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

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

General model with experimental validation of electrical resonant frequency tuning of electromagnetic vibration energy harvesters

This paper presents a general model and its experimental validation for electrically tunable electromagnetic energy harvesters. Electrical tuning relies on the adjustment of the electrical load so that the maximum output power of the energy harvester occurs at a frequency which is different from the mechanical resonant frequency of the energy harvester. Theoretical analysis shows that for this approach to be feasible the electromagnetic vibration energy harvester’s coupling factor must be maximized so that its resonant frequency can be tuned with the minimum decrease of output power. Two different-sized electromagnetic energy harvesters were built and tested to validate the model. Experimentally, the micro-scale energy harvester has a coupling factor of 0.0035 and an untuned resonant frequency of 70.05 Hz. When excited at 30 mg, it was tuned by 0.23 Hz by changing its capacitive load from 0 to 4000 nF; its effective tuning range is 0.15 Hz for a capacitive load variation from 0 to 1500 nF. The macro-scale energy harvester has a coupling factor of 552.25 and an untuned resonant frequency of 95.1 Hz and 95.5 Hz when excited at 10 mg and 25 mg, respectively. When excited at 10 mg, it was tuned by 3.8 Hz by changing its capacitive load from 0 to 1400 nF; it has an effective tuning range of 3.5 Hz for a capacitive load variation from 0 to 1200 nF. When excited at 25 mg, its resonant frequency was tuned by 4.2 Hz by changing its capacitive load from 0 to 1400 nF; it has an effective tuning range of about 5 Hz. Experimental results were found to agree with the theoretical analysis to within 10%

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

Разработка, тестирование и внедрение кластерного агента динамической настройки AIX WPAR для кластера высокой доступности Veritas Cluster Server

Разрабатываемый агент для кластера высокой доступности Veritas Cluster Server создается с целью ускорения и усовершенствования процесса конфигурирования WPAR-разделов в операционной системе AIX, а также для предоставления кластеру возможности использовать максимально возможное количество штатных средств обеспечения высокой доступности приложений. Объектом исследования является обеспечение высокой доступности биллинговых систем на серверах макрорегионального филиала "Сибирь" компании ПАО "Ростелеком", работающих под управлением Veritas Cluster Server.The developed agent for the high availability cluster Veritas Cluster Server is created to accelerate and improve the process of configuring the WPAR partitions on the AIX operating system, and to allow the cluster to use the maximum possible number of native high availability applications. The object of the study is to ensure high availability of billing systems on the servers of the macro-regional filial branch "Siberia" of PJSC "Rostelecom", operating under the management of Veritas Cluster Server

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 kΩ to 200 kΩ affects the amplitude of power harvesting as well as resulting in a shift of the first natural frequency from 76 Hz to 79 Hz