Boundary Conditions in the Waveguide Network

If the ideal beam is of finite length, then we are required to supply boundary conditions at the termination; we show here how to apply such conditions in the waveguide mesh described in the previous section. We will assume that one end of the beam is positioned at $x=0$; all discussion of boundary conditions applies equally at the other end (or we may assume that the beam is of semi-infinite extent). It is of note that because the Euler-Bernoulli Equation (5.1) is of fourth order in the spatial variable, we are required to provide two boundary conditions at each termination [176]. The simplest boundary conditions for the ideal beam are correspondingly simple to implement in the waveguide mesh. From [77], the most physically relevant such boundary conditions are the following: