Microscopic control actions for distributed LaSMP patches laminated on paraboloidal thin shells

Abstract

Paraboloidal shells are widely used for antennas, reflectors, optical mirrors, etc. LaSMP is a novel light-actuated shape memory polymer (LaSMP) with dynamic Young’s modulus which can act as actuators. This study focuses on the microscopic control actions and distributed control effectiveness of LaSMP patches laminated on a paraboloidal thin shell. With the light-induced strain model, the dynamic governing equations of paraboloidal structures laminated with LaSMP patches are established. Based on an assumed mode shape function for the simply-supported paraboloidal thin shell, the total control force and its contributing components resulting from bending control moments and membrane control forces in the meridional/circumferential directions are defined respectively. In case studies, distributed control actions of two kinds of paraboloidal thin shells with different geometrical parameters, i.e. deep and shallow, are evaluated. The distributed control forces, components, normalized control forces, as well as the effects of shell and LaSMP thickness are evaluated for the first three natural modes by varying laminated LaSMP patch locations in the meridional direction. The results suggest: (a) the magnitude of control actions and normalized control actions are affected by the actuation location and vibration modes; (b) the moment-induced control actions dominate the total control forces; (c) there are optimal LaSMP actuator locations on the simply-supported paraboloidal thin shell with the maximal control actions per unit area for each natural mode; and (d) the control forces increase with the increasing of LaSMP thickness and decreasing of shell thickness.