Modeling and control of sound radiation by simply supported and cantilever beam coupled with smart material - Makarenko, Vitaly (Proceedings of National Aviation University (archive), 2007)
In this paper forced vibration of the beam due to bonded piezoelectric patch is considered. When an external excitation is applied to the beam, it starts to vibrate, and the resulting acoustic response is predicted from the analytical model, which is based on Bernoulli-Euler theory of beam vibration. Analytical research of the sound radiation by a finite elastic beam is done for criteria based on minimal total sound power level. Helmholtz equation and inhomogeneous differential equation for beam transverse motion defines the solution to this problem. Such solutions were found for boundary conditions of simply supported and cantilever beams. In order to solve the task two analytical methods were used for simply supported beam. The solutions received by Fourier transform and Green functions approach give the very similar results, thus, proving methods reliability. At the case studies the exerted voltage, phase, location and piezoelectric actuator length are varied in order to establish their influence on noise attenuation.