On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models

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 pro...

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Vydané v:Nonlinear dynamics Ročník 97; číslo 2; s. 1747 - 1781
Hlavní autori: Givois, Arthur, Grolet, Aurélien, Thomas, Olivier, Deü, Jean-François
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Dordrecht Springer Netherlands 01.07.2019
Springer Nature B.V
Springer Verlag
Predmet:
Asymptotic methods
Automotive Engineering
Beams (structural)
Circular plates
Classical Mechanics
Computation
Computer simulation
Control
Dynamical Systems
Engineering
Engineering Sciences
Finite element method
Forced vibration
Frequency response
Harmonic balance method
Mathematical models
Mechanical Engineering
Mechanics
Nonlinear phenomena
Nonlinear response
Numerical methods
Original Paper
Oscillators
Perforated plates
Reduced order models
Structural mechanics
Thickness
Transverse oscillation
Vibration
Geometric nonlinearities
Non-intrusive stiffness evaluation procedure
Continuation method
Reduced-order finite element model
ISSN:0924-090X, 1573-269X
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Popis
Shrnutí: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 the ROM. 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.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05021-6