Active H Control of Sound Radiation from Thin Cylindrical Panels

Abstract

Activecontrol of sound radiated by thin-walled cylindrical panels using arrays of spatially discrete piezoelectric sensors and actuators is addressed. A new general methodology for the design of controllers to reduce structure radiated noise is presented. The methodology utilizes e nite element modeling to perform structural discretization. The structure dynamics model, presented in state-space form, incorporates simplie ed models of the piezoelectric sensing and actuation and accounts for the mass and stiffness of the piezoelectric elements. The acoustic power radiated by thestructureinto thefare eld is expressed asa quadraticform ofthesystem statesthatis used to dee ne an acoustic performance criterion in an H1 disturbance rejection controller design setup. The methodology is applied for active control of sound radiated by a vibrating thin cylindrical panel excited by a persistent external force. The controller performance is evaluated using numerical simulations of the controlled structure. It is shown that the sound radiated by the panel into the far e eld is effectively controlled and reduced. CTIVE structural acoustic control (ASAC) has been exten- sively addressed in the literature. In essence, ASAC can be interpreted as attenuation of structure radiated sound resulting from a persistent excitation/disturbance. In controller design terms, it can be viewed as a disturbance rejection problem, the control objective of which is to minimize structure radiated sound, specie ed by an analytical sound radiation model. This is closely related to conven- tional vibration suppression control, often obtained by increasing (passivelyoractively )thedampingofthecontrolledstructure,which also reduces the structure radiated sound. Because effective ASAC should tackle the sound radiation mechanisms directly, which, in addition to the vibrational power, includes additional important pa- rameters such as vibrationalmodeshapes, excitation frequency,and others, use of a controller specie cally designed to minimize the sound radiation should be more effective. As an application of intelligent structures technology, ASAC re- lies on integrating piezoelectric sensors and actuators, for example, PVDF and PZT, into the structure. Modeling of such an integrated structure has been the subject of on-going research, with initial re- sultsreportedbyCrawleyanddeLuis, 1 followedbyWang 2 andmore recently by Pletner and Abramovich, 3 to name but a few. The sound radiated by a vibrating structure into the far e eld from measure- ments of the structural velocity e eld was investigated, both analyt- ically and experimentally, by Clark and Fuller, 4 Mathur and Tran, 5 and others. The analytical formulation presented in these studies was exclusively performed on simple structures (simply supported beams and plates ), while neglecting the mass and stiffness of the sensors and actuators. More complex structures, such as cylindri- calshells 6 and airplane fuselage, 7 were treated only experimentally. The ASAC controller designs documented in the literature are lim- ited to proportional and least mean squares algorithms, which are used to control the experimental structure. TomakeASACapplicableforcommercialapplications,areliable methodology that covers the design and analysis of adaptive struc- tures with complex geometric and material properties, incorporates a model of the sound radiation mechanism, and includes appropri- ate control synthesis algorithms is needed. This goal is undertaken in this study, which presents a new methodology that attempts to address ASAC objectives. This methodology, which utilizes e nite element(FE) tools to obtain a discrete representation of the contin- uous structure dynamics of (almostany)linearly elastic thin-walled structural element, incorporating piezoelectric sensing and actua- tion, uses the recent results of Pletner and Abramovich. 3 Because FEmodelsofcontinuousstructurestendtobeverylarge,makingthe synthesis, analysis, and implementation of the controlled structure extremely dife cult, static condensation and/or balanced truncation 8 techniques are employed to reduce the model dimensions. The acoustic power radiated by the structure into the far e eld can be expressed as a quadratic form of the system states. This formsthebasisfor a controllerdesign setup,where the performance specie cations are given by requirements on the allowable acoustic power.The controllersynthesis,whichincludes thesoundreduction criteria, sensor noise, and actuation limits, is stated as a disturbance rejection problem in the H1 framework. Theadvantageofthemethodologyproposedhereinisinitsgener- ality. It is applicable to any linearly elastic structure and permits the application of the latest techniques in state-space multi-input/multi- output control design tools. This study aims at demonstrating the performanceandeffectivenessoftheresultingcontrollerinreducing the sound radiated by a vibrating cylindrical panel.