A time domain spectral layerwise finite element for wave structural health monitoring in composite strips with physically modeled active piezoelectric actuators and sensors

A new explicit, two-dimensional plane strain, time domain spectral finite element is developed to enhance the simulation of guided waves generated by active piezoelectric sensors in laminated composite strips. A new multi-field layerwise theory is formulated for composite laminates with piezoelectric actuators and sensors which captures straight-crested symmetric and anti-symmetric Lamb waves. Third-order Hermite polynomial splines are employed for the approximation of displacements and electric potential through the thickness, and the piezoelectric actuators and sensors are physically modeled through coupled electromechanical governing equations. A multi-node finite element formulation is presented entailing displacement and electric degrees of freedom at nodes collocated with Gauss–Lobatto–Legendre integration points. Stiffness, diagonal mass, piezoelectric, and electric permittivity matrices are described, and the coupled transient electromechanical response is predicted by a properly formulated explicit time integration scheme. The numerical results of a nine-node time domain spectral finite element are correlated with the reported numerical results and with measured Lamb wave data generated by piezoceramic active sensor pairs in carbon/epoxy plate strips. Important effects introduced by the stiffness and mass of the active actuator/sensor system on Lamb wave propagation are captured by the developed finite element and quantified.