Mixed-variational formulation for phononic band-structure calculation of arbitrary unit cells

Abstract

This paper presents phononic band-structure calculation results obtained using a mixed variational formulation for 1-, and 2-dimensional unit cells. The formulation itself is presented in a form which is equally applicable to 3-dimensiomal cases. It has been established that the mixed-variational formulation presented in this paper shows faster convergence with considerably greater accuracy than variational principles based purely on the displacement field, especially for problems involving unit cells with discontinuous constituent properties. However, the application of this formulation has been limited to fairly simple unit cells. In this paper we have extended the scope of the formulation by employing numerical integration techniques making it applicable for the evaluation of the phononic band-structure of unit cells displaying arbitrary complexity in their Bravais structure and in the shape, size, number, and anisotropicity of their micro-constituents. The approach is demonstrated through specific examples

arXiv admin note: substantial text overlap with arXiv:1310.6380

References in corpus (2)

• Ultrawide phononic band gap for combined in-plane and out-of-plane waves
• Reduced Bloch mode expansion for periodic media band structure calculations

Cited by in corpus (5)

• On the Properties of Phononic Eigenvalue Problems
• Spectral extended finite element method for band structure calculations in phononic crystals
• Variational Methods For Phononic Calculations
• Combining plane wave expansion and variational techniques for fast phononic computations
• 3-D phononic crystals with ultra-wide band gaps