Shaping distributed piezoelectric self‐sensing layers for static shape control of smart structures

Abstract

AbstractIn the present paper, spatially distributed self‐sensing layers with an axially varying intensity of piezoelectric activity are studied within the context of an electromechanically coupled theory for plane flexural deformations of slender smart beams. The main purpose of our derivations is to find shape functions for a piezoelectric self‐sensing layer such that quasi‐static deflections due to known external forces can be exactly annihilated by the piezoelectric actuation. It is shown that shape functions corresponding to the bending moment distributions due to these external forces do represent solutions of this static shape control problem. In the context of self‐sensing layers, the shaped actuator can be also used as a collocated sensor, which is discussed in detail in the present paper. If the span‐wise distribution of the external forces is not known, it may be useful to design self‐sensing layers with the purpose of controlling the deflection at specific locations of the beam axis by means of shape functions with a particularly simple form. Such a concept is also presented. Furthermore, we make reference to so‐called nilpotent shape functions which are neither able to produce actuating effects nor to measure deflections of the beam. The presented theoretical findings are demonstrated for one‐span beams with various boundary conditions.