The structural design sensitivity problem of a discrete mechanical system with a single viscous damper is considered. The sensitivity of the eigenvalues and the eigenvectors with respect to the damping parameter is evaluated. Exact analytical expressions for the eigenvalues and the eigenvectors of the modified system are obtained in addition to approximate expressions. A uniform n-mass oscillator viscously damped by a single damper is taken as an application example. Good agreement between the exact and approximate formulae is observed.
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