Darmawijoyo, Darmawijoyo (2003) On a Rayleigh Wave Equation with Boundary Damping. Reports of the Department of Applied Mathematical Analysis. ISSN 13896520

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Abstract
In this paper an initialboundary value problem for a weakly nonlinear string (or wave) equation with nonclassical boundary conditions is considered. One end of the string is assumed to be ?xed and the other end of the string is attached to a dashpot system, where the damping generated by the dashpot is assumed to be small. This problem can be regarded as a simple model describing oscillations of exible structures such as overhead transmission lines in a wind?eld. An asymptotic theory for a class of initialboundary value problems for nonlinear wave equations is presented. It will be shown that the problems considered are wellposed for all time t. A multiple timescales perturbation method in combination with the method of characteristics will be used to construct asymptotic approximations of the solution. It will also be shown that all solutions tend to zero for a sufficiently large value of the damping parameter. For smaller values of the damping parameter it will be shown how the stringsystem eventually will oscillate. Some numerical results are also presented in this paper.
Item Type:  Article 

Uncontrolled Keywords:  Wave equation, galloping, boundary damping, asymptotics, twotimescales perturbation method. 
Subjects:  Q Science > QA Mathematics > QA1939 Mathematics > QA37.3.1.64 Applied Mathematics 
Divisions:  06Faculty of Education and Educational Science > 84202Mathematics Education (S1) 
Depositing User:  Dr. Darmawijoyo Hanapi 
Date Deposited:  01 Oct 2019 09:10 
Last Modified:  01 Oct 2019 09:10 
URI:  http://repository.unsri.ac.id/id/eprint/9186 
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