Exact solution to finite amplitude oscillation of an anisotropic thin rubber tube

1974 ◽  
Vol 56 (2) ◽  
pp. 477-480 ◽  
Author(s):  
M. Shahinpoor
Keyword(s):  
Exact Solution ◽  
Finite Amplitude ◽  
Rubber Tube ◽  
Amplitude Oscillation

Formation and recurrence of ion wave solitons

1975 ◽  
Vol 13 (2) ◽  
pp. 217-230 ◽  
Author(s):  
S. Watanabe
Keyword(s):  
Exact Solution ◽  
Numerical Analysis ◽  
Nonlinear Wave ◽  
Vries Equation ◽  
Dispersive Medium ◽  
Second Harmonic ◽  
Sine Wave ◽  
Finite Amplitude ◽  
Initial State ◽  
Coupled Mode

The interaction between an ion wave and its second harmonic is discussed theoretically, on the basis of coupled-mode equations derived from the Korteweg–de Vries equation. Using an exact solution of the coupled-mode equations, we give a numerical analysis of the properties of the solutions; and we show that superposition of two waves can describe the formation of two solitons, the interaction between them, and the recurrence of an initial state. Our theory can explain completely recent experimental results on ion wave solitons excited by a continuous sine wave.The propagation of a nonlinear wave in a dispersive medium has been extensively studied in the last decade. In a plasma, a finite-amplitude ion wave can form solitons in the course of its evolution, if wave damping is neglected.

An exact solution to the equation of propagation of magneto-acoustic waves

1975 ◽  
Vol 343 (1634) ◽  
pp. 421-425
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Acoustic Waves ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equation ◽  
Finite Amplitude ◽  
Uniform Density ◽  
Sound Waves ◽  
Horizontal Magnetic Field ◽  
Specific Heats

By assuming a uniform horizontal magnetic field and using Lagrangian coordinates the equations of motion, continuity, and magnetic induction are combined to give the exact nonlinear partial differential equation of propagation of vertically travelling magneto-acoustic waves in an atmosphere of uniform density. By means of an intermediary integral, an exact solution is then derived for the cases of a polytropic gas with the ratio of the principal specific heats equal to 5/3 and 2. The solutions are compared with the classical solution of Riemann which describes pure, finite amplitude sound waves propagating in a uniform atmosphere. The degeneration of a magneto-acoustic wave into a shock is illustrated, and the effect of increasing the permanent magnetic field is found to decrease the time for the creation of the discontinuity.

Frequency Scaling at the Onset of Finite Amplitude Oscillation

1986 ◽  
Vol 41 (12) ◽  
pp. 1412-1414 ◽  
Author(s):  
H. Bruce Stewart
Keyword(s):  
Scaling Law ◽  
Finite Amplitude ◽  
Bifurcation Parameter ◽  
Frequency Scaling ◽  
Amplitude Oscillation

The onset of oscillation at non-zero finite amplitude is shown to be governed in the generic case by a scaling law for the frequency of oscillation f in terms of the bifurcation parameter μ – μc namely f ~ (μ – μ)c1/2. This law can be expected to hold whenever such a bifurcation occurs in a nondegenerate system without hysteresis.

scholarly journals An Investigation of Bend Connection Effect on the Finite Amplitude Oscillation in Circular Ducts

2017 ◽  
Vol 17 (AEROSPACE SCIENCES) ◽  
pp. 1-17
Author(s):  
M. Nasr ◽  
W. El-Askary ◽  
M. Hosien ◽  
K. Yousef ◽  
M. Saleh
Keyword(s):  
Finite Amplitude ◽  
Amplitude Oscillation
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