Modal approach to dynamic analysis of structures with attachments at uncertain locations

This paper presents an approach to calculate the natural frequency and frequency response function (FRF) statistics of structures connected to attachments at uncertain locations. The main structure is divided into two regions to which the attachment can, or cannot, be connected. The approach is based on component mode synthesis analysis of finite element models of these regions. Multi-point constraints are used to connect the attachment to the main structure to avoid the need to re-mesh the structure. The use of characteristic constraint modes is used to reduce the number of interface degrees of freedom (DOFs) and hence reduce the computational cost further. One or more baseline systems, for which the attachment is connected at a given position, are analysed and the eigensolution found. A perturbation is then applied to the baseline solution to estimate the solution for other attachment locations. The method can be applied to any problem requiring multiple re-analysis. Here, emphasis is placed on probabilistic approaches using Monte Carlo Simulation (MCS), and the natural frequency and FRF statistics are then estimated through MCS. To illustrate the approach, numerical results are presented for a beam and a plate with a randomly attached mass and a plate with an attachment with a number of internal and attachment DOFs. Numerical results are compared with experimental measurements for the cases of a beam and a plate with an attached mass. The results indicate that the method provides accurate predictions at a significantly reduced computation cost when compared to multiple direct solutions.