Distributed signal analysis of free-floating paraboloidal membrane shells

Multifarious thin paraboloidal shell structures with unique geometric characteristics are utilized in aerospace, telecommunication and other engineering applications over the years. Governing equations of motion of paraboloidal shells are complicated and closed-form analytical solutions of these partial differential equations (PDEs) are difficult to derive. Furthermore, distributed monitoring technique and its resulting global sensing signals of thin flexible membrane shells are not well understood. This study focuses on spatially distributed modal sensing characteristics of free-floating flexible paraboloidal membrane shells laminated with distributed sensor patches based on a new set of assumed mode shape functions. In order to evaluate overall sensing/control effects, microscopic sensing signal characteristic, sensor segmentation and location of distributed sensors on thin paraboloidal membrane shells with different curvatures are investigated. Parametric analysis suggests that the signal generation depends on modal membrane strains in the meridional and circumferential directions in which the latter is more significant than the former, while all bending strains vanish in membrane shells. This study (1) demonstrates an analysis method for distributed sensors laminated on lightweight paraboloidal flexible structures and (2) identifies critical components and regions that generate significant signals for various shell modes.