A coupled efficient layerwise finite element model for free vibration analysis of smart piezo-bonded laminated shells featuring delaminations and transducer debonding

Abstract

This paper presents a computationally efficient multifield finite element (FE) model for accurate analysis of smart composite and sandwich shells equipped with piezoelectric patch actuators and sensors, featuring multiple delaminations and transducer debonding. It employs a facet shell element with four physical nodes and one electric node, based on the third order zigzag theory approximations for displacements and a piecewise quadratic through-thickness variation for the electric potential. A hybrid point-least squares method recently proposed by the authors is extended to impose the condition of continuity of the nonlinear displacement field at the delamination, debonding, and patch fronts. The methodology is generic for multiple patch transducers, delaminations, and debonding, occurring at any arbitrary interface and in-plane locations. The model shows excellent accuracy in comparison with the coupled full-field 3D FE solutions, for the natural frequencies and complex global, local and hybrid mode shapes of delaminated smart composite shells and soft-core sandwich plates, with partially debonded actuators and sensors. The developed model will be of immense use for the design of active vibration control and structural health monitoring strategies for smart laminated shell-type structures featuring such damages.