A modal superposition method for non-linear base-isolated multistorey structures

A modal procedure for non-linear analysis of multistorey structures with highdamping base-isolation systems is developed. At first it is observed that simple bilinear approximations to hysteresis loops can be defined for non-linear modelling of seismic isolators. Then material non-linearities are treated as pseudo-forces, and equivalent linear equations are uncoupled in the complex field. The modal responses are obtained with an extension of Nigam-Jennings method to non-classically damped systems, in conjunction with a specific iterative technique. Since the isolation loop parameters usually change with the design-displacement, some iterations are needed to obtain calculated and assumed peak displacements very close. The modal approach herein proposed avoids the solution of the tangent eigenproblem at every stiffness change, provides useful dynamic informations (such as natural frequencies and mode-shapes of the isolated structure), and can give accurate solutions even with a few modes superposition.