TY - JOUR

T1 - Stabilization via parametric excitation of multi-dof statically unstable systems

AU - Arkhipova, Inga M.

AU - Luongo, Angelo

PY - 2014

Y1 - 2014

N2 - The problem of re-stabilization via parametric excitation of statically unstable linear Hamiltonian systems is addressed. An n-degree-of-freedom dynamical system is considered, at rest in a critical equilibrium position, possessing a pair of zero-eigenvalues and n - 1 pairs of distinct purely imaginary conjugate eigenvalues. The response of the system to a small static load, making the zero eigenvalues real and opposite, simultaneous to a harmonic parametric excitation of small amplitude, is studied by the Multiple Scale perturbation method, and the stability of the equilibrium position is investigated. Several cases of resonance between the excitation frequency and the natural non-zero frequencies are studied, calling for standard and non-standard applications of the method. It is found that the parametric excitation is able to re-stabilize the equilibrium for any value of the excitation frequencies, except for frequencies close to resonant values, provided a sufficiently large excitation amplitude is enforc

AB - The problem of re-stabilization via parametric excitation of statically unstable linear Hamiltonian systems is addressed. An n-degree-of-freedom dynamical system is considered, at rest in a critical equilibrium position, possessing a pair of zero-eigenvalues and n - 1 pairs of distinct purely imaginary conjugate eigenvalues. The response of the system to a small static load, making the zero eigenvalues real and opposite, simultaneous to a harmonic parametric excitation of small amplitude, is studied by the Multiple Scale perturbation method, and the stability of the equilibrium position is investigated. Several cases of resonance between the excitation frequency and the natural non-zero frequencies are studied, calling for standard and non-standard applications of the method. It is found that the parametric excitation is able to re-stabilize the equilibrium for any value of the excitation frequencies, except for frequencies close to resonant values, provided a sufficiently large excitation amplitude is enforc

U2 - 10.1016/j.cnsns.2014.02.028

DO - 10.1016/j.cnsns.2014.02.028

M3 - Article

VL - 19

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

IS - 10

ER -