Seismic response of nonclassically damped systems

Abstract There are many practical problems in which the damping matrix cannot be represented in a classical form, thus leading to complex mode shapes and frequencies. A modal superposition method making use of the complex mode shapes is presented. In the method a complex mode shape is replaced by two real modal vectors. The modal equations are integrated in the same fashion as in the classically damped systems, except we now also use the modal velocities in addition to the usual modal displacements. It is shown that the modal superposition method for the nonclassically damped system gives response values almost identical to those given by the direct integration method. A method of constructing the damping matrix for a coupled primary and secondary system is also presented.