Transfer Function Modeling of Distributed Piezoelectric Vibration Energy Harvesters

2009 ◽  
Author(s):  
Chin An Tan ◽  
Heather L. Lai
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Vibration Energy ◽  
System Response ◽  
Distributed Parameter ◽  
Domain Modeling ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Adjoint Systems ◽  
The Stability

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.

Transfer Functions of One-Dimensional Distributed Parameter Systems

1992 ◽  
Vol 59 (4) ◽  
pp. 1009-1014 ◽  
Author(s):  
B. Yang ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Axially Moving Beam ◽  
System Response ◽  
Distributed Parameter ◽  
One Dimensional ◽  
Adjoint Systems ◽  
The Laplace Transform ◽  
Axially Moving

Distributed parameter systems describe many important physical processes. The transfer function of a distributed parameter system contains all information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. This paper presents a new method for evaluating transfer functions for a class of one-dimensional distributed parameter systems. The system equations are cast into a matrix form in the Laplace transform domain. Through determination of a fundamental matrix, the system transfer function is precisely evaluated in closed form. The method proposed is valid for both self-adjoint and non-self-adjoint systems, and is extremely convenient in computer coding. The method is applied to a damped, axially moving beam with different boundary conditions.

Transfer Function Analysis of Constrained, Distributed Piezoelectric Vibration Energy Harvesting Beam Systems

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Chin An Tan ◽  
Shahram Amoozegar ◽  
Heather L. Lai
Keyword(s):  
Energy Harvesting ◽  
Transfer Function ◽  
Boundary Conditions ◽  
Vibration Energy ◽  
System Response ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Transfer Function Analysis ◽  
Intermediate Constraints

This paper presents a novel formulation and exact solution of the frequency response function (FRF) of vibration energy harvesting beam systems by the distributed transfer function method (TFM). The method is applicable for coupled electromechanical systems with nonproportional damping, intermediate constraints, and nonclassical boundary conditions, for which the system transfer functions are either very difficult or cumbersome to obtain using available methods. Such systems may offer new opportunities for optimized designs of energy harvesters via parameter tuning. The proposed formulation is also systematic and amenable to algorithmic numerical coding, allowing the system response and its derivatives to be computed by only simple modifications of the parameters in the system operators for different boundary conditions and the incorporation of feedback control principles. Examples of piezoelectric energy harvesters with nonclassical boundary conditions and intermediate constraints are presented to demonstrate the efficacy of the proposed method and its use as a design tool for vibration energy harvesters via tuning of system parameters. The results can also be used to provide benchmarks for assessing the accuracies of approximate techniques.

scholarly journals Dynamic control of maximal ventricular elastance via the baroreflex and force-frequency relation in awake dogs before and after pacing-induced heart failure

2010 ◽  
Vol 299 (1) ◽  
pp. H62-H69 ◽  
Author(s):  
Xiaoxiao Chen ◽  
Javier A. Sala-Mercado ◽  
Robert L. Hammond ◽  
Masashi Ichinose ◽  
Soroor Soltani ◽  
...  
Keyword(s):  
Heart Failure ◽  
Transfer Function ◽  
Transfer Functions ◽  
Dynamic Properties ◽  
System Response ◽  
Force Frequency ◽  
Arterial Baroreflex ◽  
Ventricular Elastance ◽  
Arterial Blood ◽  
Frequency Relation

We investigated to what extent maximal ventricular elastance ( Emax) is dynamically controlled by the arterial baroreflex and force-frequency relation in conscious dogs and to what extent these mechanisms are attenuated after the induction of heart failure (HF). We mathematically analyzed spontaneous beat-to-beat hemodynamic variability. First, we estimated Emax for each beat during a baseline period using the ventricular unstressed volume determined with the traditional multiple beat method during vena cava occlusion. We then jointly identified the transfer functions (system gain value and time delay per frequency) relating beat-to-beat fluctuations in arterial blood pressure (ABP) to Emax (ABP→ Emax) and beat-to-beat fluctuations in heart rate (HR) to Emax (HR→ Emax) to characterize the dynamic properties of the arterial baroreflex and force-frequency relation, respectively. During the control condition, the ABP→ Emax transfer function revealed that ABP perturbations caused opposite direction Emax changes with a gain value of −0.023 ± 0.012 ml−1, whereas the HR→ Emax transfer function indicated that HR alterations caused same direction Emax changes with a gain value of 0.013 ± 0.005 mmHg·ml−1·(beats/min)−1. Both transfer functions behaved as low-pass filters. However, the ABP→ Emax transfer function was more sluggish than the HR→ Emax transfer function with overall time constants (indicator of full system response time to a sudden input change) of 11.2 ± 2.8 and 1.7 ± 0.5 s ( P < 0.05), respectively. During the HF condition, the ABP→ Emax and HR→ Emax transfer functions were markedly depressed with gain values reduced to −0.0002 ± 0.007 ml−1 and −0.001 ± 0.004 mmHg·ml−1·(beats/min)−1 ( P < 0.1). Emax is rapidly and significantly controlled at rest, but this modulation is virtually abolished in HF.

scholarly journals Enhanced low-frequency vibration energy harvesting with inertial amplifiers

2021 ◽  
pp. 1045389X2110322
Author(s):  
Sondipon Adhikari ◽  
Arnab Banerjee
Keyword(s):  
Low Frequency ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Micro Scale ◽  
Energy Harvesters ◽  
Low Frequency Vibration ◽  
Different Types ◽  
Mechanical Approach ◽  
Ambient Excitation ◽  
Piezoelectric Vibration

Piezoelectric vibration energy harvesters have demonstrated the potential for sustainable energy generation from diverse ambient sources in the context of low-powered micro-scale systems. However, challenges remain concerning harvesting more power from low-frequency input excitations and broadband random excitations. To address this, here we propose a purely mechanical approach by employing inertial amplifiers with cantilever piezoelectric vibration energy harvesters. The proposed mechanism can achieve inertial amplification amounting to orders of magnitude under certain conditions. Harmonic, as well as broadband random excitations, are considered. Two types of harvesting circuits, namely, without and with an inductor, have been employed. We explicitly demonstrate how different parameters describing the inertial amplifiers should be optimally tuned to maximise harvested power under different types of excitations and circuit configurations. It is possible to harvest five times more power at a 50% lower frequency when the ambient excitation is harmonic. Under random broadband ambient excitations, it is possible to harvest 10 times more power with optimally selected parameters.

Transfer Function Analysis of Non-Uniformly Distributed Parameter Systems

1993 ◽  
Author(s):  
Bingen Yang ◽  
Houfei Fang
Keyword(s):  
Distributed Systems ◽  
Transfer Function ◽  
State Space ◽  
Fundamental Matrix ◽  
Function Analysis ◽  
Distributed Parameter Systems ◽  
System Response ◽  
Distributed Parameter ◽  
Transfer Function Analysis ◽  
Function Formulation

Abstract This paper studies a transfer function formulation for general one-dimensional, non-uniformly distributed systems subject to arbitrary boundary conditions and external disturbances. The purpose is to provide an useful alternative for modeling and analysis of distributed parameter systems. In the development, the system equations of the non-uniform system are cast into a state space form in the Laplace transform domain. The system response and distributed transfer functions are derived in term of the fundamental matrix of the state space equation. Two approximate methods for evaluating the fundamental matrix are proposed. With the transfer function formulation, various dynamics and control problems for the non-uniformly distributed system can be conveniently addressed. The transfer function analysis is also applied to constrained/combined non-uniformly distributed systems.

Multi-Modal Vibration Energy Harvesting Using a Trapezoidal Plate

2011 ◽  
Author(s):  
Mustafa H. Arafa
Keyword(s):  
System Performance ◽  
Energy Harvester ◽  
Natural Frequencies ◽  
Vibration Energy ◽  
Vibration Modes ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Trapezoidal Plate ◽  
Plate Geometry ◽  
Modal Vibration

Vibration-based energy harvesters are usually designed to exhibit natural frequencies that match those of the excitation for maximum power output. This has spurred interest into the design of devices that respond to variable frequency sources. In this work, an electromagnetic energy harvester in the form of a base excited trapezoidal plate is proposed. The plate geometry is designed to achieve two closely spaced vibration modes in order to harvest energy across a broader bandwidth. The ensuing bending and twisting vibrations are utilized in this capacity by placing a magnet on the plate tip that moves past a stationary coil. A dynamic model is presented to predict the system performance and is verified experimentally.

Stiffness control of a nonlinear mechanical folded beam for wideband vibration energy harvesters

2018 ◽  
Vol 85 (9) ◽  
pp. 553-564 ◽  
Author(s):  
Mohamed Amri ◽  
Philippe Basset ◽  
Dimitri Galayko ◽  
Francesco Cottone ◽  
Einar Halvorsen ◽  
...  
Keyword(s):  
Numerical Solutions ◽  
Order Approximation ◽  
Perturbation Technique ◽  
Time Integration ◽  
Vibration Energy ◽  
Vibration Energy Harvesting ◽  
Folding Angle ◽  
Energy Harvesters ◽  
Nonlinear Springs ◽  
Novel Approach

Abstract This paper presents a novel approach to design and optimize geometric nonlinear springs for wideband vibration energy harvesting. To this end, we designed a spring with several folds to increase its geometric nonlinearities. A numerical analysis is performed using the Finite Element Method to estimate its quadratic and cubic spring stiffness. A nonlinear effective spring constant is then calculated for different values of the main folding angle. We demonstrate that this angle can increase nonlinearities within the structure resulting in higher bandwidths, and that it is possible to control the behavior of the system to have softening-type or hardening-type response depending on the choice of the folding angle. Based on the Lindstedt-Poincaré perturbation technique, a first order approximation is determined to predict the frequency-response of the system. In order to validate the perturbation analysis, numerical solutions based on long-time integration method and mixed VHDL-AMS/Spice simulations are presented. Finally, this method is applied to a previously published device and shows a good agreement with experiments.

scholarly journals On the Essential Instabilities Caused by Fractional-Order Transfer Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Farshad Merrikh-Bayat ◽  
Masoud Karimi-Ghartemani
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Characteristic Equation ◽  
Stability Condition ◽  
Transfer Functions ◽  
Branch Points ◽  
The Stability ◽  
Unstable Branch

The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles. So, in this case, not only the characteristic equation but the numerator term is of significant importance. In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback. Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term. The effect of unstable branch points is studied and simulations are presented.

Investigation of Vibration Energy Harvesting Using Two Cantilevers With Random Input

2017 ◽  
Author(s):  
Wei Yang ◽  
Panagiotis Alevras ◽  
Shahrzad Towfighian
Keyword(s):  
Mechanical Energy ◽  
Duffing Oscillator ◽  
Electrical Energy ◽  
Potential Energy Function ◽  
Excitation Level ◽  
Vibration Energy ◽  
Random Input ◽  
Vibration Energy Harvesting ◽  
Energy Harvesters ◽  
Low Performance

There is a growing interest to convert ambient mechanical energy to electrical energy by vibration energy harvesters. Realistic vibrations are random and spread over a large frequency range. Most energy harvesters are linear with narrow frequency bandwidth and show low performance, which led to creation of nonlinear harvesters that have larger bandwidth. This article presents a simulation study of a nonlinear energy harvester that contains two cantilever beams coupled by magnetic force. One of the cantilever beam is covered partially by piezoelectric material, while the other beam is normal to the first one and is used to create a variable potential energy function. The variable double-well potential function enables optimum conversion of the kinetic energy and thus larger output. The system is modeled by coupled Duffing oscillator equations. To represent the ambient vibrations, the response to Gaussian random input signal (generated by Shinozuka formula) is studied using power spectral density. The effects of different parameters on the system are also investigated. The results show that the double cantilever harvester has a threshold distance, where the harvester can perform optimally regardless of the excitation level. This observation is opposite to that of the conventional fixed magnet cantilever system where the optimal distance varies with the excitation level. Results of this study can be used to enhance energy efficiency of vibration energy harvesters.

Transfer Functions of One-Dimensional Distributed Parameter Systems by Wave Approach

2006 ◽  
Vol 129 (2) ◽  
pp. 193-201 ◽  
Author(s):  
B. Kang
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Wave Reflection ◽  
Transfer Functions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Complex Frequency ◽  
Reflection And Transmission ◽  
One Dimensional ◽  
Analysis Technique

An alternative analysis technique, which does not require eigensolutions as a priori, for the dynamic response solutions, in terms of the transfer function, of one-dimensional distributed parameter systems with arbitrary supporting conditions, is presented. The technique is based on the fact that the dynamic displacement of any point in a waveguide can be determined by superimposing the amplitudes of the wave components traveling along the waveguide, where the wave numbers of the constituent waves are defined in the Laplace domain instead of the frequency domain. The spatial amplitude variations of individual waves are represented by the field transfer matrix and the distortions of the wave amplitudes at point discontinuities due to constraints or boundaries are described by the wave reflection and transmission matrices. Combining these matrices in a progressive manner along the waveguide using the concepts of generalized wave reflection and transmission matrices leads to the exact transfer function of a complex distributed parameter system subjected to an externally applied force. The transient response solution can be obtained through the Laplace inversion using the fixed Talbot method. The exact frequency response solution, which includes infinite normal modes of the system, can be obtained in terms of the complex frequency response function from the system’s transfer function. This wave-based analysis technique is applicable to any one-dimensional viscoelastic structure (strings, axial rods, torsional bar, and beams), in particular systems with multiple point discontinuities such as viscoelastic supports, attached mass, and geometric/material property changes. In this paper, the proposed approach is applied to the flexural vibration analysis of a classical Euler–Bernoulli beam with multiple spans to demonstrate its systematic and recursive formulation technique.

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