Extended Bond Graph Reticulation of Piezoelectric Continua

Abstract

Extended Bond Graph (EBG) reticulations for general and linear piezoelectric continua are developed in this paper. The EBG formulation is especially advantageous for modeling the distributed coupled electromechanical effects of these materials and for combining this representation with other discrete models. The electromechanical coupling effects are represented by a multiport C-element for the general piezoelectric material. For linear constitutive properties, the coupling effects are represented by two multiport C-elements; one for the strain energy and the other for the capacitance storage, and a transformer that converts the power flows between the two energy domains. Details of the developments of the general formulation and of the specific models are provided. This work represents the first application of EBGs to electric fields.