Wave Propagation In Strongly Nonlinear Two-Mass Chains

Abstract This work studies elastic wave propagation in strongly nonlinear periodic systems and its active control with specific attention to an infinite mass-in-mass lattice. Piezoelectric materials are applied to it to provide active control loads to manipulate band structures of the lattice. Governing equations of the active mass-in-mass lattice with cubic nonlinearities are established. The control loads are modeled by using linear piezoelectric springs. Due to phase differences among vibrations of different cells during wave propagation, a series of delay functions with different delays are used to represent the steady-state of a traveling wave. The incremental harmonic balance method for delay dynamic systems is employed in this case to calculate periodic solutions of the lattice. The fast Fourier transform is employed to construct the Jacobian matrix of the Newton–Raphson iteration to avoid a large number of Galerkin integrations, and thus, the efficiency is significantly improved. Amplitude-dependent dispersion curves are calculated using results of the linearized system as an initial guess for the iteration. The results are compared with existing results in the literature, which demonstrates that the present method is efficient for wave propagation analysis of strongly nonlinear structures. Effects of nonlinearities, the mass ratio, and different control actions on band structures of the mass-in-mass lattice are investigated through a comprehensive parametric study. Numerical results show that the band structures can be influenced by nonlinearities of the lattice. New stopbands and critical wave numbers can be created by the control actions.

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Modeling of strongly-nonlinear wave propagation using the extended Rankine-Hugoniot shock relations

10.1063/1.4934448 ◽

2015 ◽

Author(s):

J.-W. Lee ◽

W.-S. Ohm ◽

W. Shim

Keyword(s):

Wave Propagation ◽

Nonlinear Wave ◽

Nonlinear Wave Propagation ◽

Strongly Nonlinear

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Dynamics and Wave Propagation in Nonlinear Piezoelectric Metastructures

10.21203/rs.3.rs-211726/v1 ◽

2021 ◽

Author(s):

Jaime Alberto Mosquera-Sánchez ◽

Carlos De Marqui

Keyword(s):

Wave Propagation ◽

Vibration Control ◽

Harmonic Balance ◽

Electrical Circuit ◽

Dispersion Relations ◽

Dynamical Response ◽

Negative Capacitance ◽

Strongly Nonlinear ◽

Time Domains ◽

Nonlinear Regimes

Abstract This paper reports dynamical effects in onedimensional locally resonant piezoelectric metastructures that can be leveraged by nonlinear electrical attachments featuring either combined quadratic and quartic, or essentially quartic potentials. The nonlinear electromechanical unit cell is built upon a linear host oscillator coupled to a nonlinear electrical circuit via piezoelectricity. Its dynamical response to prescribed longitudinal harmonic displacements is approached in the frequency and time domains. Semi-analytical harmonic balance (HB)-based dispersion relations are derived to predict the location and edges of the nonlinear attenuation band. Numerical responses show that weakly and moderately nonlinear piezoelectric metastructures (NPMSs) promote a class of nonlinear attenuation band where a bandgap and a wave supratransmission band coexist, while also imparting nonlinear attenuation at the resonances around the underlying linear bandgap. Besides, strongly nonlinear regimes are shown to elicit broadband chaotic attenuation. Negative capacitance (NC)-based essentially cubic piezoelectric attachments are found to potentiate the aforementioned effects over a broader bandwidth. Excellent agreement is found between the predictions of the HB based dispersion relations and the nonlinear transmissibility functions of undamped and weakly damped NPMSs at weakly and moderately nonlinear regimes, even in the presence of NC circuits. This research is expected to pave the way towards fully tunable smart periodic metastructures for vibration control via nonlinear piezoelectric attachments.PACS 05.45.-a . 62.30.+d . 62.65.+kMathematics Subject Classification (2010) 37N15 . 74H45 . 74H65 . 74J30

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Wave propagation in a strongly nonlinear locally resonant granular crystal

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2017.10.007 ◽

2018 ◽

Vol 365 ◽

pp. 27-41 ◽

Cited By ~ 17

Author(s):

K. Vorotnikov ◽

Y. Starosvetsky ◽

G. Theocharis ◽

P.G. Kevrekidis

Keyword(s):

Wave Propagation ◽

Strongly Nonlinear ◽

Granular Crystal

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Study of wave propagation in strongly nonlinear periodic lattices using a harmonic balance approach

Wave Motion ◽

10.1016/j.wavemoti.2011.12.005 ◽

2012 ◽

Vol 49 (2) ◽

pp. 394-410 ◽

Cited By ~ 41

Author(s):

Raj K. Narisetti ◽

Massimo Ruzzene ◽

Michael J. Leamy

Keyword(s):

Wave Propagation ◽

Harmonic Balance ◽

Strongly Nonlinear ◽

Balance Approach

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Electron Microscopy of Shock Loaded Polycrystalline Beryllium

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100052547 ◽

1974 ◽

Vol 32 ◽

pp. 506-507 ◽

Cited By ~ 1

Author(s):

J. M. Galbraith ◽

L. E. Murr ◽

A. L. Stevens

Keyword(s):

Electron Microscopy ◽

Wave Propagation ◽

Structural Change ◽

Single Crystal ◽

Diffraction Pattern ◽

Shock Loading ◽

Slip Systems ◽

Compression Tests ◽

X Ray Diffraction ◽

X Ray

Uniaxial compression tests and hydrostatic tests at pressures up to 27 kbars have been performed to determine operating slip systems in single crystal and polycrystal1ine beryllium. A recent study has been made of wave propagation in single crystal beryllium by shock loading to selectively activate various slip systems, and this has been followed by a study of wave propagation and spallation in textured, polycrystal1ine beryllium. An alteration in the X-ray diffraction pattern has been noted after shock loading, but this alteration has not yet been correlated with any structural change occurring during shock loading of polycrystal1ine beryllium.This study is being conducted in an effort to characterize the effects of shock loading on textured, polycrystal1ine beryllium. Samples were fabricated from a billet of Kawecki-Berylco hot pressed HP-10 beryllium.

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