Dynamic Substructuring for Efficient Vibrational Studies in Buildings

Abstract

As a reaction to urban densication, light weight building is an attractive concept for optimally utilizing the capacity of the existing built environment. A common issue paired with light weight construction is the need to engage in vibrational design, in order to minimize hindrance due to human activities such as walking, that cause vibrations in buildings. The Finite Element Method (FEM) is a crucial tool for accurately predicting structural behaviour in such a context. The typical problem with FEM considering large, complex or detailed structures, is that analyses may demand intolerably large computational eort to perform design studies. As a solution, a component-wise approach called Component Mode Synthesis (CMS) is proposed. CMS technique involves separating a construction into substructures, after which Model Order Reduction (MOR) is performed on each substructure individually. With this, the substructures are eciently described by a limited amount of Degrees of Freedom (DoF), after which they are assembled by means of Dynamic Substructuring (DS) techniques. Considering the large amounts of substructure DoF to be coupled to other assembly parts (typically containing 1%-10% of the total amount), an additional measure is required for analyses to be viable: a reliable interface reduction should be performed to deal with the number of unreduced interface DoF that still exist. This research investigates interface reduction by means of Orthogonal Polynomial Series, creating an a priori determined, generic reduction basis which closely resembles the true vibration modes along substructure interfaces. Its performance is investigated with several conceptual case studies, conducting reduced order analysis in Matlab and comparing the results with a full order solution. Alterations are explored, including dierent polynomial bases (Legendre and Fourier), exible couplings and viscoelasticity at either coupled substructure boundaries or bodies. The relevance of complex modes in viscoelastic structures with lightly varying damping and stiness is examined, as well as accuracy of approximations of complex modes, with the prospect of enabling arbitrary frequency dependent material properties to be represented in an ecient manner. This involves approximation of complex modes, obtained by superposition of undamped modes, for which a strategy is developed to optimize considered inclusion of undamped modes. Ultimately, a representative building is modelled in order to relate test results of OPS interface reduction to an applicable context, and to prove the overall eectiveness of the enhanced CMS strategy for large light weight building models. OPS interface reduction using Legendre series has shown to be a reliable and ecient technique depending on the frequency range considered. Its general error trends are mostly insignicant or manageable and exible/ viscoelastic boundary couplings do not de ate this. Disproportional viscoelasticity in substructure bodies, with respect to their mass and stiness matrices, are not necessarily beneted by the use of complex vibration modes when its dynamic modulus varies lightly over frequency. Though the potential which is beyond this scope, yet remains undetermined, the presented approximation technique for complex modes also comes with additional limitations besides the amount of damping. With regards to the applicative value of CMS, the analyses of the light weight building model prove that OPS interface reduction enables signicant improvement of computational eciency, yet yielding accurate results, as a valuable solution for modern-day problems.