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

Melnik R.V.N. and Melnik, K.N.

International Journal of Struct. Stability and Dynamics , 2(2), 241--264, 2002

Abstract:

Many problems in applications of piezoelectric materials are essentially time-dependent, and a conventional treatment of such problems with analytical and 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. We show that the stability conditions for our numerical approximation can be obtained from a discrete conservation law, and be cast in a form similar to that of the classical CFL condition. However, in our case the velocities of wave propagation, participating in the formulation of the stability conditions, are clearly dependent on the pattern of electromechanical coupling. Our discussion here is centered around finite piezoelectric shells of cylindrical shape and we present several results of computational experiments where both weak and strong couplings are discussed.