Multi-Parameter Linear Periodic Systems: Sensitivity Analysis and Applications

Sensitivity Analysis as a Method of Absorber Tuning for Reduction of Steady State Response of Linear Parametric Systems

“…This is the most dangerous resonance combination for this system. The best way to stabilize the system could be to apply the stabilization method presented in reference [7]. Another way to stabilize the system is to introduce damping for mass M of the primary parametric system (Figure 1).…”

“…Provided that eigenvalues G of monodromy matrix D lie within a unit circle on a complex plane, the trivial solution of the parametric periodic linear systems is (asymptotically) stable in the Lyapunov sense [6,7]. Alternatively, stability can be expressed in terms of characteristic system exponents G "ln" G "/¹ .…”

“…Alternatively, stability can be expressed in terms of characteristic system exponents G "ln" G "/¹ . In this case, stability requires that the highest Lyapunov's characteristic exponent of the system has a negative value [6,7].…”

“…This stability analysis is necessary as it makes little sense to talk about a steady state response of the system if the system is unstable [1,2,6]. Therefore, the optimization method ought to contain an e!ective stabilization method, for instance, similar to the one proposed by Seyranian et al [7]. Thus, the stability of the system has to be checked continuously and an objective optimization function is di$cult to de"ne.…”

Stability analysis for multi-parameter linear periodic systems

“…In a parallel paper, [22], we have added sensitivity analysis to the Floquet method, and shown that e.g. optimal design formulations can then be solved.…”