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http://hdl.handle.net/10985/19598
Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements
VIZZACCARO, Alessandra; GIVOIS, Arthur; LONGOBARDI, Pierluigi; SHEN, Yichang; DEÜ, Jean-François; SALLES, Loïc; TOUZÉ, Cyril; THOMAS, Olivier
Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory.We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/195982020-01-01T00:00:00ZVIZZACCARO, AlessandraGIVOIS, ArthurLONGOBARDI, PierluigiSHEN, YichangDEÜ, Jean-FrançoisSALLES, LoïcTOUZÉ, CyrilTHOMAS, OlivierNon-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory.We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification
http://hdl.handle.net/10985/22645
Backbone curves of coupled cubic oscillators in one-to-one internal resonance: bifurcation scenario, measurements and parameter identification
GIVOIS, Arthur; TAN, Jin-Jack; TOUZÉ, Cyril; THOMAS, Olivier
A system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone
curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally
measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete
identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.
Sat, 01 Feb 2020 00:00:00 GMThttp://hdl.handle.net/10985/226452020-02-01T00:00:00ZGIVOIS, ArthurTAN, Jin-JackTOUZÉ, CyrilTHOMAS, OlivierA system composed of two cubic nonlinear oscillators with close natural frequencies, and thus displaying a 1:1 internal resonance, is studied both theoretically and experimentally, with a special emphasis on the free oscillations and the backbone
curves. The instability regions of uncoupled solutions are derived and the bifurcation scenario as a function of the parameters of the problem is established, showing in an exhaustive manner all possible solutions. The backbone curves are then experimentally
measured on a circular plate, where the asymmetric modes are known to display companion configurations with close eigenfrequencies. A control system based on a Phase-Locked Loop (PLL) is used to measure the backbone curves and also the frequency response function in the forced and damped case, including unstable branches. The model is used for a complete
identification of the unknown parameters and an excellent comparison is drawn out between theoretical prediction and measurements.Dynamics of piezoelectric structures with geometric nonlinearities: A non-intrusive reduced order modelling strategy
http://hdl.handle.net/10985/22658
Dynamics of piezoelectric structures with geometric nonlinearities: A non-intrusive reduced order modelling strategy
GIVOIS, Arthur; DEÜ, Jean-François; THOMAS, Olivier
A reduced-order modelling to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities is proposed in this paper. A formulation of three-dimensional finite element models with global electric variables per piezoelectric patch, and suitable with any commercial finite element code equipped with geometrically nonlinear and piezoelectric capabilities, is proposed. A modal expansion leads to a reduced model where both nonlinear and electromechanical coupling effects are governed by modal coefficients, identified thanks to a non-intrusive procedure relying on the static application of prescribed displacements. Numerical simulations can be efficiently performed on the reduced modal model, thus defining a convenient procedure to study accurately the nonlinear dynamics of any piezoelectric structure. A particular focus is made on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity. Reference results are provided in terms of coefficients of the reduced-order model as well as of dynamic responses, computed for different test cases including realistic structures.
Wed, 01 Sep 2021 00:00:00 GMThttp://hdl.handle.net/10985/226582021-09-01T00:00:00ZGIVOIS, ArthurDEÜ, Jean-FrançoisTHOMAS, OlivierA reduced-order modelling to predictively simulate the dynamics of piezoelectric structures with geometric nonlinearities is proposed in this paper. A formulation of three-dimensional finite element models with global electric variables per piezoelectric patch, and suitable with any commercial finite element code equipped with geometrically nonlinear and piezoelectric capabilities, is proposed. A modal expansion leads to a reduced model where both nonlinear and electromechanical coupling effects are governed by modal coefficients, identified thanks to a non-intrusive procedure relying on the static application of prescribed displacements. Numerical simulations can be efficiently performed on the reduced modal model, thus defining a convenient procedure to study accurately the nonlinear dynamics of any piezoelectric structure. A particular focus is made on the parametric effect resulting from the combination of geometric nonlinearities and piezoelectricity. Reference results are provided in terms of coefficients of the reduced-order model as well as of dynamic responses, computed for different test cases including realistic structures.Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches
http://hdl.handle.net/10985/22676
Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches
GUILLOT, Vinciane; GIVOIS, Arthur; COLIN, Mathieu; THOMAS, Olivier; TURE SAVADKOOHI, Alireza; LAMARQUE, Claude-Henri
Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.
Sun, 01 Mar 2020 00:00:00 GMThttp://hdl.handle.net/10985/226762020-03-01T00:00:00ZGUILLOT, VincianeGIVOIS, ArthurCOLIN, MathieuTHOMAS, OlivierTURE SAVADKOOHI, AlirezaLAMARQUE, Claude-HenriExperimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities
http://hdl.handle.net/10985/22640
Experimental analysis of nonlinear resonances in piezoelectric plates with geometric nonlinearities
GIVOIS, Arthur; GIRAUD-AUDINE, Christophe; DEÜ, Jean-François; THOMAS, Olivier
Piezoelectric devices with integrated actuation and sensing capabilities are often used for the development of electromechanical systems. The present paper addresses experimentally the nonlinear dynamics of a fully integrated circular piezoelectric
thin structure, with piezoelectric patches used for actuationand other for sensing. A phase-locked loop control system is used to measure the resonant periodic response of the system under harmonic forcing, in both its stable and unstable parts. The single-mode response around a symmetric resonance as well as the coupled response around an asymmetric resonance, involving two companion modes in 1:1 internal resonance, is accurately measured. For the latter, a particular location of the patches and additional signal processing is proposed to spatially discriminate the response of each companion mode. In addition to a hardening behavior associated with geometric nonlinearities of the plate, a softening behavior predominant at low actuation amplitudes is observed, resulting from the material piezoelectric nonlinearities.
Thu, 01 Oct 2020 00:00:00 GMThttp://hdl.handle.net/10985/226402020-10-01T00:00:00ZGIVOIS, ArthurGIRAUD-AUDINE, ChristopheDEÜ, Jean-FrançoisTHOMAS, OlivierPiezoelectric devices with integrated actuation and sensing capabilities are often used for the development of electromechanical systems. The present paper addresses experimentally the nonlinear dynamics of a fully integrated circular piezoelectric
thin structure, with piezoelectric patches used for actuationand other for sensing. A phase-locked loop control system is used to measure the resonant periodic response of the system under harmonic forcing, in both its stable and unstable parts. The single-mode response around a symmetric resonance as well as the coupled response around an asymmetric resonance, involving two companion modes in 1:1 internal resonance, is accurately measured. For the latter, a particular location of the patches and additional signal processing is proposed to spatially discriminate the response of each companion mode. In addition to a hardening behavior associated with geometric nonlinearities of the plate, a softening behavior predominant at low actuation amplitudes is observed, resulting from the material piezoelectric nonlinearities.On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models
http://hdl.handle.net/10985/16775
On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models
GIVOIS, Arthur; GROLET, Aurélien; THOMAS, Olivier; DEÜ, Jean-François
This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/167752019-01-01T00:00:00ZGIVOIS, ArthurGROLET, AurélienTHOMAS, OlivierDEÜ, Jean-FrançoisThis paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.