Equivalent bilinear elastic single degree of freedom system of multi-degree of freedom structure with negative stiffness

The advantage of negative stiffness (NS) is to reduce the structural internal force, especially base shear, which is necessary to be considered during structural design. During design procedures, the structural response should be estimated. For the purpose of estimating the response of the structure with NS, this paper presents an innovative approximate method to transfer a multi degree of freedom (MDOF) structure with NS in the 1st story (MNS1) to an approximate single degree of freedom (SDOF) bilinear elastic system (ASBS). The accuracy of approximation from the MNS1 to the ASBS is studied by the sensitivity method of mode shapes in which the relative changes in structural mode shapes are related to the variation of stiffness. An eight-story numerical example is employed to illustrate the accuracy of approximation by the proposed method. The results show that the accuracy of approach is acceptable, and ASBS can estimate the response of the MNS1.