Systems with Reflection Symmetry Elements

Abstract

Let us consider a chain system of n regular elements (cells). Let each of the system elements have a symmetry plane П-П (Figs. 8.1 and 8.2). The symmetry is understood both in the geometrical and the physicomechanical sense of the word. All connections of an element at the input into and the output from it must be symmetric with respect to П-П. We will call the system that satisfies the above-mentioned conditions an unidirectional (chain) system with reflection symmetry elements. A homogeneous elastic body with a constant cross section (string, beam, cylindrical shell) with some additional regular point-type “inclusions,” for example concentrated masses, rigid and elastic supports, elastic internal connections, etc., can be considered as a special case of such systems.