Abstract

A new method is presented to determine approximate closed-form solutions for the complex-valued frequencies of moderately damped linearly elastic structures. The approach is equally applicable to finite degree of freedom systems and distributed parameter systems. The damping operator is split into two components, the first of which uncouples the quadratic eigenvalue equation, and the eigenvalues are expressed as a power series in the second component of the damping operator. Specific numerical examples include both finite degree of freedom and distributed parameter systems. It is shown that for moderate damping, that is, when the second component of the damping operator is small, but not negligible, the series solution truncated after quadratic terms provides an excellent approximation to the true eigenvalues.

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