Dimension Reduction for Damping Optimization in Linear Vibrating Systems

摘要: We consider a mathematical model of linear vibrational system described by the second-order differential equation Mẍ + Dẋ Kx = 0, where M and K are positive definite matrices, called mass, stiffness, respectively. case damping matrix D is semidefinite. The main problem considered in paper construction an efficient algorithm for calculating optimal damping. As optimization criterion we use minimization average total energy which equivalent to trace solution corresponding Lyapunov AX XA T ―I, A obtained from linearizing equation. Finding such that X minimal very demanding problem, caused large number calculations, required bigger dimensions. propose dimension reduction accelerate process. will present approximation structured error bound approximation. Our based on this Numerical results illustrate effectiveness our approach.