mid-frequency vibration analysis of a T-beam

This thesis describes a numerical technique for modeling the vibrational behavior of a complex structure in the mid-frequency range. The structure is divided into subsystems, and each subsystem is modeled using Finite Elements. The obtained results are then manipulated to model variations in the response due to nominal variations in the structure. Based on a Component Mode Synthesis representation, the calculations lead to a deterministic energy flow model. The model represents the deterministic dynamic behavior of the structure for mid frequencies. However, in mid frequencies, the response is sensitive to perturbations in the properties of the structure. An appropriate way to represent those perturbations is to calculate the response of an ensemble of structures. The ensemble is defined in terms of the statistics of the local natural frequencies. A technique combining a Monte Carlo simulation with the Perturbation approach is used to relate the perturbations in the local natural frequencies to the statistics of the energy flow. This combined method is computationally tractable, being several times faster than a full Monte Carlo simulation of the whole global structure.