PhD Graduate

PhD program:: XXXIII

supervisor: Daniele Dessi
advisor: Antonio Culla

Thesis title: Multidisciplinary modelling and parameter optimization of piezoelectric beams for energy harvesting from vibrations

The present thesis deals with numerical and experimental modelling of energy harvesting from ambient vibrations with piezoelectric materials. The aim of the work is indeed to study the system with a multiphysics approach, describing not only the electromechanical behaviour of the device, but also its interaction with the electric conversion system closing the circuit on the external load. This holistic procedure fills a gap in past literature, in which usually mechanical and electrical description are addressed separately for this kind of devices, thus preventing from a global optimization. Indeed, finding the optimum set of material, geometrical, and electric parameters is fundamental to maximise the overall efficiency and make the power produced by the energy harvester suitable for real-life applications. Moreover, exploring optimal combinations of mechanical and electrical parameters through optimization techniques, or even new configurations, requires efficient numerical tools to evaluate a large number of times the concurrent solutions. Thus, as a second main point of thesis, reduced-order models of the electro-mechanical system are developed here to overcome problems usually occurring when to interfacing computational expensive models, and are experimentally validated to demonstrate their effectiveness. The investigated system, aimed at harvesting energy from basement vibrations, is a cantilever multilayer structure with a unique piezoelectric lamina glued on the supporting material (unimorph configuration, like in many commercial devices), the latter being in charge of several functions: facilitating the device installation, ensuring structural integrity and mechanical stability, and avoiding charge cancellation. The connection between support layer and piezoelectric lamina is supposed to be perfect, without any loss in mechanical energy transmission. Since piezoceramics perform only if working in their narrow resonance bandwidth, the cantilevered plate configuration allows for accurate prediction of its bending frequencies with a simple and efficient layout. Indeed, the investigated device exhibits significant oscillation amplitudes at resonance frequencies under vertical basement vibrations applied at the clamped end. Nonetheless, this layout can be easily adapted for different energy sources, like wind (for fluttering flags) or waves (for wave energy converters). Furthermore, the conversion circuit connected to the device is modelled as well, being indispensable to convert AC voltage produced by the piezoelectric harvester into a DC voltage suitable for electronic devices, and so of primary concern in building realistic energy harvesters. The circuit can also play a role in enhancing the power production, increasing the efficiency of the whole energy chain. Moreover, storage capacitance, fundamental to decouple power demand and production, is introduced. Finally, segmentation of the device electrodes in width or length is explored, showing the benefit in supporting with the conversion circuit functionalities and in avoiding charge cancellation, respectively. Being the latter not a frequent topic in a thesis of the PhD course of Theoretical and Applied Mechanics, the electric system is explained in detail to clarify every aspect of the investigated circuits behaviour. As said previously, the system has been described with a reduced-order model (ROM), allowing an easier data exchange between piezoelectric plate and electric conversion system, and a simple interaction with the optimization algorithm. The piezoelectric plate is described as a multi-layer composite cantilevered Euler – Bernoulli beam model with non-uniform material distribution through its length. Though geometrically approximated, the beam model captures the system response in design excitation conditions. The electromechanical coupling has been introduced in the structural model by using the linear piezoelectric constitutive equations. A tip mass is positioned on the free edge to tune harvester’s natural frequencies 1 Contents with lower excitation frequencies and to enhance oscillations. Although a concentrated mass model is initially considered, the not-negligible mass extension and associated rotational inertia effect are later taken into account to obtain a more accurate natural frequency estimation. Finally, to simulate a non-perfect clamping, yielding in rotation, a torsional spring is added at x = 0. The elastic constant K will be defined by tuning the eigenfrequencies of the structure, analytically found, with those measured in dedicating vibration testing of the simulated device. Both tip mass and yielding clamp have been introduced to better describe possible commercial and custom solutions. By analytically developing Lagrange equations from extended Hamilton’s principle including also electrical potential energy and electric load interactions, a partial differential equation system is found and then projected on the exact bending modes of the structure. Thanks to the analytical determination of the not-uniform beam modes, the developed ROM allows mechanically decoupling modal oscillators and then easily neglecting those modes not contributing to energy production. The set of ordinary differential equations is numerically solved both in MATLAB and Simulink. The electric conversion system is developed in Simulink by Simscape’s blocks, allowing for a simple simulation of voltage rectifier, storage capacitance, Maximum Power Point Tracking system, and resistive load, with an easy data exchange with the ROM model. Results on non-uniform bending modes, and thus resonance frequencies, are then compared with a 3D high-fidelity model of the harvester in Comsol Multiphysics, to show that geometrical and mechanical hypothesis do not undermine the overall consistency of the ROM. To enhance the accuracy of the model, an identification of the torsional spring and modal damping coefficients is carried out. Then, the developed theory is compared with experiments on a prototype of the investigated energy harvester. The device is tested under sinusoidal excitation, imposed by a shaker, finding the acceleration - voltage frequency transfer function of the energy harvester for different resistive load and tip mass conditions. Experimental data and numerical results of the ROM model are found in good agreement and thus validating the developed theory. Finally, some mechanical and electrical parameters describing the main features of the system are chosen as design variables to be optimized so as to maximise the power output. Different optimization procedures are carried out with the patternsearch algorithm in MATLAB, investigating the device sensitivity to parameters change and underlying the crucial co-dependency of mechanical and electrical behaviour, linked together by means of the piezoelectric effect. Moreover, it is demonstrated how an optimization procedure comprehensive of both mechanical and electrical design variables leads to better results than separate and single discipline optimizations. Finally, the optimization problem with duty cycle as design variable is explored, finding a more efficient solution than Open Circuit Voltage MPPT method, and thus, leading the way for further studies on Machine Learning MPPT implementation. As a concluding remark, the combination of a multi-physics efficient and robust ROM model with an optimization approach constitutes the novelty proposed in this thesis to provide a useful tool for improving the design of piezoelectric energy harvesters for real life applications, paving the way for a significant increase in the device performances.

Research products

  • 11573/1191107 - 2018 - Energy harvesting from waves using piezoelectric floaters (04b Atto di convegno in volume)
  • 11573/1336015 - 2018 - Performance testing of piezoelectric energy harvesting for extracting energy from vibration (04b Atto di convegno in volume)
  • 11573/1336042 - 2019 - Performance testing of a piezoelectric device for extracting energy from vibrations (04b Atto di convegno in volume)
  • 11573/1336047 - 2019 - Energy harvesting from waves using tandem floaters connected by piezoelectric beams (04b Atto di convegno in volume)
  • 11573/1564972 - 2021 - Multidisciplinary modelling and parameter optimization of piezoelectric beams for energy harvesting from vibrations (07a Tesi di Dottorato)

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