Wave propagation in substructural chain-type structures excited by harmonic forces (Q1315741)

The wave propagation of substructural chain-type structures (SBCHS) excited by harmonic sources is discussed. Such an object is composed of substructures (SBS) which are connected end-to-end and form a one- dimensional periodic system. Each SBS has two terminal nodes and an internal one, to which an external force could be impressed. When applying the finite element method, two matrices are associated to each object: the mass matrix and the stiffness matrix. It is shown that a SBCHS is described via a matrix which is a symplectic one. In deriving the forced solutions, the properties of symplectic matrices are largely used. At the end numerical examples are presented. The paper is finely written. However, we want to point out two facts pertaining to the content of it: when speaking about wave propagation in periodic structures, one ought to quote the classical work of Brillouin on this topic, and the discussed problem is similar (but it is a scalar case only) to the problem of electric propagation in ladder-type filter; there one finds pass bands and stop ones. The methods used in filter theory are different from these which are used in the paper, but the conclusions are the same.