The University of Southampton
Engineering

# Research project: Wave and Finite Element Modelling

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Waves provide a common approach to structural dynamics and acoustics. However, synthesizing the types of waves that travel through a structure is not a simple task. This can be performed analytically for simple structures only. Analyzing wave propagation in composite/sandwiched structures can be a formidable task, if at all possible. Thus, there is a need for numerical techniques that can yield the wave properties of structures. These in turn can be used in various ways to analyse the vibration of the structure or an assembly of structures.

The wave and finite element (WFE) method is a method that can be used to model one- and two- dimensional structures that are homogeneous/piece-wise periodic. A small segment of the structure is meshed using any in-house/commercial finite element (FE) package. This relatively small FE model is post-processed using periodic structure theory to formulate an eigenvalue problem. The solution of this eigenvalue problem yields the full wave behavior of the structure. This includes the dispersion curves that relate the wavenumber to frequency and the wavemodes. The power of the WFE method lies in its usage of the FE method as a basis for formulating the model. Regardless of the complexity through the thickness for two-dimensional or over the cross-section for one-dimensional structures, the FE method can be used to model the small segment of the structure. Thus, in the context of the WFE method, the smaller model doesn't compromise the representation of the details of the structure. This is particularly relevant at higher frequencies.

For example, extruded aluminium profile are typically used as the floor panels in railway cabins. The panel is periodic in one direction and homogeneous along the other. Modelling the wave behaviour of this panel is important for many vibroacoustic applications. To model the floor panel using the WFE method, a single periodic cell, with arbitrary length in the homogeneous direction, is modelled using any FE package.

In the periodic direction (along the x-axis), wave propagation is clearly influenced by the geometric periodicity of the floor panels with visible stop- and pass-bands. On the other hand, wave propagation in the y-direction is much more distinct and exists in the full frequency range. This is due to the continuity of the structure in the y-direction.

At low frequencies, three types of wavemodes are distinct and these are global vibrations of the whole floor panel. The three waves correspond to axial, flexural and bending vibration of the whole floor panel. At higher frequencies, more complicated wavemodes cut on and local vibrations will probably become significant.

Dynamics Group