Vibration analysis of structures with uncertain located attachments

Abstract

Attachments affect the dynamic response of an assembled structure. When engineers are modelling structures, small attachments will often not be included in the "bare" model, especially in the initial design stages. The location of these attachments might be poorly known, yet they affect the response of the structure. Generally, the finite element method is always combined with Monte Carlo simulation (MCS) to calculate the response of the structures with uncertain parameters. However, the attachment will be connected to a main structure having a large number of degree of freedoms (DOFs), and each new connected location will lead to a re-analyse of the model, which is usually computationally expensive. In this thesis, two methods to efficiently quantify the variability in the dynamic characteristics of a structure due to uncertainty in the connected location of the attachment are proposed. Multi-point constraints are used to connect the attachment to the main structure to avoid the need to re-mesh the structure. The first method is based on a modal based model order reduction method (MOR), and component mode synthesis (CMS) with characteristic constraint modes. The CMS method is combined with perturbation and sensitivity methods to efficiently and accurately estimate the component model properties without the need to repeatedly solve the full eigenvalue problem. The second method is based on a non-modal based MOR method, Krylov subspace method. The reduction is achieved by using low-order projection matrices. One (or more) analysis is performed for the attachment located at a given position(s) and at a given frequencies to obtain the projection matrices. Afterwards, a parametric MOR method is applied to reduce the model order. For both methods, uncertainty in the location of the attachment is included in a MCS. Based on the frequency range of interest, different methods can be selected. The methods are equally applicable to possibilistic, interval-based uncertainties. Numerical results are compared to experimental measurements for the cases of a beam and a plate with an attached mass, and a plate with an attachment with a number of internal and attachment DOFs. The results indicate that the methods provide accurate predictions at a significantly reduced computation cost when compared to multiple direct solutions.