I've been trying to find an explanation for why bandgaps can form in periodic elastic laminates but so far I haven't found a good explanation. Can anyone point me to any resources which might provide an explanation or give a good analogy between this and other areas of physics where bandgaps may occur?
A bandgap is a range of energy levels in a solid where no electron states can exist. It is the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to move freely in the conduction band, but are bound to their atoms in the valence band. The size of the bandgap determines the electrical conductivity of the solid.
Periodic elastic laminates are structures made up of alternating layers of different materials. The periodicity of the structure leads to the formation of bandgaps. This is because the periodic structure causes a wave interference effect, where waves of certain frequencies are either amplified or cancelled out. This is similar to the way that light waves interfere to create a rainbow pattern in a soap bubble.
When a wave encounters a periodic structure, it can either be transmitted through the structure, reflected back, or trapped within the structure. The frequency of the wave determines which of these outcomes will occur. For certain frequencies, the wave will interfere destructively with itself, leading to a cancellation of the wave. This results in a bandgap, where no wave propagation is possible.
The concept of bandgaps in periodic elastic laminates is analogous to the concept of bandgaps in semiconductors in electronics. In semiconductors, the bandgap refers to the energy difference between the valence band and the conduction band. Electrons can jump from the valence band to the conduction band when they absorb enough energy. The size of the bandgap determines the electrical properties of the semiconductor.
Bandgaps in periodic elastic laminates are caused by the wave interference effect due to the periodic structure of the laminate. This is similar to the concept of bandgaps in semiconductors in electronics, where the bandgap refers to the energy difference between the valence band and the conduction band.
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