Finite Element and Dynamic Stiffness Analysis of Concrete Beam-Plate Junctions

University essay from KTH/MWL Marcus Wallenberg Laboratoriet

Abstract: Measurements and predictions of railway-induced vibrations are becoming a necessity in today’s society where land scarcity causes buildings to be put close to railway traffic. The short distances mean an increased risk of the indoor vibration and noise disturbances experienced by residents. In short, the scope of the project is to investigate the transmission loss and vibration level decrease across various junction geometries. The junctions are modelled in both the Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM). Resonances are avoided when possible by using semi-infinite building components. A two-dimensional model that included Timoshenko beams was set up by Wijkmark [1] and solved using the variational formulation of the DSM by Finnveden [2]. The model is efficient and user-friendly but there is no easy way to adjust the junction geometry since the depths of the walls and the floor slabs are the same. From that study, the current topic was formulated. The results presented in this paper indicate that both the Euler-Bernoulli DS model and the three-dimensional FE model have good potential in describing the vibration transmission across the different junction geometries. The two modelling types show more similar results in the analyses of the bending wave attenuation than in the analyses of the quasilongitudinal wave attenuation. One of the probable causes is that the set length of the Perfectly Matched Layers (PML) is not sufficient at such low frequencies. Larger PMLs require bigger geometries that lead to an increase of the computational time. The other proposed reason is the fact that bending waves are created above the asymmetrical junction when the lower beam is excited by a vertical harmonic force. The flexural displacements are neglected in those cases. The results however, were good enough to be satisfactory. Three junction models were investigated and the attenuation is the highest for both wave types in the case with a beam pair attached to the “middle” of an infinite plate. The attenuation is the second highest across the edge of a semi-infinite plate and the lowest across a junction corner of a semi-infinite plate. As part of the suggested future work, the wave transmission between beam and plate needs to be investigated when Timoshenko beams are included in the DS model. In the Euler-Bernoulli beam theory the cross-section remains perpendicular to the beam axis, which is different to the behaviour of solid elements in FEM.

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