An analytical solution for the vibrational response of stepped smart cross-ply laminated composite beams with experimental validation

This paper investigates the vibrational behaviour of smart orthotropic cross-ply laminated stepped beams. Specifically, an analytical closed-form model based on the first-order shear deformation theory (FSDT) is developed to consider a step change in laminate configuration along the beam axis due to integration of a piezoelectric patch for actuation applications. The 6th order governing equation within each element, along with appropriate continuity, equilibrium, and boundary equations, were formulated. State-space approach was utilised to find the beam's response to piezoelectric sinusoidal actuation. Results of the natural frequency analysis were compared with results in the literature and finite element modelling. An experimental investigation examined the accuracy of the analytical method to find the natural frequencies and forced vibrational response of a smart carbon-fibre/polyetheretherketone (PEEK) cantilever beam. Comparisons demonstrate that the provided closed-form method is capable of efficiently predicting the free and forced vibrational behaviour of smart stepped laminated composite beams with high accuracy.