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In the dynamic analysis of structures including the effect of foundation flexibility, the soil is often represented by a horizontal and a rocking spring and associated dashpots. Damping in the different components of this system then varies greatly both in magnitude and nature. Because of the damping terms the resulting model will not have, in general, modes in the classical sense. While a rigorous solution is possible in the frequency domain through the use of Fourier transforms, modal analysis would offer definite advantages from a practical point of view. A rule is presented to apply modal analysis in an approximate way, assigning to each mode a weighted value of damping. Results obtained by application of this rule are compared to exact solutions in the frequency domain. For many cases of interest the error is small. It is also shown that, for these problems, the usual assumption of constant modal damping is not realistic.
Roësset et al. (Thu,) studied this question.