Diaz I., Pereira Gonzalez E., Lopez Cela J., Feliu Batlle V.

This work presents an optimization criterion and its experimental validation for the positioning of strain sensors on thin plates considering bending and torsional modes simultaneously. The development of smart structures has provided new ways of measuring and reducing vibrations. In that way, an efficient positioning is an important issue in active damping of vibrations in flexible structures. The optimal placement of sensors has been addressed by a great number of researchers. For instance, the placement of strain sensors is found in some works by determining the position sensitivity function of each controlled mode, which is proportional to the sum of the deformation in two directions. Others address the problem of sensor positioning using modal and spatial controllability and observability measure. The mentioned methods connect the controllability and observability problems. Unlike these references, we propose a criterion that takes into account the longitudinal strain in three directions and places the sensors where the measured variables are best observable. To this end, the von Mises equivalent strain, which is a unique representative value of a three-dimensional strain state, is utilised to develop a criterion that detects the optimal locations for the sensors to monitor bending and torsional modes. The aim is to find an efficient placement of strain sensors in order to maximise the observability of the first N modes of vibration by using the von Mises equivalent strain. The sensors should be placed at points where this equivalent strain presents significant values for the dynamic plate behaviour defined by the first N modes. Numerical and experimental validation of the optimal placement is provided on a cantilever thin plate with triaxial rosettes of strain gauges by impact, harmonic and transient response analyses.