## A multilevel component mode synthesis approach for the calculation of the phonon density of states of nanocomposite structures.(English)Zbl 1310.74003

Summary: In this paper, a multilevel component mode synthesis (MCMS) approach is presented for the calculation of the phonon density of states (PDOS) of nanocomposite structures. In this approach, the nanocomposite structures are described by hierarchical levels of substructures. The phonon frequencies and modes are first computed for the bottom level substructures by using the theory of lattice dynamics. The computed component modes are then synthesized by using a quasi-static component mode synthesis (QSM) technique to obtain the phonon modes of the upper-level substructures in a bottom-up manner. By repeating this procedure, the PDOS of the entire nanostructure can be obtained. The proposed approach, while retains the atomic description of the nanocomposite structure, significantly reduces the computational cost of the calculation. Numerical calculations show that the proposed approach provides accurate results with a much less computational cost. The PDOS of several 1-D atom chains and 2-D atom sheets are computed by using the MCMS.

### MSC:

 74A25 Molecular, statistical, and kinetic theories in solid mechanics 74S30 Other numerical methods in solid mechanics (MSC2010) 74A60 Micromechanical theories 74A40 Random materials and composite materials
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