Mikail F. Lumentut

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 orthonormalized 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 applications in many different geometrical models, including micro-electro-mechanical system 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 discretized 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 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.

Analytical techniques for broadband multielectromechanical piezoelectric bimorph beams with multifrequency power harvesting

This paper presents the multifrequency responses of multielectromechanical piezoelectric bimorph beams using a novel analytical model based on the closed-form boundary value method reduced from the strong form of Hamiltonians principle. The reduced constitutive multielectromechanical dynamic equations for the multiple bimorph beams connected in series, parallel, and mixed series-parallel connections can be further formulated using Laplace transformation to give new formulas for power harvesting multifrequency response functions. The parametric case studies based on the change in geometrical structures of the multiple bimorphs with and without tip masses are discussed to analyze the trend of multifrequency power harvesting optimization under resistive load. Nyquist responses based on varying geometrical structures and load resistances were used to analyze the multifrequency power amplitudes in the complex domain. Overall, the trend of system response using multiple tiers consisting of multiple bimorphs was found to significantly widen the multifrequency band followed by increasing the power amplitudes.

Analytical modeling of self-powered electromechanical piezoelectric bimorph beams with multidirectional excitation

Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment, vehicles, aircraft, piping systems, fluid flow, and even external movement of the human body. A portion of the vibrational energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology. The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions, simultaneously or singularly. This paper presents the development of analytical methods for modeling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonians principle and space- and time-dependent eigenfunction series which were further formulated using orthonormalization. The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analyzed using Laplace transforms and frequency analysis to give multi-mode frequency response functions (FRFs). The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.

Electromechanical Piezoelectric Power Harvester Frequency Response Modeling Using Closed-Form Boundary Value Methods

The conversion of mechanical vibration to electrical energy has shown great promise for extending battery life of smart sensor wireless devices for various engineering applications. This paper presents novel analytical models of a piezoelectric bimorph, using the closed-form boundary value (CFBV) method, for predicting the electromechanical power harvester frequency response. The derivations of the coupled electromechanical dynamic response of the transverse-longitudinal (CEDRTL) form based on the CFBV method were developed using the reduced strong form method of the Hamiltonian principle. The equations from CEDRTL can be reduced to give the coupled electromechanical dynamic response of the transverse (CEDRT) form. The electromechanical frequency response functions with variable load resistance were also given in detail using Laplace transformation. The two theoretical studies are compared together and validated with an experimental study. For some cases, when the load resistance approached open circuit, the difference between CEDRTL and CEDRT tended to be more pronounced. Conversely, the CEDRTL and CEDRT models tended to overlap when the load resistance approached short circuit. Nyquist plots are used to demonstrate the shifting frequency and amplitude changes due to variable resistance. Overall, the experimental and CEDRTL model results were very close to each other.

Computational FEA Model of A Coupled Piezoelectric Sensor and Plate Structure for Energy Harvesting

his paper presents a mathematical model of a piezo-plate energy-harvesting scheme. An analytical method is used to generate a finite element model of the coupled piezoelectric sensor element using Love-Kirchhoff’s plate theory. Constitutive equations for a single layer plate element are formulated. The polarisation of the piezoelectric sensor bounded on the upper plate structure is due to ambient vibration exerted on the structure. Forced vibration of the smart structure will create strain energy within the crystalline structure of the piezoelectric material. The resulting electric field generated by the sensor element was mO’Delled using a linear thickness interpolation function and the meshed plate elements were mO’Delled using four-node rectangular elements with three degrees of freedom for each node. The structural eigenmodes and dynamic response of the coupled piezo- plate system were solved by using modal analysis and Newmark-β integration methods respectively. The analysis is demonstrated with both dynamic displacement and electric voltage responses to an applied step force. Further mO’Delling of the smart structure is aimed at maximising the power generation capability.

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 orthonormalized 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 frequency response functions and the 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 optimize 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.

The analysis of a piezoelectric bimorph beam with two input base motions for power harvesting

The exploitation of usable power from vibration environments shows potential benefit for recharging batteries and powering wireless transmission. In this paper, we present a novel technique for simulating the electromechanical cantilevered piezoelectric bimorph beam system with two input base transverse and longitudinal motions for predicting power harvesting. The piezoelectric bimorph beam with tip mass was modelled using the Euler-Bernoulli beam assumptions. The strain fields from transverse bending and longitudinal forms can affect the physical behaviour of the polarity and electric field in terms of the series and parallel connections of the piezoelectric bimorph, in such way that each connection has two vector configurations of X-poling and Y-poling due to input base motions. This situation must be correctly identified to form the piezoelectric couplings. The piezoelectric couplings can create the electrical force and moment of each piezoelectric layer in the mechanical domain. At this point, we introduce a new method of modelling the piezoelectric bimorph beam under two input base-motions using coupling superposition of the elastic-polarity field for predicting power harvesting. The constitutive dynamic equations were derived using the weak form from the Hamiltonian theorem, with Laplace transforms being used to obtain the multi-mode frequency response functions (FRFs) relating the input mechanical vibrations with the output dynamic displacement, velocity and power harvesting. The power harvesting predictions under parallel connection at frequencies close to the fundamental bending frequency demonstrate a possibility of being able to produce around 0.4 mW per unit input base transverse acceleration of 3 m/s2. Furthermore, it is shown that varying the load resistance from 20 k? to 200 k? affects the amplitude of power harvesting as well as resulting in a shift of the first natural frequency from 76 Hz to 79 Hz.

Comparative numerical studies of electromechanical finite element vibration power harvester approaches of a piezoelectric unimorph

Emerging micro-power harvester research using smart material components shows viable self-powered devices capable of capturing mechanical motion and converting it into useful electrical energy that can be further used to supply electrical voltage into rechargeable power storage via a power management electronic circuit. The micro-power harvesters using piezoelectric materials cover a wide range of applications for powering thin film battery technology and wireless sensor systems that can be used to monitor the health condition of machines and infrastructure and biomedical implant devices. This research focuses on the development of a novel numerical direct method technique with non-orthonormality based on the electromechanical vector transformation for modelling the self-powered cantilevered piezoelectric unimorph beam under input base excitation. The proposed finite element piezoelectric unimorph beam equations were formulated using Hamiltonians principle for formulating the global matrices of electromechanical dynamic equations based on the electromechanical vector transformation that can be further employed to derive the electromechanical frequency response functions. This numerical technique was modelled using electromechanical discretisation consisting of mechanical and electrical discretised elements due to the electrode layers covering the surfaces of the piezoelectric structure, giving the single voltage output. The reduced equations are based on the Euler-Bernoulli beam assumption for designing the typical power harvesting device. The proposed finite element models were also compared with orthonormalised electromechanical finite element response techniques, giving accurate results in the frequency domains.

Theoretical study of piezoelectric bimorph beams with two input base-motion for power harvesting

This paper presents a dynamic model of a piezoelectric bimorph beam with a tip mass for low level power harvesting. The piezoelectric bimorph beam is modelled as an Euler-Bernoulli beam with two input transversal and longitudinal base excitations. The strain field due to the longitudinal base input excitation can affect the piezoelectric response parameters although the transverse bending field has most often been considered in the use of the cantilevered piezoelectric bimorph in stimulating polarity and electric field for the energy harvester. The piezoelectric bimorph beam with centre brass shim can be analysed using series and parallel connections depending on the piezoelectric coupling and electric field parameters. The extracted power from the piezoelectric bimorph beam can be used for the powering of electronic storage devices, electronic media and wireless sensors. In this paper, we propose analytical methods for developing constitutive energy field differential equations using virtual work concepts (Weak form) from the interlayer elements of the piezoelectric bimorph beam. Analytical solutions of the constitutive dynamic equations from longitudinal extension, transverse bending and electrostatic fields are solved using Laplace transforms to obtain transfer functions between their relationships.

Theoretical and experimental investigations of a non-linear single degree of freedom electromagnetic vibration energy harvester

There is an increasing need for sensors to be self-powered and hence autonomous in order to operate in remote and inaccessible locations for long periods of time. Amongst the various ambient sources of energy, mechanical vibration is a viable wasted source of energy and can be found in rotating equipment including generators, motors and compressors as well as structures including bridges. The current research deals with developing a novel non-linear single degree of freedom electromagnetic vibration energy harvester using spatial variation of the magnetic field. Initially, approximate linear methods using Laplace transforms and the linear state space methods were considered, where the magnetic field and hence the coupling coefficient were considered as constants. The linear methods were used to derive the frequency response behavior of the system and also its eigenvalues to determine the approximate resonant frequency range. This was followed by more accurate non-linear single degree of freedom electromagnetic energy harvester model simulation considering the spatial variation of the magnetic field and hence a spatially varying coupling coefficient. An experiment of the single degree-of-freedom one-direction electromagnetic vibration energy harvester (SDOF1D EMVEH) prototype was conducted for a range of frequencies to obtain the time domain data to validate against the theoretical data obtained from theoretical time domain simulation.