Relation of a frequency-dependent structure with the corresponding frequency-independent structure

is shown that the second theorem in the previous paper [Nakamura and Takewaki (1989) Optimal elastic structures with frequency-dependent elastic supports. Infernalional Journal of Solids and Structures 25(5), 539-5511 can be extended to a more general case where there is no special restriction on the characteristics of frequency-dependent stiffnesses except their positive definiteness and a characteristic as a single-valued function. This theorem enables one to disclose the relationship between the design space of elastic structures with frequency-dependent stiffnesses and that of elastic structures with the corresponding frequency-independent stiffnesses, both with respect to fundamental natural frequency. It facilitates not only clarification of lowest-mode qualification conditions for the frequency-dependent model with the help of the frequency-independent model, but also use of the modal analysis technique via the substitute model (the frequencyindependent model). 0 1998 Elsevier Science Ltd