Problem of Forced Oscillations
The problem of diffraction of a plane wave on a system of wedge-shaped regions with the common edge is the key problem of the mathematical theory of diffraction. Its solution helps us understand the physical mechanism of edge diffraction and can be used for the description of edge-diffracted waves by the method of the geometrical theory of diffraction. Section 1of this chapter considers a special formulation of this problem aimed at obtaining formulas for the edge waves only. We begin with the simplest case-diffraction of an acoustic wave on a system of wedge-shaped regions with conditions of rigid contact at the interfaces. The statement of this problem is based on the development of the Sommerfeld-Malyuzhinetz method (Malyuzhinetz, 1951), which is considered briefly in Section 1. A modification of this approach is considered in Section 2. Using the modified approach, we state the diffraction problem in Section 3 as a problem of forced oscillations. In Section 4 we generalize the approach on a case of diffraction of the vector waves of any physical nature on a system of wedge-shaped regions with the arbitrary linear conditions of contact at the interfaces.