This page holds a series of animations relating to various research topics. The animations can be viewed directly on this page, or higher quality videos may be downloaded.
Lattice Simulations
These simulations are related to standing waves, localisation and focusing of elastic waves in periodic lattices formed from Euler-Bernoulli beams. The animations were produced using the finite element software COMSOL Multiphysics®.
Relevant publication: Colquitt D.J., Jones I.S., Movchan N.V., Movchan A.B. 2011 Dispersion and localization of elastic waves in materials with microstructure. Proc. R. Soc. A 467(2134), 2874-2895. (doi: 10.1098/rspa.2011.0126).
The animations presented here correspond to the following figures in the above paper. Click on the title to be taken to the corresponding figure. A 7z compressed archive containing uncompressed AVI movies of all the lattice simulations shown below can be download here (9.82 MB). You will need an appropriate application to extract the archive, such as 7-Zip.
The animations are presented here as YouTube™ videos. High quality files are also available for download.
Total reflection
This animation represents a harmonic wave interacting with a specially constructed finite slab of a diatomic lattice. The wave is generated by the time-harmonic vibration of a point source, in a homogeneous monatomic lattice on the left. The wave then interacts with the heterogeneous slab. In this instance, the forcing frequency is chosen such that it lies in a band gap on the dispersion diagram corresponding to the diatomic slab. As expected virtually all of the wave is reflected, with very little transmission.
A high quality version of this animation can be downloaded here (AVI, 959 KB).
Focussing & a second source
This animation is from the same numerical experiment as the previous example. However, the forcing frequency is chosen such there is a clear preferential direction of propagation. The animation on the left clearly illustrates the preferential direction, which is clearly visible within the slab. Moreover, one can observe the apparent formation of second source on the right hand side of the slab. This second source forms a mirror image of the original source of the left hand side. The second source is shifted due to the strong preferential direction is the diatomic interface.
A high quality version of this animation can be downloaded here (AVI, 1.33 MB).
Focussing & image formation
This computation is a modified version of the previous experiment. Here the source has been shifted further away from the structured interface. Once again one can observe the clear preferential direction of propagation within the structured interface. The image of the source can also be observed on the right hand side of the interface region. It is noted that the second source is also shifted when compared with the previous case.
A high quality version of this animation can be downloaded here (AVI, 1.27 MB).
A standing rotational wave
This animation corresponds to a standing rotational mode. The linear displacement of the junctions is small compared with the rotation at the junctions. The magnitude of the group velocity is zero.
A high quality version of this animation can be downloaded here (AVI, 519 KB).
A second standing wave
This animation corresponds to a standing mode where the two junctions in the irreducible cell undergo relative translations, with no rotation at the junctions. The magnitude of the group velocity is zero.
A high quality version of this animation can be downloaded here (AVI, 379 KB).
Fundamental modes of the lattice beams
This animation corresponds to the case when there are no junction displacements. Instead, the lattice beams vibrate at their natural frequencies.
A high quality version of this animation can be downloaded here (AVI, 353 KB).
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The University of Liverpool | Department of Mathematical Sciences | Waves & Solid Mechanics Research Cluster