Energy Harvesting is a promising solution for powering Structural Health Monitoring (SHM) systems since various mechanical energy sources are generated by aircraft. Today, the main technique to harvest energy consists of using a specific conversion device to provide power to the SHM system. In this paper however, a novel technique to obtain a self-powered SHM system for aeronautical structures is proposed. This SHM system aims to have a double functionality: it will carry out classical SHM tasks using piezoelectric transducers bonded onto the aircraft structure and will also be fully autonomous since the same transducers will convert the mechanical vibrations of the structure into electrical power. Using a bonded piezoelectric transducer to harvest energy will also bring wideband frequency energy harvesting capability. This autonomous system using a unique transducer being particularly innovative, the objective of this paper is to provide a complete Bond Graph model of the energy harvesting process in order to allow the optimisation of its performances. This approach is well-suited to monitor the power and energy transfer carried out during the process since it takes into account the interaction between multiphysics systems, here the electrical and mechanical domains in terms of power and energy variables. Consequently, each part of the energy harvesting, i.e. the mechanical vibration of the host structure, the vibration within the SHM energy harvester volume, the piezoelectric electromechanical conversion and the terminal electric load have been modelled analytically using this Bond Graph approach. Then, each submodel has been verified with a baseline Finite Element model. Good agreements have been found and it has been possible to carry out an estimation of the power harvested by the SHM energy harvester for a given mechanical excitation using this innovative complete analytical Bond Graph model.