A cubic spline layerwise time domain spectral FE for guided wave simulation in laminated composite plate structures with physically modeled active piezoelectric sensors

A novel theoretical framework is presented enabling enhanced simulation of guided waves generated by piezoelectric actuators in laminated composite plates. A new multi-field multi-physics layerwise theory is formulated for laminated plates with piezoelectric actuators and sensors which captures symmetric and anti-symmetric stress waves. Third-order Hermite splines are employed in the approximation of displacements and electric potential through the thickness. The piezoelectric actuators and sensors are physically modeled though coupled electromechanical governing equations. An explicit time-domain spectral finite element is formulated entailing displacement and electric degrees of freedom at the nodes which are further collocated with Gauss-Lobatto-Legendre integration points. The stiffness, consistent semi-diagonal mass, piezoelectric and electric permittivity matrices are calculated. Furthermore, an explicit time integration scheme is presented for the calculation of the coupled transient electromechanical response including the free sensor response. Numerical guided wave predictions of the developed multi-node time domain spectral finite elements are correlated with well established numerical tools and with experiments conducted on laminated carbon/epoxy plates with active piezoceramic sensor networks. Important effects introduced by the physical presence of the active actuator/sensor system on guided wave propagation, such as wave reflections, mode conversions and sensor signal attenuation, are successfully captured by the developed finite element and correlated and evaluated with numerical and experimental results.