A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

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.