Keywords: model reduction, finite element method, vibrations, buildings, multistorey, lightweight, wood.

The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build lightweight structures without noise and disturbing vibrations between storeys and rooms. The dynamic response of floor and wall structures may be investigated using finite element models with three-dimensional solid elements [1]. In order to analyse the global response of complete buildings, finite element models may be created by assembling models of floor and wall structures into large models of complete buildings. When assembling the floor and wall models, the number of degrees of freedom quickly increases to exceed the limits of computer capacity, at least in a reasonable amount of computational time. The objective of the analyses presented in this paper is to evaluate methods for model reduction of detailed finite element models of floor and wall structures and to investigate the influence of reducing the number of degrees of freedom and computational cost on the dynamic response of the models in terms of eigenfrequencies, eigenmodes and vibration transmission.

The finite element model of a floor [1], created and validated by measurements on a full-scale experimental wooden floor-wall structure, that was used as a reference model in the model reduction studies. The studies were restricted to frequencies below 100 Hz. Three different methods of model reduction were investigated; Guyan reduction, component mode synthesis and a third approach where a new finite element model was created with structural elements. Eigenvalue and steady-state analyses were performed in order to compare the errors in eigenfrequencies, eigenmodes and vibration transmission for the reduced models relative the reference model. It was concluded that both Guyan reduction and structural elements leads to large errors in the frequency range studied. However, the model with structural elements behaves similar to the full model but with a shift in frequencies which produces large errors at particular frequencies. In order to obtain good accuracy, it is concluded that component mode synthesis is preferable. With a proper amount of retained eigenmodes in the component mode synthesis, a very good correlation in eigenmodes is obtained. The drawback of component mode synthesis compared to modelling with structural elements is the increased computational cost, although the number of degrees of freedom is small in comparison, as a result of the large bandwidth of the system matrices.

1

O. Flodén, J. Ejenstam, "Vibration Analyses of a Wooden Floor-Wall Structure - Experimental and Finite Element Studies", Report TVSM-5176, Division of Structural Mechanics, Lund University, Sweden, 2011.

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