Distributed transfer function-based unified static solutions for piezoelectric short/open-circuit sensing and voltage/charge actuation of beam cantilevers

Closed-form unified solutions using the distributed transfer functions (DTFs) method are presented for first time static short/open-circuit sensing and voltage/charge actuation of moderately thick beam cantilevers with co-localized surface-bonded piezoelectric patches. For this purpose, smart is divided into three segments, which clamp free sides parts elastic, while middle one made an elastic core sandwiched between two electroded The latter can be different in material properties thickness but should have same length, their widths from host beam. theoretical formulation based on Timoshenko’s first-order shear deformation theory kinematics constitutive equations principle virtual works variational equations. integrate explicitly physical equipotential constraints patches electrodes. balance boundary conditions derived segments independently then connected at interfaces by equilibrium continuity conditions. resulting four problems analytically closed form DTF approach. These validated against only open literature benchmarks having tabulated results or analytical formulas order to avoid curves induced inherent additional deviations. Very good correlations were obtained comparison found reference two-dimensional (2D) plane strain/stress 2D three-dimensional finite element results.