Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings

Observation spillover can introduce system instability to undamped distributed structural systems. This problem can be prevented via modal filtering using distributed piezoelectric modal sensors which are spatially shaped and convoluted such that they are only sensitive to specific modal mode(s). In this paper, detailed electro-mechanics—sensor mechanics—of spatially distributed piezoelectric shell convolving sensors are analyzed and results presented. It is observed that sensor sensitivity can be classified into two components: (1) the transverse modal sensitivity and (2) the membrane modal sensitivity in which the former is primarily contributed by bending strains and the later is by membrane strains. Design of spatially distributed cosine-shaped convolving sensors for ring structures is proposed and evaluated. Parametric studies suggest that the transverse sensitivity increases and the circumferential sensitivity remained constant when the ring becomes thicker. Both transverse and circumferential sensitivities increase when the piezoelectric layer becomes thicker or with higher piezoelectric constants.