Controllability of Structures with Closely Spaced Natural Frequencies Based on Perturbation Analysis

Abstract:

An investigation was made into the influence of frequency intensity on the controllability of structures with closelyspaced natural frequencies.The perturbation equations were established for a closedloop system to study the relationship of frequencies,modal damping ratios and perturbation parameters.The analysis focused on a threedegreefreedom structure with closely spaced natural frequencies.The velocity and displacement feedbacks were considered in the calculation.Several cases with velocity feedback and state feedback were considered.And the preciseness of perturbation methods was checked.The calculation results show that the damping ratios of two modes are decreasing with the decreasing of intensity parameter values of the structure with closely spaced natural frequencies,indicating that the controllability of corresponding modes is diminishing.The uncertainties in mass and stiffness matrices were also discussed in this paper.The calculation results show that the degrees of mode coupling will change due to the structural uncertainties and the controllability will be influenced subsequently.