Strongly nonlinear stationary waves

1987 ◽  
pp. 173-190
Author(s):  
Klaus Baumgärtel ◽  
Konrad Sauer
Keyword(s):  
Stationary Waves ◽  
Strongly Nonlinear

Numerical simulation of plane and spatial nonlinear stationary waves in a two-layer fluid of arbitrary depth

2008 ◽  
Vol 43 (1) ◽  
pp. 118-124
Author(s):  
A. A. Bocharov ◽  
G. A. Khabakhpashev ◽  
O. Yu. Tsvelodub
Keyword(s):  
Numerical Simulation ◽  
Stationary Waves

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

scholarly journals Stationary waves in a superfluid gas of electron-hole pairs in bilayers

2021 ◽  
Vol 103 (20) ◽  
Author(s):  
D. V. Fil ◽  
S. I. Shevchenko
Keyword(s):  
Stationary Waves ◽  
Electron Hole

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.

Ultrasonic Stationary Waves

Nature ◽  
1927 ◽  
Vol 120 (3022) ◽  
pp. 476-477 ◽  
Author(s):  
R. W. BOYLE
Keyword(s):  
Stationary Waves
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