Abstract
The localization phenomenon for high-frequency vibration modes of imperfectly repetitive structures is considered by using an analogy between computational structural mechanics theory and optimal control theory. In particular, the simplectic matrix method of control theory is applied to the dynamic external stiffness matrix of a typical repeating sub-structure. The eigensolution of the simplectic matrix for the case where the sub-structures are connected by a single line of springs is solved analytically. This gives the passband for the frequency of the travelling waves along the sub-structural chain and the corresponding eigenmode. Hence it is shown how the influence of local disturbances of the sub-structural chain on the behaviour of the whole chain can be considered analytically, thus explaining the mechanism of the localization of high-frequency vibration modes. Numerical examples are therefore not needed, although a few are introduced solely to confirm the correctness of conclusions already drawn from the analytical method.
Get full access to this article
View all access options for this article.