A strip speaker using the traveling bending wave on a beam controlled by three actuators
Introduction
The panel speaker, which radiates sound from a vibration field over flat or curved plates, has been proposed to supplement the conventional moving-coil loudspeakers. Because the panel is usually thin, it is undoubtedly advantageous from the viewpoint of the occupied volume compared with cone-type moving-coil loudspeakers. The design concept of the panel speaker has various potential applications in the age of the Internet-of-Things (IoT) because the technology could be extended to use in machine coverings and other built-in structure surfaces. However, due to its finite structure, the vibrating panel is unavoidably afflicted by the well-known problem of multi-modal behavior, which causes severe peaks and troughs in the radiated sound spectrum, resulting in low sound quality.
To improve the acoustic performance by suppressing the multi-modal superposition effect, commercial panel speakers usually adopt passive measures to modify the physical properties of the plate. To this end, materials with a low density, high elastic modulus, and good damping are used to induce a smearing effect among adjacent modes, but such measures are only applicable for small panel sizes or narrow-band operation [1]. Alternatively, one can shift the resonant frequencies out of the frequency band of interest by attaching additional masses or installing a porous layer in front of the speaker [2], [3], [4]. Despite the partial success of passive treatments for controlling vibration modes, the applicable frequency range is limited to a narrow band, and fine-tuning is needed.
Active control methods, which use additional actuators to control the modal behavior of plate vibration, have been proposed to enhance the acoustic performance of panel speakers without physical modifications. The plate is usually controlled to evoke the first mode shape only, which is the most efficient for sound radiation in the frequency range of interest [6]. Alternatively, one can generate a vibration field on the plate with a specified, or rendered, distribution of amplitude and phase that is analogous to a virtual speaker–baffle system by superposing the mode shapes appropriately [5], [6], [7], [8], [9], [10]. An alternative control principle exploits the fact that an active sink can be realized if a feedback control algorithm is applied to cancel the incident and reflected bending waves at a point in the plate [11]. Based on this fact, adaptive control methods for the vibration of beam or panel structures have been proposed to eliminate one of the propagating wave components under ideal boundary conditions [12], [13], [14], [15], [16], [17], [18]. However, the boundary conditions of the structure are difficult to determine in practical situations. To apply this control principle to a panel speaker with generally unknown boundary conditions, it is necessary to adopt measured frequency response functions [19]. This converts the panel boundary to a connected line of control actuators on the panel periphery, and studies show that this arrangement can be transformed to a virtually anechoic termination by the precise determination of the control gains of the control actuators. When using the modal control method, the number of modes to be controlled is restricted by the number of actuators; in contrast, the traveling-wave control method (TCM) can control all of the modal contributions. Therefore, the TCM enables vibration control, and subsequently sound radiation control, for a wider frequency band than the modal control method. Notwithstanding the great improvement in the acoustic performance of panel speakers achieved with the TCM, an inconveniently high number of actuators are still required to control the panel structure.
In this study, a thin-beam speaker, called a strip speaker, which is controlled by the TCM, is proposed to achieve the economical usage of actuators while guaranteeing the desired acoustic quality. Compared with the panel structure, the advantage of the one-dimensional vibration field on the thin beam is to reduce the control difficulty and the number of actuators. Fig. 1 shows the conceptual design of the strip speaker using three actuators. A primary actuator is placed at the middle of the beam, and two control actuators are located at each end of the beam, which is symmetrically located about the primary actuator position. It is noted that the figure illustrates the beam as a transparent one to show the actuators concealed inside of the backing cavity. The beam is fixed at both ends, and a tiny gap is provided to secure the free oscillating motion along the side edges. The tiny gap in the side edge suppresses the amount of interference between the radiated sound in the frontal and rear faces of the beam. A backing cavity in the rear side of the beam prevents the actuator motion from interfering with an external object and provide some reactivity. The desired vibration field is the traveling bending wavefield, analogous to a wave propagating on an infinite beam, which can be achieved by nullifying the reflected waves at either end of the beam. An inverse problem is derived by constructing a transfer matrix between the input voltage of the control actuators and the coefficient of the reflected bending waves. The control gain of the actuators is obtained as the inverse solution to eliminate the reflected waves at the edges. A simulation is conducted to investigate the control performance and appropriate location of the control actuators, followed by an experiment to validate the predicted results.
Section snippets
Control of bending wave field on a beam using two actuators
For suppressing the wave reflection at the boundary of a thin structure, the wave control requires the full information of the propagating and non-propagating wave components in the perpendicular direction to each edge of the structure. For a rectangular plate, one should consider the bi-directional propagation of the decomposed bending waves [19]. The best position for the control actuators is near the edges of the plate, so the number of the actuators increases significantly with the area of
Simulation condition
Fig. 4 illustrates a 2-mm thick aluminum test beam with a size of 315 (lx) 40 (ly) mm2. The density is ρ = 2700 kg/m3, Young's modulus E = 60 GPa, Poisson's ratio ν = 0.3, and loss factor η = 0.01. The calculated quasi-longitudinal wave speed is = 4714 m/s. The clamped boundary conditions are imposed to either end, from which the modal characteristics of the beam can be defined analytically [32]. The resonance frequency of the identical actuators is assumed as 100 Hz, and it is also
Test set-up
Aluminum and acrylic beams of 2-mm in thickness are prepared in the experiment. The dimension and material properties of each beam are the same as the simulation. Either end of the beam is fixed to the steel frame. The moving-coil type exciter (Tectonic, TEAX14C02-8) is selected for the primary and control actuators. It has a size of 37 20 10 mm3, 13 g in weight, 8 Ω in electric impedance, and 100 Hz in the fundamental resonance frequency. In accordance with the preceding methodology, the
Conclusions
The traveling wave control method is applied to convert a beam strip into a hi-fi speaker to faithfully radiate the desired sound. A total of three actuators are used for vibration control: the primary actuator located at the middle of the beam to inject dynamic energy, and two control actuators positioned near each end to suppress the reflected waves. The resonance response of the beam is suppressed by applying the TCM. The controlled vibration field has a phase distribution that changes
CRediT authorship contribution statement
Ki-Ho Lee: Data curation, Methodology, Software, Validation, Formal analysis, Investigation, Visualization, Writing - original draft. Jeong-Guon Ih: Conceptualization, Investigation, Methodology, Resources, Supervision, Project administration, Funding acquisition, Writing - review & editing. Donghyun Jung: Resources.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was partially supported by the NRF grant (No. 2020R1I1A2066751) and Samsung Electronics Co.
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