Modal detection for non-uniform thickness beams using continuous strain sensors and a strain-energy-based orthogonality condition

Modal detection of regular-shape uniform thickness beams and plates using polyvinylidene fluoride (PVDF) sensors has been widely reported, especially related to active structural acoustic control. Here the application of PVDF sensors to a simply supported non-uniform thickness beam for modal detection is considered. As traditional kinetic-energy-based orthogonality conditions, based on displacement or temporal derivatives, are not applicable a new (approximate) strain-energy-based orthogonality condition is developed. Modal sensors are designed using one-dimensional (1-D) models of the beam and PVDF sensor, and then their performance is fully modelled in 2-D. Generally good modal discrimination is found but errors were significant for the two lowest modes. The effects of modelling and implementation errors were studied. An experimental modal sensor produced good agreement. Comprehensive details of the experimental system are given, especially with respect to the preparation of the PVDF sensors. Finally, the disadvantages of using strain sensors over other types of sensing are discussed, and it is shown that the new orthogonality condition cannot be extended to non-uniform plates.