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Peer ReviewedPostprint (author's final draft

Vibration transmission through structural connections is modelled in a deterministic way by means of modal analysis. This model is used first to study the effect of elastic joints across the floor in the transmission of impact noise. They are an effective means of reducing impact noise propagation, and can almost eliminate it for small values of the joint stiffness. The method is also used to study the acoustic relevance of studs in lightweight floor transmission. Different ways of modelling the studs are presented and compared. For the examples developed, the best option is to use springs for modelling the studs rather than more complex models involving springs and beams. Also the different behaviour of point and line connections is verified, as well as the influence of the position of the studs.

SUMMARYIn finite element (FE) analysis, traditional penalty methods impose constraints by adding virtual stiffness to the FE system. In dynamics, this can decrease the critical time step of the system when conditionally stable time integration schemes are used by introducing spurious modes with high eigenfrequencies. Recent studies have shown that using mass penalties alongside traditional stiffness penalties can mitigate this effect for systems with a one single-point constraint. In the present work, we extend this finding to include systems with an arbitrary set of multipoint constraints. By analysing the generalised eigenvalue problem, we show that the values of spurious eigenfrequencies may be controlled by the choice of stiffness and mass penalty parameters. The method is demonstrated using numerical examples, including a one-dimensional contact-impact formulation and a two-dimensional crack propagation analysis. The results show that constraint imposition using the bipenalty method can be employed such that the critical time step of an analysis is unaffected, whereas also displaying superiority over the mass penalty method in terms of accuracy and versatility.

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