Component-Mode-Based Monte Carlo Simulation for Efficient Probabilistic Vibration Analysis

In this paper, component-mode-based implementations of Monte Carlo simulation (MCS) are presented for efficient probabilistic vibration analysis of complex structures with parameter uncertainties. First, a substructuring technique is used to generate reduced-order models of lowto mid-frequency vibration and power flow. The reduced-order model (ROM) is generated using component mode synthesis of finite element models, followed by a secondary modal analysis to reduce the number of degrees of freedom associated with the substructure interfaces. This formulation allows for efficient and accurate prediction of vibration transmission in complex structural systems. Then, the response is approximated over an uncertainty space to study the statistics of the power flow for a structure with parametric uncertainties. Two MCS techniques that employ first-order approximations of the ROMs are presented: (1) a nominal-ROM-based MCS for a case with many component-mode interactions over the uncertainty space, and (2) a mode-based MCS for a case with a few component-mode interactions. An iterative maximum search procedure is presented, which is used to find the upper bound of the power flow at a specific frequency. For the second MCS approach, this iterative procedure is also extended to yield various statistical properties of the response in addition to the upper bound. These statistical approximations of vibration power flow are demonstrated for two example structures, a reinforced L-shaped plate and a stiffened plate.