Piezoelectric structures are widely used in engineering designs including sensors, actuators, and energy-harvesting devices. In this paper, we present the development of a three-dimensional finite element model for simulations of piezoelectric actuators and quantification of their responses under uncertain parameter inputs. The implementation of the finite element model is based on standard nodal approach extended for piezoelectric materials using three-dimensional tetrahedral and hexahedral elements. To account for electrical-mechanical coupling in piezoelectric materials, an additional degree of freedom for electrical potential is added to each node in those elements together with their usual mechanical displacement unknowns. The development was validated with analytical and experimental data for a range of problems from a single-layer piezoelectric beam to multiple layer beams in unimorph and bimorph arrangement. A more detailed analysis is conducted for a unimorph composite plate actuator with different design parameters. Uncertainty quantification was also performed to evaluate the sensitivity of the responses of the piezoelectric composite plate with an uncertain input of material properties. This sheds light on understanding the variations in reported responses of the device; at the same time, providing extra confidence to the numerical model.

The ink drop generation process in piezoelectric droplet-on-demand devices is a complex multiphysics process. A fully resolved simulation of such a system involves a coupled fluid–structure interaction approach employing both computational fluid dynamics (CFD) and computational structural mechanics (CSM) models; thus, it is computationally expensive for engineering design and analysis. In this work, a simplified lumped element model (LEM) is proposed for the simulation of piezoelectric inkjet printheads using the analogy of equivalent electrical circuits. The model’s parameters are computed from three-dimensional fluid and structural simulations, taking into account the detailed geometrical features of the inkjet printhead. Inherently, this multifidelity LEM approach is much faster in simulations of the whole inkjet printhead, while it ably captures fundamental electro-mechanical coupling effects. The approach is validated with experimental data for an existing commercial inkjet printhead with good agreement in droplet speed prediction and frequency responses. The sensitivity analysis of droplet generation conducted for the variation of ink channel geometrical parameters shows the importance of different design variables on the performance of inkjet printheads. It further illustrates the effectiveness of the proposed approach in practical engineering usage.