Physics-based computational models play a key role in the study of wave propagation for structural health monitoring (SHM) and the development of improved damage detection methodologies. Due to the complex nature of guided waves (GWs), accurate and efficient computation tools are necessary to investigate the mechanisms responsible for dispersion, coupling, and interaction with damage. In this paper, a fully coupled electromechanical elastodynamic model for wave propagation in a heterogeneous, anisotropic material system is developed. The final framework provides the full three dimensional displacement and electrical potential fields for arbitrary plate and transducer geometries and excitation waveform and frequency. The model is validated theoretically and proven computationally efficient. Studies are performed with surface bonded piezoelectric sensors to gain insight into the physics of experimental techniques used for SHM. Collocated actuation of the fundamental Lamb wave modes is modeled over a range of frequencies to demonstrate mode tuning capabilities. The effect of various actuation types commonly used in numerical wave propagation models on Lamb wave speed are studied and compared. Since many studies, including the ones investigated in this paper, are difficult to perform experimentally, the developed model provides a valuable tool for the improvement of SHM techniques.