ASYMPTOTIC-DISTRIBUTION OF EIGENVALUES OF A CONSTRAINED TRANSLATING STRING

A new spectral analysis for the asymptotic locations of eigenvalues of a constrained translating string is presented. The constraint modeled by a spring-mass-dashpot is located at any position along the string. Asymptotic solutions for the eigenvalues are determined from the char acteristic equation of the coupled system of constraint and string for all constraint parameters. Damping in the constraint dissipates vibra tion energy in all modes whenever its dimensionless location along the string is an irrational number. It is shown that although all eigenva lues have strictly negative real parts, an infinite number of them app roach the imaginary axis. The analytical predictions for the distribut ion of eigenvalues are validated by numerical analyses.