Modeling and design of materials for controlled wave propagation in plane grid structures.

摘要

Periodic band-gap structures prevent waves in certain frequency ranges from propagating. Materials or structures with large band gaps are desirable for many applications, including frequency filters, vibration protection devices, and wave guides. In this thesis, a simple finite element (FE) model of a periodic plane grid structure is presented. Using the Bloch-Floquet theorem and Lagrange's equations, an FE expression of an eigenvalue problem for harmonic wave propagation in an infinite periodic plane grid structure is derived. Two optimization problems are then formulated to maximize the band gap above a particular band in infinite periodic plane grid structures: one is by selective addition of non-structural masses, and the other is by a combination of selective addition of non-structural masses and adjusting of the cross section dimension (radius) of selective grid elements. Numerical implementation issues for the optimization problems are discussed and examples using symmetric periodic plane grid structures are presented. Finally, wave propagation in finite periodic plane grid structures is analyzed by considering the response of finite periodic plane grid structures subjected to harmonic loading using two applications: filter and wave guide. Special attention is paid to the response in frequency ranges of the band gaps for the corresponding infinite periodic structures.