LONGITUDINAL IMPACT INTO PIEZOELECTRIC MEDIA

Abstract eng:
We consider several elastodynamic impact problems involving one-dimensional (1-D) finite or semiinfinite, elastic or piezoelectric flyers traveling at initial velocity V0 that collide and weld to a finite stationary piezoelectric target backed by a semi-infinite elastic half-space. A combined d’Alembert and Laplace transform method is used to derive new numerically-based solutions for this class of transient wave propagation problems. A Dubner-Abate-Crump (DAC) algorithm [1], modified in [2], is used to invert the analytical Laplace domain solutions to the time domain. A newly derived impact boundary condition applied to solve elastodynamic impact problems in semi-infinite elastic media [3] is extended for use in problems involving piezoelectric impact. We find that the transient impact solutions into lead zirconate titanate (PZT-4) targets obtained using the modified-DAC algorithm compare well with those obtained using both a finite-difference time-domain method, and the commercial finite element code, COMSOL Multiphysics [4]. Unlike many authors who neglect electromechanical coupling in the initially unstressed region ahead of the shock, we consider this effect, which gives rise to the development of a tensile stress wave within the piezoelectric target ahead of the shock. In certain instances, the Final Value Theorem is used to derive an explicit expression for the asymptotic (long-time) displacement current in the target.

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