Mikail F Lumentut

The piezoelectric device, connected to the circuit interface and subjected to the consecutive periodic rotary magnetic excitations, is presented for an energy harvesting application. The proposed system consists of a cantilevered piezoelectric plate structure with multiple attached magnets, along with a revolving disc carrying a single magnet. This study sets out to explore the primary development of explicit analytical and finite element formulations that consider magnetic coupling and time-delayed magnetic response. The two theoretical models are used to formulate the optimal power output frequency response equations using Fourier analysis. Due to the asymmetrical magnet locations and time-delayed magnetic response, the consecutive dynamic excitations periodically occur, resulting in dipole-dipole interactions in both spatial and temporal conditions. Consequently, the piezoelectric plate structure, designed to operate higher vibration modes, exhibits a predominant effect of frequency up-converting energy harvesters. The previous work is initially validated by using a single magnetic excitation and examining both cases with and without time-delayed magnetic responses. The analyses of broadband optimal power generations are based on Fourier's harmonic numbers and frequency domains, including time-tracking magnetic excitations. Finally, various case studies are presented to examine the effects of different physical components, such as magnet numbers, magnet locations and masses, piezoelectric materials and thicknesses, and locations of electrode segments.

The dynamics of elastic cantilevered smart pipes conveying fluid with non-uniform flow velocity profiles is presented for optimal power generation. The Navier-Stokes equations are used to model the incompressible flow in the circular smart pipe, and flow profile modification factors are formulated based on the Reynolds number and Darcy friction factor. The coupled constitutive dynamic equations, including the electrical circuit, are formulated for laminar and turbulent flows. Due to viscosity in a real fluid, non-uniform flow profiles induce dynamic stability and instability phenomena that affect the generated power. The system consists of an elastic pipe with segmented smart material located on the circumference and longitudinal regions, the circuit, and the electromechanical components. The modified coupled constitutive equations are solved using the weak form extended Ritz method. For faster convergence, this model is reduced from the exact solution of the pipe structure with proof mass offset. Initial validation with a uniform flow profile from previous work is conducted. With increasing flow velocity, the optimal power output and their frequency shifts are investigated both with and without the flow profile modification factors, to identify the level of instability. Further parametric studies with and without flow pulsation and base excitation are given.

A piezoelectric device connected to the standard interface circuit is proposed for harvesting energy by inducing the mixed resonant modes of vibration under the two-point rotary magnetic plucking. It consists of a piezoelectric cantilever beam attached to a tip magnet and a second magnet placed on the middle of the beam. Both magnets are excited by another two magnets aligned radically and attached to a rotating host. The two impulsive forces from these magnets are made in opposite directions for the ease of inducing the second resonant mode. As a result, the harvester device exhibits the pronounced broadband energy harvesting which can not be achieved by the conventional design based on the one-point magnetic plucking for exciting a single resonant mode. The analysis is based on the Fourier decomposition of magnetic impulsive forces for realizing the phenomenon of frequency up-conversion. In addition, the estimate of harvested power is analytically derived based on using the equivalent load impedance which is originally proposed for analyzing harvester arrays. The result shows that the theoretical prediction agrees well with the experimental observation. Further, the rotary frequency response exhibits the remarkable feature of broadband energy harvesting as the output power is increased up to 2500% higher than that in the off-resonance region of the setup allowing plucking only on the tip magnet.

This paper focuses on the primary development of novel analytical and numerical studies for the smart plate structure due to the effects of point mass locations, dynamic motions, and network segmentations. Instead of the alternative capabilities in active and passive control systems, the technical application of the present work can also be found in the energy harvesting system. The simplified theoretical studies have shown the simultaneous derivations with full variational parameters. In particular, these parameters consist of the mechanical and electromechanical systems, the mixed series-parallel electrode segment connection, and the harvesting circuit. The mechanical system parameters include elasticity with stress-strain relation, internal damping stress, air damping, and dynamics of the integrated physical system. The electromechanical system parameters include electrical displacement, electrical stress and electric-polarity field of the piezoelectricity. For the analytical approach, the governing equations of motion based on the Gram-Schmidt iterative process have been derived using the extended Hamiltonian principle and Ritz method-based weak form system. For validation, the elec-tromechanical finite element equations reduced from the extended Lagrange's equations have been developed using electromechanical discretisation and coupling transformation techniques. As a result, the two theoretical models have shown distinct frequency response equations for the dynamic solutions of the integrated physical system. In parametric studies, the two theoretical models of the smart plates with variable geometrical aspect ratio and different locations of point mass are discussed, giving good agreement. The strain mode analysis is utilised to identify the shape patterns at the region of the smart plate due to the change of strains. As a result, it can affect the electric power productions at the frequency domain. At certain cases, the appearance of asym-metric strain mode shapes may occur, resulting in the electric power reductions. To alleviate such condition, the activation of arbitrary electrode segments using the network connection can be implemented. Moreover, the smart structural model with different point mass locations is also subjected to the base excitation and the dynamic force. The proposed technique can adaptively and accumulatively generate the optimal power outputs and shift the resonance frequencies. All results of the parametric studies quantitatively show the dynamic system behaviours.

This paper presents an adaptive dynamic analysis of discontinuous smart beam energy harvester systems using a shunt vibration control. The smart structural systems, connected with the shunt and harvesting circuit interfaces, consist of the three types of non-homogeneous structural combinations with different piezoelectric materials. The constitutive coupled dynamic equations with full variational parameters are reduced using the charge type-based Hamiltonian mechanics and the Ritz method-based weak-form analytical approach. Unlike the conventional techniques, this study elaborates the appearance of the two resonances with a wider shift on a specific range of the optimal power output frequencies, using only the first mode of the smart structural systems. Moreover, the two-equal peak of the optimal response may potentially occur to appear not only at the first resonance, but also at the second resonance. This intrinsically represents strong electromechanical effect, depending on the properties and thicknesses of piezoelectric materials and the circuit parameters. The accuracy of the theoretical method is tested using the iterative computational process of the optimal frequency response with full coupled electromechanical system parameters. Further details of the parametric studies are discussed to show the prediction of the energy harvesting with the ability of tuning an adaptive frequency response.

This paper presents the techniques for formulating the multiple segmented smart plate structures with different circuit connection patterns using the electromechanical finite element dynamic analysis. There are three major contributions in the proposed numerical studies. First, the electromechanical discretization has been developed for generalizing the coupled system of Kirchhoff's smart plate structures with circuit connection patterns. Such constitutive numerical models reduced from the extended Lagrange equations can be used for the physical systems including, but not restricted to, the multiple piezoelectric and electrode segments. Second, the multiple piezoelectric or electrode segments can be arranged electrically in parallel, series, and mixed series–parallel connections with the on–off switching techniques where the electrical outputs of each connection are further connected with the standard AC–DC circuit interfaces. Third, the coupling transformation technique (CTT) has been introduced by modifying the orthonormalized global element matrices into the scalar form equations. As a result, the multimode frequency response function and time-waveform signal response equations are distinctly formulated for each circuit connection. Further parametric numerical case studies are also discussed in this paper. The benefit of using the circuit connection patterns with the on–off switching techniques is that the studies can be used for an adaptive vibration power harvester.

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.

Acta Mechanica, 2017, DOI: 10.1007/s00707-016-1775-2

This paper presents an adaptive power harvester using a shunted piezoelectric control system with segmented electrodes. This technique has spurred new capability for widening the three simultaneous resonance frequency peaks using only a single piezoelectric laminated beam where normally previous works only provide a single peak for the resonance at the first mode. The benefit of the proposed techniques is that it provides effective and robust broadband power generation for application in self-powered wireless sensor devices. The smart structure beam with proof mass offset is considered to have simultaneous combination between vibration-based power harvesting and shunt circuit control-based electrode segments. As a result, the system spurs new development of the two mathematical methods using electromechanical closed-boundary value techniques and Ritz method-based weak-form analytical approach. The two methods have been used for comparison giving accurate results. For different electrode lengths using certain parametric tuning and harvesting circuit systems, the technique enables the prediction of the power harvesting that can be further proved to identify the performance of the system using the effect of varying circuit parameters so as to visualize the frequency and time waveform responses.

Acta Mechanica, vol. 228 (2), pp 631–650, 2017

This paper discusses, compares and contrasts two important techniques for formulating the electromechanical piezoelectric equations for power harvesting system applications. It presents important additions to existing literature by providing intrinsic formulation techniques of the harvesting system for the two different electromechanical dynamic equation-based voltage and charge-type systems associated with the standard AC–DC circuit interface developed using the extended Hamiltonian principle. The derivations of the two analytical methods rely on the fundamental continuum thermopiezoelectricity concepts of the electrical enthalpy energy and Helmholtz free energy. The benefit of using analytical charge-type modelling is that the technique shows more compact formulation for developing simultaneous derivations by coupling the mechanical and electromechanical systems of the piezoelectric devices and electronic system so that the frequency response functions (FRFs) and time wave form systems can be formulated. On the other hand, the analytical voltage-type modelling is obviously convenient but can show tedious derivation process for joining with the electronic circuit part. To tackle this situation, the analytical voltage type with mechanical and electromechanical forms of the piezoelectric structure can be derived separately from the electronic system where they can be combined together after applying further derivations to formulate the FRFs. In this paper, the two analytical techniques also show particular benefit and even further development of how to model the power harvesting scheme with the combinations of piezoelectric structure and electronic system. Moreover, validations of the two analytical methods show good agreement with previous authors’ electromechanical finite element analysis and experimental works. Further parametric electromechanical energy harvesting behaviours have been explored to study the system responses.

This paper focuses on the primary development of novel numerical and analytical techniques of the modal damped vibration energy harvesters with arbitrary proof mass offset. The key equations of electromechanical finite element discretisation using the extended Lagrangian principle are revealed and simplified to give matrix and scalar forms of the coupled system equations, indicating the most relevant numerical technique for the power harvester research. To evaluate the performance of the numerical study, the analytical closed-form boundary value equations have been developed using the extended Hamiltonian principle. The results from the electromechanical frequency response functions (EFRFs) derived from two theoretical studies show excellent agreement with experimental studies. The benefit of the numerical technique is in providing effective and quick predictions for analysing parametric designs and physical properties of piezoelectric materials. Although analytical technique provides a challenging process for analysing the complex smart structure, it shows complementary study for validating the numerical technique.

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.

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.

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 Hamiltonian¿s 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.

Autonomous self-powered wireless sensor devices are inevitable future technology that will potentially become ubiquitous in many sectors such as industry, intelligent infrastructure and biomedical devices. This has spurred a great attention from researchers to develop self-sustained power harvesting devices. For this paper, we present a new numerical technique for modelling the MEMS power harvesters using parametric design optimisation and physical properties for various piezoelectric materials. This technique enables the prediction of optimal power harvesting responses that can be used to identify the performance of piezoelectric materials and particular piezoelectric geometry where this technique can alleviate tedious analytical methods for analysing parametric design optimisation and can assist for analysing piezo-MEMS system response before conducting the microfabrication process.

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 Hamiltonian's 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.