Stability of Numerical Discretizations in Modelling Vibrational Characteristics of Piezoelectric Cylindrical Shells

Many problems in applications of piezoelectric materials are essentially time-dependent, and a conventional treatment of such problems with analytical or semi-analytical techniques based on the analysis of harmonic oscillations become inadequate in those cases where a complete dynamic picture of electromechanical energy transfer is required. For such situations we have developed an efficient explicit numerical methodology allowing us to compute dynamic electromechanical characteristics of piezoelectric structures and devices under various loading conditions. In this paper we demonstrate that the stability conditions for our numerical approximation can be obtained from a discrete conservation law, and can be cast in a form similar to that of the classical CFL condition. However, in our case the velocities of wave propagations, participating in the formulation of the stability conditions, are clearly dependent on the pattern of electromectromechanical coupling. Our discussion in this paper, including computational examples, is centred around finite piezoelectric shells of cylindrical shape.