Abstract
In this paper, we derive a dynamical model for a controllable flexible membrane which is point-actuated by distributed voice coil motors (VCM) connected to it. Besides the modal analysis of the membrane motion, which is the only dynamics discussed in most of related published works treating external pressures as inputs, we integrate the dynamics of the voice coil motors including mechanics and electrical dynamics into the whole system, leaving the electrical signals as inputs to the VCM-actuated membrane system, which is useful for practical application. Also, the multiple-input-multiple-output (MIMO) system is simplified by transforming the dynamics equations into Laplace domain and into a matrix form, which makes the derived transfer functions concise and easier for analysis. It is demonstrated that the eigenmodes of an undamped free-vibration model can be used for approximating the deflection of a forced damping membrane. Furthermore, a reduced-order model is constructed for the flexible membrane system with two voice coil motors symmetrically located on the diameter of the membrane, which is subsequently validated with experimental results obtained on a 2-by-1-VCM-actuated membrane prototype.
