AN ASYMPTOTIC AVERAGE DECAY-RATE FOR THE WAVE-EQUATION WITH VARIABLE-COEFFICIENT VISCOUS DAMPING Academic Article

abstract

• The analysis of the damping rate for eigenmodes of a vibrating system with variable coefficient viscous damping is usually difficult because no explicit formulas are available in general. In this paper, using the one-dimensional wave equation as a model, it is shown that for such a system there is an asymptotic average decay rate of eigenmodes that is equal to the uniform damping rate of high frequencies of a wave equation with homogenized constant damping coefficient. The proof is obtained by asymptotic estimation of eigenfrequencies based on an earlier work of Birkhoff and Langer [Proc. Amer. Acad. Arts Sci., 58 (1923), pp. 51-128]. Numerical confirmation is also included, with details of computations given in [C. Qi, Computing the Spectrum of a Vibrating String with Positive and Negative Locally Distributed Viscous Damping, Masters Thesis, Pennsylvania State University, 1987].

authors

• Chen, Goong
• Narcowich, Francis

published proceedings

• SIAM JOURNAL ON APPLIED MATHEMATICS

author list (cited authors)

• CHEN, G., FULLING, S. A., NARCOWICH, F. J., & QI, C.

citation count

• 8

complete list of authors

• CHEN, G||FULLING, SA||NARCOWICH, FJ||QI, C

publication date

• October 1990

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Applied Mathematics  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics

Digital Object Identifier (DOI)

• 10.1137/0150080

start page

• 1341

end page

• 1347

volume

• 50

issue

• 5

URL

• http://dx.doi.org/10.1137/0150080