Probabilistic approach for nonlinear modal control of MDOF structures subjected to multiple excitations

A nonlinear control strategy with limited control force is applied to the modal control of the multi-degree-of-freedom (MDOF) structure subjected to multiple excitations. For the modal control of the MDOF structure, a new eigenvalue assignment algorithm that modifies the dynamic characteristics of only the specific mode is proposed. For the probabilistic evaluation of the proposed nonlinear modal control, the joint probability density function (PDF) of the equivalent nonlinearly controlled single-degree-of-freedom (SDOF) system is obtained by the solution ofthe reduced Fokker-Planck equation for the equivalent nonlinear system. To overcome the difficulty in the application of the joint PDF to the MDOF structure controlled by the hybrid mass damper (HMD) system and subjected to multiple excitations, the equivalent damping ratio is proposed. The results of the analysis indicate that the proposed nonlinear modal control strategy is effective for the control of MDOF structures requiring a significantly smaller peak control force than the linear quadratic Gaussian (LQG) controller to produce a similar control performance level.