On the effect of damping on the stabilization of mechanical systems via parametric excitation

摘要: The effect of damping on the re-stabilization statically unstable linear Hamiltonian systems, performed via parametric excitation, is studied. A general multi-degree-of-freedom mechanical system considered, close to a divergence point, at which mode incipiently stable and n − 1 modes are (marginally) stable. asymptotic dynamics studied Multiple Scale Method, supplies amplitude modulation equations ruling slow flow. Several resonances between excitation natural frequencies, direct 1:1, 1:2, 2:1, or sum difference combination types, algorithm calls for using integer fractional power expansions performing nonstandard steps. It found that slight able increase performances control system, but only far from resonance. Results relevant sample compared with numerical findings based Floquet theory.