DYNAMICAL RELIABILITY MAXIMIZATION OF MDOF QUASI-INTEGRABLE HAMILTONIAN SYSTEMS WITH INTERNAL RESONANCES

Theoretically, the control problem of maximizing dynamical reliability of MDOF quasi-integrable Hamiltonian system is discussed in this paper. The excitation is modeled as Gaussian white noise (GWN). In the case of internal resonances, the averaging method and the dynamical programming principle are combined to obtain the equations of motion of the optimally controlled system, which are represented by Ito stochastic differential equations about the amplitude and the phase variables. The conditional reliability function and mean first-passage time of the optimally controlled system are obtained from solving the corresponding partial differential equations, respectively. A 2-DOF system is given as an example to illustrate the effectiveness of the proposed procedure.