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The influence of multiplicative white noise on the resonance capture of strongly nonlinear oscillatory systems under chirped-frequency excitations is investigated. It is assumed that the intensity of the perturbation decays polynomially…

Dynamical Systems · Mathematics 2024-03-22 Oskar A. Sultanov

In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending element based on field and edge consistency…

Numerical Analysis · Mathematics 2011-07-21 S Natarajan , PM Baiz , S Bordas , T Rabczuk , P Kerfriden

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize…

Fluid Dynamics · Physics 2021-02-24 Georgios Rigas , Denis Sipp , Tim Colonius

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies.…

Soft Condensed Matter · Physics 2017-10-25 Nicolas Mordant , Benjamin Miquel

The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic…

Pattern Formation and Solitons · Physics 2016-10-18 Noé Jiménez , Ahmed Mehrem , Rubén Picó , Lluís M. García-Raffi , Víctor J. Sánchez-Morcillo

Thin elastic sheets supported on compliant media form wrinkles under lateral compression. Since the lateral pressure is coupled to the sheet's deformation, varying it periodically in time creates a parametric excitation. We study the…

Soft Condensed Matter · Physics 2021-06-25 Haim Diamant

Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The…

Other Condensed Matter · Physics 2016-02-22 A. Arreola-Lucas , J. A. Franco-Villafañe , G. Báez , R. A. Méndez-Sánchez

The nonlinear interaction of waves in a driven medium may lead to wave turbulence, a state such that energy is transferred from large to small lengthscales. Here, wave turbulence is observed in experiments on a vibrating plate. The…

Chaotic Dynamics · Physics 2008-10-07 Arezki Boudaoud , Olivier Cadot , Benoît Odille , Cyril Touzé

Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…

Numerical Analysis · Mathematics 2024-02-21 Elwin van 't Wout

A new mechanism for the enhanced generation of compressible fluctuations by Alfven waves is presented. A strongly nonlinear regime of Alfven wave phase-mixing is numerically simulated in a one-dimensionally inhomogeneous plasma of finite…

Astrophysics · Physics 2007-05-23 V. M. Nakariakov , D. Tsiklauri , T. D. Arber

A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a statistically steady state of elastic wave turbulence. The analytical representation of the nonlinear frequency is obtained by evaluating the extended self-nonlinear…

Chaotic Dynamics · Physics 2014-01-15 Naoto Yokoyama , Masanori Takaoka

We develop a perturbation-based frequency-response framework for analyzing amplification mechanisms that are central to subcritical routes to transition in wall-bounded shear flows. By systematically expanding the input-output dynamics of…

Fluid Dynamics · Physics 2026-05-04 Dušan Božić , Anubhav Dwivedi , Mihailo R. Jovanović

The acoustic wave-propagation without mean flow and heat flux can be described in terms of velocity and pressure by the compressible nonlinear Navier-Stokes equations, where boundary layers appear at walls due to the viscosity and a…

Analysis of PDEs · Mathematics 2017-01-10 Anastasia Thoens-Zueva , Kersten Schmidt , Adrien Semin

Circuits provide ideal platforms of topological phases and matter, yet the study of topological circuits in the strongly nonlinear regime, has been lacking. We propose and experimentally demonstrate strongly nonlinear topological phases and…

Mesoscale and Nanoscale Physics · Physics 2023-07-03 Jijie Tang , Fangyuan Ma , Feng Li , Honglian Guo , Di Zhou

Nonlinear phenomena are inherent in most systems in nature. Second or higher-order harmonic generations, three-wave and four-wave mixing are typical phenomena in nonlinear optics. To obtain a nonzero signal for second-harmonic generation in…

Mesoscale and Nanoscale Physics · Physics 2019-04-29 Zhou Li , Franco Nori

In this paper, the flutter behaviour of simply supported square functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used for this…

Numerical Analysis · Mathematics 2012-03-14 S Natarajan , M Ganapathi , S Bordas

We show that, nonlinear optical processes of nanoparticles can be controlled by the presence of interactions with a molecule or a quantum dot. By choosing the appropriate level spacing for the quantum emitter, one can either suppress or…

Mesoscale and Nanoscale Physics · Physics 2014-09-22 Deniz Turkpence , Gursoy B. Akguc , Alpan Bek , Mehmet Emre Tasgin

We report an observation of the extraordinary high reflection of acoustic waves in water by thin epoxy plates partitioned by subwavelength cuts, whereas such plates without structure are acoustically-transparent as the acoustic properties…

Other Condensed Matter · Physics 2013-05-29 Zhaojian He , Shasha Peng , Chunyin Qiu , Rui Hao , Gangqiang Liu , Manzhu Ke , Jun Mei , Weijia Wen , Zhengyou Liu?

We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…

Fluid Dynamics · Physics 2014-02-10 Luc Deike , Jean-Claude Bacri , Eric Falcon

The nonlinear formulation developed based on von Karman's assumptions is employed to study the free vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature field is assumed to be…

Numerical Analysis · Mathematics 2011-07-28 N Sundararajan , T Prakash , M Ganapathi