On the design of modal actuators and sensors

Modal actuators and sensors may be used to excite or measure either single modes or combinations of modes. In beam structures they may be implemented using either discrete transducers or continuous, distributed transducers. This paper determines the transducer gains to obtain given modal responses. For discrete transducers, when there are more transducers than modes of interest, this generally results an underdetermined problem. Side constraints, either by choosing a subset of transducers, or ensuring orthogonality to higher modes, make use of this redundancy. For distributed transducers this paper introduces the idea of approximating the width of the transducer using the underlying finite element model shape functions. The transducers may then be designed using a discrete model, and the shape recovered by using the shape functions. The side constraint of minimising the curvature of the transducer shape is introduced to ensure that the resulting shape is as simple as possible. A clamped-clamped beam example is used to demonstrate the effectiveness of the proposed methods, and also to demonstrate the errors introduced for non-proportionally damped structures.