Reduced-order modeling with multiple scales of electromechanical systems for energy harvesting

New technologies that aim at powering wireless nodes by scavenging the energy from ambient vibrations can be a practical solution for some structural monitoring applications in the near future. In view of possible large-scale applications of piezoelectric energy harvesters, an accurate modeling of the interfaces in these devices is needed for more advanced and reliable simulations, since they might have large influence on functionality and performance of smart monitoring infrastructures. In this perspective, a novel multiscale and multiphysics hybrid approach is proposed to assess the dynamic response of piezoelectric energy harvesting devices. Within the framework of the presented approach, the FE2 method is employed to compute stress and strain levels at the microscale in the most critical interfaces. The displacement-load curve of the whole device (so-called capacity curve or pushover curve) is then obtained by means of the application of a suitable pattern of static forces. Finally, the parameters of a reduced-order model are calibrated on the basis of the nonlinear static analysis. This reduced-order model, in turn, is employed for the efficient dynamic analysis of the energy harvesting device.

[1]  R. E. Nickell,et al.  Nonlinear dynamics by mode superposition , 1976 .

[2]  Claudio Maruccio,et al.  Analysis of piezoelectric energy harvester under modulated and filtered white Gaussian noise , 2018 .

[3]  Alex Elvin,et al.  Feasibility of structural monitoring with vibration powered sensors , 2006 .

[4]  Giuseppe Quaranta,et al.  Nonlinear normal modes for damage detection , 2016 .

[5]  Frédéric Feyel,et al.  Multiscale FE2 elastoviscoplastic analysis of composite structures , 1999 .

[6]  Paul Steinmann,et al.  Towards an efficient two-scale approach to model technical textiles , 2017 .

[7]  Gaëtan Kerschen,et al.  Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques , 2009 .

[8]  Jože Korelc,et al.  Automation of primal and sensitivity analysis of transient coupled problems , 2009 .

[9]  Claudio Maruccio,et al.  Computational homogenization of fibrous piezoelectric materials , 2014, ArXiv.

[10]  Alex Elvin,et al.  Large deflection effects in flexible energy harvesters , 2012 .

[11]  P. Steinmann,et al.  Two-scale computational homogenization of electro-elasticity at finite strains , 2014 .

[12]  C. Farhat,et al.  A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics , 2017 .

[13]  L. Renson,et al.  Identification of nonlinear normal modes of engineering structures under broadband forcing , 2016, 1604.08069.

[14]  F. Fritzen,et al.  Reduced order homogenization for viscoplastic composite materials including dissipative imperfect interfaces , 2017 .

[15]  C. Miehe,et al.  Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy , 2003 .

[16]  J. Schröder,et al.  A 3D Magnetostrictive Preisach Model for the Simulation of Magneto-Electric Composites on Multiple Scales , 2018 .

[17]  Urša Šolinc,et al.  A simple way to improved formulation of $$\hbox {FE}^2$$FE2 analysis , 2015 .

[18]  D. Inman,et al.  Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification , 2010 .

[19]  Sonia Marfia,et al.  Comparison of reduced order homogenization techniques: pRBMOR, NUTFA and MxTFA , 2018 .

[20]  N. Kikuchi,et al.  A class of general algorithms for multi-scale analyses of heterogeneous media , 2001 .

[21]  Erkan Oterkus,et al.  Modelling and parameter identification of electromechanical systems for energy harvesting and sensing , 2019, Mechanical Systems and Signal Processing.

[22]  Paolo Tiso,et al.  Reduction Method for Finite Element Nonlinear Dynamic Analysis of Shells , 2011 .

[23]  J. Schröder,et al.  Two-scale homogenization of electromechanically coupled boundary value problems , 2012 .

[24]  Nizar Lajnef,et al.  Tunable Energy Harvesting from Ambient Vibrations in Civil Structures , 2012 .

[25]  Marc G. D. Geers,et al.  A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials , 2017, J. Comput. Phys..

[26]  Canan Dagdeviren,et al.  Cooperativity in the Enhanced Piezoelectric Response of Polymer Nanowires , 2014, Advanced materials.

[27]  Paul Cahill,et al.  Experimental Validation of Piezoelectric Energy-Harvesting Device for Built Infrastructure Applications , 2018, Journal of Bridge Engineering.

[28]  L. Renson,et al.  An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems , 2014, Meccanica.

[29]  F. Feyel.  A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua , 2003 .

[30]  C. Reina,et al.  Variational coarse-graining procedure for dynamic homogenization , 2017 .

[31]  Alexander F. Vakakis,et al.  Nonlinear normal modes, Part I: A useful framework for the structural dynamicist , 2009 .

[32]  Anil K. Chopra,et al.  A modal pushover analysis procedure for estimating seismic demands for buildings , 2002 .

[33]  J. Golinval,et al.  Propagation of material and surface profile uncertainties on MEMS micro‐resonators using a stochastic second‐order computational multi‐scale approach , 2017 .

[34]  Dominique Siegert,et al.  Piezoelectric energy harvesting from traffic-induced bridge vibrations , 2013 .

[35]  Kapil Khandelwal,et al.  A framework for implementation of RVE‐based multiscale models in computational homogenization using isogeometric analysis , 2018 .

[36]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[37]  Emmanuel Roubin,et al.  Reduced order modeling strategies for computational multiscale fracture , 2017 .

[38]  Claudio Maruccio,et al.  Numerical homogenization of piezoelectric textiles with electrospun fibers for energy harvesting , 2014 .

[39]  Alberto Cardona,et al.  A reduction method for nonlinear structural dynamic analysis , 1985 .

[40]  Joze Korelc,et al.  Multi-language and Multi-environment Generation of Nonlinear Finite Element Codes , 2002, Engineering with Computers.

[41]  Marc‐André Keip,et al.  Computational stability analysis of periodic electroactive polymer composites across scales , 2018, Computer Methods in Applied Mechanics and Engineering.

[42]  Fpt Frank Baaijens,et al.  An approach to micro-macro modeling of heterogeneous materials , 2001 .

[43]  Sonia Marfia,et al.  Multiscale technique for nonlinear analysis of elastoplastic and viscoplastic composites , 2018 .

[44]  Paul Cahill,et al.  Vibration energy harvesting based monitoring of an operational bridge undergoing forced vibration and train passage , 2018, Mechanical Systems and Signal Processing.

[45]  Giuseppe Quaranta,et al.  Energy harvesting from electrospun piezoelectric nanofibers for structural health monitoring of a cable-stayed bridge , 2016 .

[46]  Timon Rabczuk,et al.  Multiscale Methods for Fracture: A Review$$^\bigstar $$★ , 2017, Journal of the Indian Institute of Science.

[47]  Sergio Oller,et al.  Multiscale Computational Homogenization: Review and Proposal of a New Enhanced-First-Order Method , 2016, Archives of Computational Methods in Engineering.

[48]  Klaus-Jürgen Bathe,et al.  On nonlinear dynamic analysis using substructuring and mode superposition , 1981 .

[49]  Marc‐André Keip,et al.  Computational and analytical investigations of shape effects in the experimental characterization of magnetorheological elastomers , 2017 .

[50]  Jacob Fish,et al.  Towards practical multiscale approach for analysis of reinforced concrete structures , 2018 .