Research on Volume Displacement and Sound Radiation Sensitivity for a Vibrating Beam
|School||Nanchang University of Aeronautics and|
|Course||Mechanical and Electronic Engineering|
|Keywords||volume displacement PVDF sensor ADM sound radiation sensitivity|
In recent years medium and low frequency noise control increasingly becomes achallenging research topic. Active structure acoustic control (ASAC) is considered to bethe most effective method to solve this problem at present. It has the advantage of moreeffectively controlling the structural acoustic radiation at the low frequency. Errorsensing strategy is one of the key rings in the active structural acoustic control systemand volume displacement cancellation is an effective error sensing strategy.In order to obtain the volume displacement of a beam with arbitrary boundary, anew solution to the problem of finding the shape of piezoelectric modal sensors for thebeam is proposed. Based on the ADM and employing some simple mathematicaloperations, the closed-form series solution of the second spatial derivative of the modeshapes of a beam with arbitrary boundary can be determined. Then the shapes of thedesigned PVDF modal sensors are obtained by modal method, in which the outputsignal of the designed sensor is proportional to the volume displacement of the vibratingbeam.Then the local volume displacement of a cantilever beam is obtained by a PVDF(polyvinylidence fluioride) array. An array of rectangular PVDF patches attached on thelocal surface of the beam is used as sensors. The output signals of the PVDF patches aremultiplied by appropriate weights so that the weighted combinations of the outputsdirectly lead to the corresponding local volume displacement of the beam. It is shownthat the weight of every PVDF patch sensor is independent of the external excitation.In order to research the sound radiation sensitivity of a vibrating beam, the soundradiation link is processed by sound radiation mode model, the vibrating velocity isexpanded with sound radiation mode, the problem of solution sound radiationsensitivity is transformed to the problem of solution the derivative of structure velocitywith respect to design variables, then the structure vibrating response is solution byusing FEM vibrating model deal with structure velocity link, eventually the problem ofstructure sound radiation sensitivity is transformed to the problem of solution thesensitivity of stiffness matrix,damping matrix and mass matrix of the structure.In order to validate the above-mentioned volume displacement acquisition of acantilever beam by a PVDF array at low frequency, one experiment is conducted withthe cantilever beam as the subject to measure the amplitudes of the volume displacement, the measurement results of PVDF and the measured accurate value byaccelerometers. The experimental results show the feasibility of using PVDF as theerror sensors.