Strongly nonlinear instationary interaction

1987 ◽  
pp. 191-212
Author(s):  
Klaus Baumgärtel ◽  
Konrad Sauer
Keyword(s):  
Strongly Nonlinear

scholarly journals Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Dominik Hahn ◽  
Juan-Diego Urbina ◽  
Klaus Richter ◽  
Rémy Dubertrand ◽  
S. L. Sondhi
Keyword(s):  
Many Body ◽  
Strongly Nonlinear ◽  
Nonlinear Lattices ◽  
Body Dynamics

Strongly Nonlinear Vibrations of a Hyperelastic Thin-walled Cylindrical Shell Based on the Modified Lindstedt–Poincaré Method

2019 ◽  
Vol 19 (12) ◽  
pp. 1950160 ◽  
Author(s):  
Jing Zhang ◽  
Jie Xu ◽  
Xuegang Yuan ◽  
Wenzheng Zhang ◽  
Datian Niu
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear System ◽  
Differential Equations ◽  
Nonlinear Vibrations ◽  
Harmonic Excitation ◽  
System Of Differential Equations ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Hardening Behavior ◽  
Thin Walled

Some significant behaviors on strongly nonlinear vibrations are examined for a thin-walled cylindrical shell composed of the classical incompressible Mooney–Rivlin material and subjected to a single radial harmonic excitation at the inner surface. First, with the aid of Donnell’s nonlinear shallow-shell theory, Lagrange’s equations and the assumption of small strains, a nonlinear system of differential equations for the large deflection vibration of a thin-walled shell is obtained. Second, based on the condensation method, the nonlinear system of differential equations is reduced to a strongly nonlinear Duffing equation with a large parameter. Finally, by the appropriate parameter transformation and modified Lindstedt–Poincar[Formula: see text] method, the response curves for the amplitude-frequency and phase-frequency relations are presented. Numerical results demonstrate that the geometrically nonlinear characteristic of the shell undergoing large vibrations shows a hardening behavior, while the nonlinearity of the hyperelastic material should weak the hardening behavior to some extent.

ON STRONGLY NONLINEAR AUTOREGRESSIVE MODELS: IMPLICATIONS FOR THE THEORY OF TRANSIENT AND STATIONARY RESPONSES OF MANY-BODY SYSTEMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350022 ◽  
Author(s):  
T. D. FRANK ◽  
S. MONGKOLSAKULVONG
Keyword(s):  
Evolution Equations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ar Model ◽  
Many Body ◽  
Response Dynamics ◽  
Process Mean ◽  
Stationary Response ◽  
Strongly Nonlinear ◽  
Many Body Systems

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

scholarly journals Strongly nonlinear magnetization above T c in Bi 2 Sr 2 CaCu 2 O 8 + δ

2005 ◽  
Vol 72 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Lu Li ◽  
Yayu Wang ◽  
M. J Naughton ◽  
S Ono ◽  
Yoichi Ando ◽  
...  
Keyword(s):  
Strongly Nonlinear ◽  
Nonlinear Magnetization

An experimental study of strongly nonlinear waves in a rotating system

1987 ◽  
Vol 177 ◽  
pp. 381-394 ◽  
Author(s):  
Dominique P. Renouard ◽  
Gabriel Chabert D'Hières ◽  
Xuizhang Zhang
Keyword(s):  
Equilibrium Shape ◽  
Scaling Law ◽  
Maximum Amplitude ◽  
Rotating Platform ◽  
Coriolis Parameter ◽  
Rotating System ◽  
Height Variation ◽  
Experimental Conditions ◽  
Strongly Nonlinear ◽  
The Right

The influence of rotation upon internal solitary waves is studied in a (10 m × 2 m × 0.6 m) channel located on the large rotating platform at Grenoble University. We observe an intumescence which moves along the right-hand side of the channel with respect to its direction of propagation. Along the side, once the intumescence reaches its equilibrium shape, the height variation of the interface with time is correctly described by the sech2 function, and the characteristic KdV scaling law linking the maximum amplitude and the wavelength along the side is fulfilled. The intumescence is a stable phenomenon which moves as a whole without deformation apart from the viscous damping. For identical experimental conditions, the amplitude of the intumescence along the side increases with increasing Coriolis parameter, and at a given period of rotation of the platform, the celerity along the side increases with increasing amplitude. But for identical conditions, we found that the celerity along the side is equal to the celerity that the wave would have for such conditions without rotation. The amplitude of the intumescence in a plane perpendicular to the wall decreases exponentially with increasing distance from the side, but the crest of the wave is curved backward.

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