Modeling low-frequency vibration in light-weight timber floor/ceiling systems

Producing practical designs for light-weight timber-framed structures that achieve high sound isolation remains a challenging task, in part because of the lack of models that can accurately predict the sound transmission through proposed designs. This work develops detailed modeling of structural vibration in timber floor/ceiling systems, from which sound transmission in the low-frequency regime (10-150 Hz) can be computed, as a design tool for producing practical timber floor/ceiling details that achieve high isolation for low-frequency sound. The mathematical model uses a variational formulation that enables straightforward modeling of complex composite structures, and introduces the notion of coupling layers to model the movement between joined materials that occurs with practical bonding methods, thereby improving on existing models that assume either perfectly bonded or perfectly slipping interfaces. The composite model structure is assembled only at the computational step, giving an efficient computational scheme that also fits well into the design-development cycle. Results from a parallel experimental program are used to validate the model and to determine effective coupling and damping parameters. The influence of coupling parameters is shown for an example floor, demonstrating that finite slippage at joints is required for the model to predict low-frequency vibration in practical constructions.