Damping optimization in vibrational systems based on amplitude

We consider the optimal damping problem for a linear vibrational system Mẍ + Dẋ + Kx = 0, where M and K are positive definite matrices. For the damping optimization we use a criterion based on minimization of the integral of the solution’s amplitude over a given time interval. Finding the optimal damping D is a very demanding problem, and using this approach the computational cost comes mainly from a large number of matrix exponential computations. We propose an efficient numerical scheme to accelerate these computations. The performance of our approach is illustrated by numerical results for an n-mass oscillator.