Control of sound radiation from a panel speaker using an actuator array

Abstract

The panel speaker, which radiates sound from a bending wave field on flat or curved plates, has been proposed to supplement the conventional dynamic loudspeakers. Owing to the thin layout, the prominent advantage is the small occupied volume for the various applications to machine coverings and other built-in structure surface in the age of the Internet-of-Things (IoT). When the plate is excited by an electro-mechanical actuator, the bending wave propagating from the driving point is reflected at the plate edges and forms a reverberant field on the entire plate, which causes a modal behavior. Because of distinct modal behavior involved even in the low- to mid-frequency vibration of the plate, the radiated sound possesses severe spectral fluctuations, which results in poor sound quality. The purpose of this study is the development of the control strategy and the control layout for several types of panel speakers to improve the radiated sound quality. As the control strategies, two active methods are considered: the mode control method (MCM) to adjust the modal participation in the vibration field and the traveling-wave control method (TCM) to control the propagating bending waves. While suppressing the other modes, the MCM is employed to excite the 1st mode shape only in a frequency range of interest, which is the most efficient for sound radiation. In contrast, the objective of the TCM is to eliminate the bending waves reflected from the edges, which avoids the modal excitation fundamentally. The proper gains of the actuators are obtained by applying the inverse technique to the transfer matrix relating the input gain of actuators and the resultant vibration field. The MCM employs transfer mobility between the actuators and the field points distributed on the plate surface. On the other hand, the TCM derives the transfer function between the actuators and the wave components decomposed from the bending wave field. The characteristics of each method are investigated by using the wave field normalized by the physical property and dimension of the panel speaker. The control results predicted via the simulation show that both control methods suppress the structural resonances resulting in a smooth sound spectrum. It is found that, in using the same actuator array, the TCM has a much wider effective frequency range because the number of actuators restricts the number of modes that can be controlled by the MCM. The TCM converts the driving-point mobility of the primary actuator into that of an infinite beam or plate. It means that the boundary of the structure is changed to the anechoic termination without the wave reflection, or one can say that the panel structure becomes an infinite one virtually. When it comes to the shape of the panel speaker, a beam with a one-dimensional vibration field possesses many advantages in vibration control. Compared with the two-dimensional plate, even though the sound radiating area becomes small and it seems the radiated power becomes small, the number of actuators and corresponding control difficulty is reduced significantly and, in fact, the area reduction effect does not exist owing to the advantage of using the traveling wave. The TCM employed to control the beam requires only three actuators, and its precise prediction of the controlled field makes it easy to achieve the desired acoustic performance. Except for the simple rectangular beam and plate, a closed circular ring and a circular plate are also tested in using the TCM and the MCM, respectively, considering the vibrational characteristics of each structure. As a result, this study suggests the design guideline of the panel speaker controlled by the actuator array based on the properties of the control methods, material, and the dimension of the radiator structure.