On static and dynamic computations of one-dimensional regular systems: PMM vol. 39, n≗ 3, 1975, pp. 513–519

Abstract

Simplifications of the computations of statics and the small vibrations of regular mechanical structures are investigated. On the basis of the method of an elemenatry cell it is shown that these simplifications hold for all regular systems which are representable as elementary in the sense of some irreduciblerepresentation of the subgroup D 2H (1) ⊂D 2G (1) ∗ where D 2H (1) ∗ is the space symmetry group of the corresponding infinite regular system. The boundary conditions of such elementary systems are described in general form. The essence of the simplifications is the passage from a computation of the regular construction over to computations of a finite number of elementary systems in the sense of the group D 2H (1) ∗ whose types are indicated. The loading of the elementary systems is defined by using a developed effective method of decomposing the load of the initial regular system. A number of investigations [1–4] is devoted to a study of regular mechanical systems. These investigations are associated with translational symmetry of an infinite regular system in [2], which permitted use of the group representation theory apparatus developed for applications [5], However, the most general and complete results in the mechanics of regular systems should be expected in a more perfect accounting of the symmetry elements of an infinite regular system. which possesses the space symmetry group D 2 H (1). In particular, the nature of all the boundary conditions specifying the decoupling (dissociation) of the system of equations under investigation for the mechanical problem is successfully clarified in this paper and specific features of this decoupling are established.