A one-dimensional shear-lag model was developed to study the high frequency, dynamic, time-harmonic mechanical behavior of the overlap zone of a piezoelastic patch attached to an elastic host layer and subjected to electric, temperature and moisture excitation. It was interesting to see that the change of the geometry of the overlap zone leads to different solutions after some frequency, which is responsible for different dynamic behavior of the considered structure. Furthermore, the model was involved in an optimization framework (genetic algorithm-GA) in order to find the optimal values of the model parameters of the patch/layer configuration.