Unified analysis approach for the energy flow in coupled vibrating systems with two types of hybrid uncertain parameters

• Two hybrid uncertain models are introduced to model the uncertain parameters in coupled vibrating systems.
• A HSIPM is presented for the unified energy flow analysis under two hybrid uncertain models.
• The effectiveness and efficiency of HSIPM are investigated.

For determining the energy flow in coupled vibrating systems with limited information, two hybrid uncertain models have been introduced to model the uncertain parameters. One is the hybrid probability and interval model in which the probability and interval variables exist simultaneously. The other one is the hybrid interval probability model in which some distribution parameters of the probability variables are given as interval variables. A hybrid stochastic interval perturbation method (HSIPM) is proposed for the unified energy flow analysis in coupled vibrating systems under two hybrid uncertain models. In the proposed method, by temporarily neglecting the uncertainties of interval variables, the first-order stochastic perturbation method is adopted to calculate the expectation and variance of the energy vector. Afterwards, the interval of the expectation and variance of the energy vector can be obtained by the first-order interval perturbation method. Two numerical examples are given to illustrate the feasibility and effectiveness of the proposed method.