed promise as a control metric. The displacement on the clamped plate has been modeled using an approximate analytical solution assuming shape functions corresponding to clamped-clamped beams. From the analytical formulation, weights, which were found to be the reciprocal of the wave number squared, have been derived to produce a uniform WSSG field across the plate. In active control simulations, this quantity has been shown to provide better global control of acoustic radiation than volume velocity. Analysis is presented which shows that comparable control, regardless of the sensor location, can be achieved using WSSG. Experimental results are presented which demonstrate that WSSG works effectively in practice, with results similar to the simulations. The results show that minimization of WSSG can be used as an effective control objective on clamped rectangular plates to achieve attenuation of acoustic radiation.
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