2D-3D interface coupling in the time domain spectral element method for the adhesive layer effects on guided wave propagation in composite plates

A new approach for numerical simulation of the wave propagation in a composite plate is presented in this paper. Problem is realized by the 2D-3D coupled time domain spectral element method. All components used in the simulation are decomposed from each other. A connection between them is guaranteed by the interface elements realized by Lagrange multipliers. With this type of scheme, one can avoid a modelling of all the components by the three-dimensional (3D) spectral elements. In particular, the computation time can be reduced by using two-dimensional (2D) elements for adhesive layer modelling. Otherwise, 3D elements are very inefficient because a convergence of Central Difference Time Integration Method applied for solving an equation of motion is strongly correlated with the size of the smallest element. Numerical calculations were performed for the composite plate modelled by the 3D solid elements with a piezoelectric transducer bonded to the plate by the adhesive layer modelled by 2D shell elements. The simulations were carried out for an adhesive layer of various thickness for the excitation frequency in the range of 50-200 kHz. The presented model was verified by experimental data obtained by the laser vibrometer.