An efficient analytical method to obtain the homogenised frequency-independent elastic material properties of cross-laminated timber elements

Abstract

Cross-Laminated Timber (CLT) is a renewable, sustainable, and cost-efficient building element that has been growing in popularity in recent years. To improve one of CLT’s weaknesses, its suboptimal noise and vibration isolation performance, computationally efficient, accessible, and extensible CLT vibro-acoustic models are required. An effective approach to achieve such models is the homogenisation of layered materials. This paper presents a validated homogenisation method based on First-order Shear Deformation Theory (FSDT) that obtains the frequency-independent elastic material properties of CLT. This method is applicable to arbitrary linear elastic material properties, orientations, and stacking sequences of the layers. The homogenised material properties are utilised with FSDT Equivalent Single-Layer (ESL) models that are readily implemented with many finite element method codes to calculate the vibro-acoustic behaviour of CLT elements, even including thickness resonance effects when applied with an appropriate model. The presented homogenisation method for CLT is validated in a numerical study by comparing the mechanical mobilities of ESL models against layerwise dynamic models. The numerical study is conducted based on an experimentally validated 5-ply model for 2- to 7-ply CLT plates with proportionally increasing thicknesses and three idealised boundary conditions. The frequency-independent material properties also allow for the graphical exploration of the anisotropic nature of CLT and the calculation of the universal anisotropic index. The flexibility of the homogenisation method, combined with its ready implementation in already widely implemented FSDT models, can have an application and impact beyond the vibro-acoustic considerations of CLT into the general mechanical modelling of CLT as it is implemented in ever more advanced applications.