scholarly journals A remark on parametric resonance for wave equations with a time periodic coefficient

2011 ◽  
Vol 87 (8) ◽  
pp. 128-129 ◽  
Author(s):  
Hideo Ueda
Keyword(s):  
Parametric Resonance ◽  
Wave Equations ◽  
Periodic Coefficient ◽  
Time Periodic

On the Parametrical Excitation of Nonlinearly Coupled Wave Equations

1995 ◽  
Author(s):  
A. H. P. van der Burgh ◽  
P. Kuznetsov ◽  
S. A. Vavilov
Keyword(s):  
Wave Equations ◽  
Operator Method ◽  
Dynamical Behaviour ◽  
Existence Theory ◽  
Rigorous Analysis ◽  
Coupled Wave Equations ◽  
Time Periodic Solutions ◽  
Transversal Vibrations ◽  
Time Periodic ◽  
Coupled Wave

Abstract In this paper a mathematical model for the study of the interaction of longitudinal and transversal vibrations in a stretched string is presented. The study implies an existence theory for time periodic transversal vibrations generated by a horizontal excitation of one of the end-points of the string. The conditions for the existence of this parametrically excited time periodic vibrations are evaluated in a practical application. The innovative character of the results obtained concern the application of an operator method to a system of nonlinearly coupled wave equations modeling the dynamical behaviour of a strectched string where unite elasticity is taken into account. It may be known that in the literature little attention has been paid to a rigorous analysis of time periodic solutions for systems of partial differential equations.

Subharmonic resonance of Venice gates in waves. Part 2. Sinusoidally modulated incident waves

1997 ◽  
Vol 349 ◽  
pp. 327-359 ◽  
Author(s):  
PAOLO SAMMARCO ◽  
HOANG H. TRAN ◽  
ODED GOTTLIEB ◽  
CHIANG C. MEI
Keyword(s):  
Laboratory Experiments ◽  
Narrow Band ◽  
Periodic Coefficient ◽  
Venice Lagoon ◽  
Global Bifurcations ◽  
Approximate Analysis ◽  
Local And Global Bifurcations ◽  
Incident Waves ◽  
Time Periodic ◽  
Autonomous Dynamical System

In order to examine the effects of finite bandwidth of the incident sea spectrum on the resonance of the articulated storm gates for Venice Lagoon, we consider a narrow band consisting of the carrier frequency and two sidebands. The evolution equation for the gate oscillations now has a time-periodic coefficient, and is equivalent to a non-autonomous dynamical system. For small damping and weak forcing, approximate analysis for local and global bifurcations are carried out, and extended by direct numerical simulation. Typical bifurcation scenarios are also examined by laboratory experiments.

Minimax estimates for functionals of solutions of wave equations with time-periodic right-hand sides

1995 ◽  
Vol 77 (5) ◽  
pp. 3452-3457
Author(s):  
L. T. Adzhubey ◽  
O. G. Nakonechy ◽  
Yu. K. Pidlypenko
Keyword(s):  
Wave Equations ◽  
Solutions Of Wave Equations ◽  
Right Hand ◽  
Time Periodic

On the rigorous foundation of short-wave asymptotics

1966 ◽  
Vol 62 (2) ◽  
pp. 227-244 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Wave Equations ◽  
Classical Mechanics ◽  
Short Wave ◽  
Two Dimensions ◽  
Linear Wave ◽  
Wave Optics ◽  
Wave Mechanics ◽  
Linear Wave Equations ◽  
Wave Limit ◽  
Time Periodic

AbstractCertain physical theories are short-wave limits of more general theories. Thus ray optics is the short-wave limit of wave optics, and classical mechanics is the short-wave limit of wave mechanics. In principle it must be possible to deduce the former from the latter theories by a rigorous mathematical limiting process; in fact the arguments found in the literature are formal, plausible and non-rigorous. (We are here concerned with linear wave equations and time-periodic phenomena.) For some wave equations there are, however, a few explicit rigorous canonical solutions relating to simple geometrical configurations, e.g. to conics in two dimensions for the equations of acoustics, and for these the asymptotics can be found rigorously. For more general configurations the solution of a typical boundary-value problem can be reduced to the solution of a Fredholm integral equation of the second kind.

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