Rheological-dynamical theory of vibrations of multi-degree-of-freedom structures: Design of viscoelastoplastic dampers

An analytical model and procedure was developed for computing the dynamic response of linear engineering structures by using the rheological-dynamical (RDA) theory of vibrations. This method is essentially in correspondence with the traditional mode-component synthesis. The eigenvalues and eigenvectors of viscoelastic structures created by the RDA theory are the eigenpairs for the whole structure. This algorithm is actually an exact technique for solving the eigenvalues in the state of critical damping, which means that RDA theory itself did not introduce any additional errors to predict the damping of structures. On the other hand, the dynamic response can also be implemented by using mode superposition when the Ritz vectors are used for computing the dynamic response of linear structures. Two types of damping are considered: viscous damping in the case of linear analysis, defined as stiffness and/or mass proportional and, in the case of nonlinear analysis, hysteretic damping caused by inelastic deformations of the damper (bar). Based on the formulas of the two types of damping, an especially attractive iterative procedure for the design of viscoelastoplastic dampers is derived.