Electromechanical finite element modelling for dynamic analysis of a cantilevered piezoelectric energy harvester with tip mass offset under base excitations

A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented in this paper. The new contributions for modelling the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretization, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations, and orthonormalised global matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously by other researchers. There are also benefits to presenting the numerical techniques proposed in this paper. First, the proposed numerical techniques can be used for Q1 applications in many different geometrical models, including MEMS power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can result in a very practical design, which avoids direct contact with piezoelectric material because of its brittle nature.Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating single voltage, we introduce the new electromechanical discretization, consisting of the mechanical and electrical discretised elements. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions (FRFs) of the displacement, velocity, voltage, current, and power, including optimal power harvesting. The normalized numerical strain node and eigenmode shapes are also further formulated using numerical discretization. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under a resistive shunt circuit show good agreement with the experimental studies

A smart pipe energy harvester excited by fluid flow and base excitation

This paper presents an electromechanical dynamic modelling of the partially smart pipe structure subject to the vibration responses from fluid flow and input base excitation for generating the electrical energy. We believe that this work shows the first attempt to formulate a unified analytical approach of flow-induced vibrational smart pipe energy harvester in application to the smart sensor-based structural health monitoring systems including those to detect flutter instability. The arbitrary topology of the thin electrode segments located at the surface of the circumference region of the smart pipe has been used so that the electric charge cancellation can be avoided. The analytical techniques of the smart pipe conveying fluid with discontinuous piezoelectric segments and proof mass offset, connected with the standard AC–DC circuit interface, have been developed using the extended charge-type Hamiltonian mechanics. The coupled field equations reduced from the Ritz method-based weak form analytical approach have been further developed to formulate the orthonormalised dynamic equations. The reduced equations show combinations of the mechanical system of the elastic pipe and fluid flow, electromechanical system of the piezoelectric component, and electrical system of the circuit interface. The electromechanical multi-mode frequency and time signal waveform response equations have also been formulated to demonstrate the power harvesting behaviours. Initially, the optimal power output due to optimal load resistance without the fluid effect is discussed to compare with previous studies. For potential application, further parametric analytical studies of varying partially piezoelectric pipe segments have been explored to analyse the dynamic stability/instability of the smart pipe energy harvester due to the effect of fluid and input base excitation. Further proof between case studies also includes the effect of variable flow velocity for optimal power output, 3-D frequency response, the dynamic evolution of the smart pipe system based on the absolute velocity-time waveform signals, and DC power output-time waveform signals

Effect of shunted piezoelectric control for tuning piezoelectric power harvesting system responses – Analytical techniques

This paper presents new analytical modelling of shunt circuit control responses for tuning electromechanical piezoelectric vibration power harvesting structures with proof mass offset. For this combination, the dynamic closed-form boundary value equations reduced from strong form variational principles were developed using the extended Hamiltonian principle to formulate the new coupled orthonormalised electromechanical power harvesting equations showing combinations of the mechanical system (dynamical behaviour of piezoelectric structure), electromechanical system (electrical piezoelectric response) and electrical system (tuning and harvesting circuits). The reduced equations can be further formulated to give the complete forms of new electromechanical multi-mode FRFs and time waveform of the standard AC-DC circuit interface. The proposed technique can demonstrate self-adaptive harvesting response capabilities for tuning the frequency band and the power amplitude of the harvesting devices. The self-adaptive tuning strategies are demonstrated by modelling the shunt circuit behaviour of the piezoelectric control layer in order to optimise the harvesting piezoelectric layer during operation under input base excitation. In such situations, with proper tuning parameters the system performance can be substantially improved. Moreover, the validation of the closed-form technique is also provided by developing the Ritz method-based weak form analytical approach giving similar results. Finally, the parametric analytical studies have been explored to identify direct and relevant contributions for vibration power harvesting behaviours