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

  • Mohamed Amri

    Mohamed Amri is a computational Geomechanics specialist at Excellence Logging with over 5 years of experience in the modeling of Oil & Gas drilling efficiency and vibrations. He received a PhD from the Mining School of Paris in 2016 in the field of Geomechanics. He was a research assistant at ESIEE Paris in 2012 at the ESYCOM laboratory. His main research included the modeling and the optimization of MEMS devices.

    , Philippe Basset

    Philippe Basset, is professor at Université Paris-Est / ESIEE Paris. He received his Ph.D from IEMN, University of Lille in 2003 in the areas of microelectronic and micro-electro-mechanical-systems (MEMS). In 2004 he was a post-doc at CMU, Pittsburgh, USA and he joined ESIEE Paris in 2005. He is currently deputy director of the ESYCOM laboratory. His current research interests include micro-power sources for autonomous systems and micro/nano-structuration of silicon. He serves in the International Steering Committee of the PowerMEMS conference since 2015.

    , Dimitri Galayko

    Dimitri Galayko was graduated from Odessa State Polytechnic University (Ukraine) in 1998, he received his master degree from Institute of Applied Sciences of Lyon (INSA-LYON, France) in 1999. He made his PhD thesis in the Institute of Microelectronics and Nanotechnologies (IEMN, Lille, France) and received the PhD degree from the University Lille-I in 2002. Since 2005 he is an associate professor in University Paris VI (UPMC, Sorbonne Universités) in the Laboratory of Computer Science (LIP6). His research interests cover design and modeling of heterogeneous systems involving a combination of classical CMOS integrated circuit with physical sensors such as MEMS devices and energy harvesters, study of different aspects of oscillating structures in microelectronics (both solid-state CMOS oscillators and MEMS oscillators), and investigation and modeling of nonlinear phenomena emerging in such systems. He is an active member of the Technical Committee Nonlinear Circuits and Systems of IEEE CAS society.

    , Francesco Cottone

    Francesco Cottone is a senior researcher and professor at Department of Physics and Geology, University of Perugia, Italy, were he obtained a Ph.D in Physics in 2008. After his Ph.D, Francesco worked outside Italy on nonlinear dynamical systems for vibration energy harvesting at Stokes Institute, University of Limerick, Ireland. In 2011, Francesco awarded a Marie Curie European Fellowship for a project related to nonlinear electrostatic MEMS energy harvesting technology at ESIEE Paris, Université de Paris-Est, France. Since 2013, Francesco re-joined the Noise in Physical System Laboratory, Italy, where he is currently working on nonlinear micro systems and innovative electro-active materials for energy harvesting. His scientific expertise includes gravitational waves detectors, nonlinear stochastic systems and electro-active materials for energy harvesting. He has record of more than 50 referred publications, holds 2 patents and several talks at international conferences on energy harvesting technology.

    , Einar Halvorsen

    Einar Halvorsen received the Siv.Ing. degree in physical electronics from the Norwegian Institute of Technology (NTH), Trondheim, Norway, in 1991, and the Dr.Ing. degree in physics from the Norwegian University of Science and Technology (NTNU, formerly NTH), Trondheim, Norway, in 1996. He has worked both in academia and the microelectronics industry. Since 2004, he has been with University College of Southeast Norway in Horten, Norway, where he is a professor of micro- and nanotechnology. His main research interest is in theory, design, and modelling of microelectromechanical devices.

    , S. Duy Nguyen

    Son Duy Nguyen received the B.E., and M.E. degrees in electronics from the Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2004 and 2006, respectively, and Ph.D. degree in Applied Micro- and Nanosytems, from the University of Oslo, Norway, in 2013. He was the postdoctoral researcher at Berkeley Sensor & Actuator Center (BSAC), University of California, Berkeley, USA from 2013 to 2015 and 2017. Since 2017, he has been the New Technology Engineer at Analog Devices Inc., USA, where he is the project manager and process development for MEMS devices and biosensors.

    , Fehmi Najar

    Fehmi Najar, is Associate Professor of Mechanical Engineering at the Tunisia Polytechnic School, University of Carthage, Tunisia. He received an Engineering Diploma in Mechanical Engineering from the National Engineering School of Tunis in 1997, and an M.S. in Structural Dynamics from the Ecole Centrale de Paris, France, in 1998. After graduation, he worked as Technical Manager in the Graphic Art industry for a period of 6 years. He obtained his PhD in Mechanical Engineering from the National Engineering School of Tunis in 2008. His research interests include MEMS and NEMS, structural dynamics, smart materials, energy harvesting, structural health monitoring, and multi-body dynamics.

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    and Tarik Bourouina

    Tarik Bourouina was born in 1967. He holds a Master of Science (Physics), a Master of Engineering (Electronics) and the Ph.D. degree, obtained in 1991 at Université Paris XII. His entire career was devoted to the field of MEMS. He started research at ESIEE Paris in 1988 among the pioneers in MEMS-based silicon microphones, which he extended to acoustic-based gyroscopes. He then had several significant contributions in the area of optical MEMS, among which the smallest MEMS-based FTIR Optical Spectrometer, jointly developed with Si-Ware-System and Hamamatsu Photonics. Among his contributions to the scientific community, he served in the Technical Program Committee of the IEEE MEMS conference (2012, 2013) and joined the Editorial Board of Nature Publishing Group for the journals Light: Science and Applications and Microsystems & Nanoengineering. Dr. Bourouina took several academic positions in France and in Japan, at the Université Paris-Sud Orsay, at the French National Center for Scientific Research (CNRS) and at The University of Tokyo. Dr. Bourouina is now full Professor at ESIEE Paris, Université Paris-Est since 2002. His current interests include optofluidics and analytical chemistry on-chip, seeking new opportunities for MEMS in the areas of Sustainable Environment and Smart-Cities.

Published/Copyright: June 7, 2018

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.

Zusammenfassung

Dieser Artikel präsentiert einen neuartigen Ansatz zum Entwurf und zur Optimierung geometrischer nichtlinearer Federn für die Energiegewinnung durch Breitbandvibrationen. Zu diesem Zweck verwenden wir ein gefaltetes Balkendesign. Wir fügen einen Faltungswinkel im Hauptstrahl hinzu, um seine geometrischen Nichtlinearitäten zu erhöhen. Eine numerische Analyse wird unter Verwendung der Finite-Elemente-Methode durchgeführt, um ihre quadratische und kubische Federsteifigkeit abzuschätzen. Eine nichtlineare effektive Federkonstante wird dann für verschiedene Werte des Faltwinkels berechnet. Wir zeigen, dass dieser Winkel Nichtlinearitäten innerhalb der Struktur erhöhen kann, was zu höheren Bandbreiten führt, und dass es möglich ist, das Verhalten des Systems so zu steuern, dass je nach Wahl des Faltwinkels eine Antwort vom Erweichungstyp oder vom Härtungstyp erhalten wird. Basierend auf der Lindstedt-Poincaré-Störungstechnik wird eine Näherung erster Ordnung zur Vorhersage der Frequenzantwort des Systems bestimmt. Um die Störungsanalyse zu validieren, werden numerische Lösungen basierend auf der Langzeit-Integrationsmethode und gemischten VHDL-AMS/Spice-Simulationen vorgestellt. Schließlich wird diese Methode auf ein zuvor veröffentlichtes Gerät angewendet und zeigt eine gute Übereinstimmung mit Experimenten.

About the authors

Mohamed Amri

Mohamed Amri is a computational Geomechanics specialist at Excellence Logging with over 5 years of experience in the modeling of Oil & Gas drilling efficiency and vibrations. He received a PhD from the Mining School of Paris in 2016 in the field of Geomechanics. He was a research assistant at ESIEE Paris in 2012 at the ESYCOM laboratory. His main research included the modeling and the optimization of MEMS devices.

Philippe Basset

Philippe Basset, is professor at Université Paris-Est / ESIEE Paris. He received his Ph.D from IEMN, University of Lille in 2003 in the areas of microelectronic and micro-electro-mechanical-systems (MEMS). In 2004 he was a post-doc at CMU, Pittsburgh, USA and he joined ESIEE Paris in 2005. He is currently deputy director of the ESYCOM laboratory. His current research interests include micro-power sources for autonomous systems and micro/nano-structuration of silicon. He serves in the International Steering Committee of the PowerMEMS conference since 2015.

Dimitri Galayko

Dimitri Galayko was graduated from Odessa State Polytechnic University (Ukraine) in 1998, he received his master degree from Institute of Applied Sciences of Lyon (INSA-LYON, France) in 1999. He made his PhD thesis in the Institute of Microelectronics and Nanotechnologies (IEMN, Lille, France) and received the PhD degree from the University Lille-I in 2002. Since 2005 he is an associate professor in University Paris VI (UPMC, Sorbonne Universités) in the Laboratory of Computer Science (LIP6). His research interests cover design and modeling of heterogeneous systems involving a combination of classical CMOS integrated circuit with physical sensors such as MEMS devices and energy harvesters, study of different aspects of oscillating structures in microelectronics (both solid-state CMOS oscillators and MEMS oscillators), and investigation and modeling of nonlinear phenomena emerging in such systems. He is an active member of the Technical Committee Nonlinear Circuits and Systems of IEEE CAS society.

Francesco Cottone

Francesco Cottone is a senior researcher and professor at Department of Physics and Geology, University of Perugia, Italy, were he obtained a Ph.D in Physics in 2008. After his Ph.D, Francesco worked outside Italy on nonlinear dynamical systems for vibration energy harvesting at Stokes Institute, University of Limerick, Ireland. In 2011, Francesco awarded a Marie Curie European Fellowship for a project related to nonlinear electrostatic MEMS energy harvesting technology at ESIEE Paris, Université de Paris-Est, France. Since 2013, Francesco re-joined the Noise in Physical System Laboratory, Italy, where he is currently working on nonlinear micro systems and innovative electro-active materials for energy harvesting. His scientific expertise includes gravitational waves detectors, nonlinear stochastic systems and electro-active materials for energy harvesting. He has record of more than 50 referred publications, holds 2 patents and several talks at international conferences on energy harvesting technology.

Einar Halvorsen

Einar Halvorsen received the Siv.Ing. degree in physical electronics from the Norwegian Institute of Technology (NTH), Trondheim, Norway, in 1991, and the Dr.Ing. degree in physics from the Norwegian University of Science and Technology (NTNU, formerly NTH), Trondheim, Norway, in 1996. He has worked both in academia and the microelectronics industry. Since 2004, he has been with University College of Southeast Norway in Horten, Norway, where he is a professor of micro- and nanotechnology. His main research interest is in theory, design, and modelling of microelectromechanical devices.

S. Duy Nguyen

Son Duy Nguyen received the B.E., and M.E. degrees in electronics from the Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam, in 2004 and 2006, respectively, and Ph.D. degree in Applied Micro- and Nanosytems, from the University of Oslo, Norway, in 2013. He was the postdoctoral researcher at Berkeley Sensor & Actuator Center (BSAC), University of California, Berkeley, USA from 2013 to 2015 and 2017. Since 2017, he has been the New Technology Engineer at Analog Devices Inc., USA, where he is the project manager and process development for MEMS devices and biosensors.

Fehmi Najar

Fehmi Najar, is Associate Professor of Mechanical Engineering at the Tunisia Polytechnic School, University of Carthage, Tunisia. He received an Engineering Diploma in Mechanical Engineering from the National Engineering School of Tunis in 1997, and an M.S. in Structural Dynamics from the Ecole Centrale de Paris, France, in 1998. After graduation, he worked as Technical Manager in the Graphic Art industry for a period of 6 years. He obtained his PhD in Mechanical Engineering from the National Engineering School of Tunis in 2008. His research interests include MEMS and NEMS, structural dynamics, smart materials, energy harvesting, structural health monitoring, and multi-body dynamics.

Tarik Bourouina

Tarik Bourouina was born in 1967. He holds a Master of Science (Physics), a Master of Engineering (Electronics) and the Ph.D. degree, obtained in 1991 at Université Paris XII. His entire career was devoted to the field of MEMS. He started research at ESIEE Paris in 1988 among the pioneers in MEMS-based silicon microphones, which he extended to acoustic-based gyroscopes. He then had several significant contributions in the area of optical MEMS, among which the smallest MEMS-based FTIR Optical Spectrometer, jointly developed with Si-Ware-System and Hamamatsu Photonics. Among his contributions to the scientific community, he served in the Technical Program Committee of the IEEE MEMS conference (2012, 2013) and joined the Editorial Board of Nature Publishing Group for the journals Light: Science and Applications and Microsystems & Nanoengineering. Dr. Bourouina took several academic positions in France and in Japan, at the Université Paris-Sud Orsay, at the French National Center for Scientific Research (CNRS) and at The University of Tokyo. Dr. Bourouina is now full Professor at ESIEE Paris, Université Paris-Est since 2002. His current interests include optofluidics and analytical chemistry on-chip, seeking new opportunities for MEMS in the areas of Sustainable Environment and Smart-Cities.

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Received: 2017-07-12
Accepted: 2018-05-21
Published Online: 2018-06-07
Published in Print: 2018-09-25

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