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The prediction of disturbance transmission, energy transport and acoustic radiation from composite structures is of great importance for many applications, especially where high stiffness-to-weight ratio is a driving design requirement. Developing analytical models for composite structures can be a very difficult task, especially when considering joined composite panels. The finite element (FE) can be used; however, FE models become impractical at high frequencies. Furthermore, due to the difficulty of developing analytical models of composite structures, analyzing their wave behavior is not a straightforward task. Indeed, the knowledge of the wave characteristics of composite structures provides an alternative for predicting the vibrational response of these structures, especially when structures are connected to each other as part of a larger built-up structure.
In this work, the scattering of waves in joined composite plates is considered. The analysis will proceed using the wave and finite element (WFE) method which can be used to model flat and curved panels that are homogenous in two directions but could be arbitrarily complicated through the thickness. The method is based on analysing the FE model of, typically, a rectangular segment of the panel through its thickness. This FE model can be obtained using standard FE libraries and commercial/in-house packages can be equally used with the only restriction being that the nodes and the corresponding degrees of freedom (dofs) are identically arranged at each edge. Consequently, any number of layers and any stacking sequence can be considered. The FE model of the segment is then processed using periodic structure theory to yield an eigenproblem whose solution includes complete information of the wave characteristics of the panel. The eigenproblem can be set in a number of ways. However, a one-dimensionalisation approach will be adopted in this paper.
When joined structures are considered, the WFE method is used to characterise the wave propagation of each panel. The joint is modelled using standard FE with a matching number of nodes at the interfaces with the panels. Then, continuity and equilibrium conditions are enforced at the interfaces. Coupling the WFE and FE models can be utilised to deduce the scattering of waves through the joint. In particular the flow of power will be investigated at different frequencies and in various incidence directions.
The presented approach can be further used in the context of conducting a Dynamic Energy Analysis (DEA) of a built up structure in the context of ray dynamics, which requires the knowledge of the scattering properties of the joint. The method relies on the analysis of small FE models and only a small segment of the joint is modelled; thus, the present approach can be used to develop optimal constructions in various applications.
