Extended plane wave expansion formulation for 1-D viscoelastic phononic crystals

Abstract

The extended plane wave expansion (EPWE) method is formulated in order to obtain the complex dispersion diagram of bulk waves in 1-D viscoelastic phononic crystal solids considering the standard linear solid model (SLSM). This new formulation is important to handle evanescent Bloch waves in 1-D viscoelastic periodic structures for mechanical wave attenuation. The viscoelastic effect can increase the unit cell wave attenuation in 1-D periodic structures. In addition, the increase of relaxation time (up to ωa/2πct=7) and the decrease of final state of shear modulus (considering ωa/2πct≤1.9) enhance the unit cell wave attenuation.

Keywords

• Spatial Fourier series
• Viscoelasticity
• Evanescent waves
• Floquet–Bloch theorem