A Constrained Energy Minimum Approach to Modal Dynamic Control of Vibrations in Ancient Nonlinear Structures

In the paper, the dynamic control of structural vibrations in ancient constructions is considered. Since the constituent material of the structure exhibits poor tensile resistance, an effective performance of the algorithm requires the nonlinearity of the structure to be considered at the very first stage of the design of the control algorithm. Inclusion of the material nonlinearity of the structure into the design of the control mathematical rule presents a number of issues of high complexity either from the theoretical or computational aspects, which make the topic poorly treated in literature, in particular through full mathematical approaches. In the first part of this paper, one sets up a full model for analysis of the spatial masonry constructions with holonomic plasticity taken into account, and, in the second part, one formulates an algorithm aimed at mitigating the dynamic effects on the structure. The implementation of the control algorithm, the development of original calculus codes and the numerical investigations show the high potential of the proposed approach in significantly improving the performance of the structure.