Flexural vibration patterning using an array of actuators

This paper describes a method to create unique vibration patterns by means of an array of actuators acting on the boundaries of the controlled structure. The method builds, in an iterative process, a black-box model by employing a series of probing external excitation vectors. Once a model has been identified, an optimization stage seeks the dynamic force-vector that generates the best approximation for a specified deformation pattern. Among the obtainable periodic responses are standing or travelling flexural waves of single or multi-frequencies in one or two spatial dimensions, as well as rotating, vortex-like, flexural waves in 2D. The paper describes the force-tuning process through which dozens of actuators can be modified automatically until the response, measured at hundreds of sensed locations, complies with the anticipated response. The excitation that yields the desired response is calculated using an over-determined set of least-squares equations that approximates the inverse of the identified model. The precise iterative tuning process can overcome some nonlinearity, manifested by additional harmonics in the response, by injecting forces that nullify their effect. Methods for wavelength optimization and wave identification in 1D and 2D are also discussed. The proposed tuning method showed good results in numerical simulation and in real world experiments.