engleski

Optimizing a damped system - a case study

We consider a second-order damped-vibrational system described by the equation M(x) double over dot + C(v)(x) over dot + Kx = 0, where M, C(v), K are real, symmetric matrices of order n. We assume that the undamped eigenfrequencies (eigenvalues of (lambda(2)M + K)x = 0) omega(1), omega(2), ... , omega(n), are multiple in the sense that omega(1) = omega(2), omega(3) = omega(4), ... , omega(n-1) = omega(n), or are given in close pairs omega(1) approximate to omega(2), omega(3) approximate to omega(4), ... , omega(n-1) approximate to omega(n). We present a formula which gives the solution of the corresponding phase space Lyapunov equation, which then allows us to calculate the first and second derivatives of the trace of the solution, with no extra cost. It can serve for the efficient trace minimization.

Lyapunov equation ; Trace minimization ; Dampers' viscosity optimization ; Multiple eigenfrequencies ; Second order vibrational system

nije evidentirano