
Analytic mechanics 167
FIGURE 11.2 Vibration of elastic membrane
11.2.2 Non-zero boundary conditions
So far we restricted ourselves to trivial boundary conditions for the sake of
clarity. In engineering practice, however, non-zero boundary conditions are
very often imposed. These, also called enforced motion, boundary conditions
are the subject of our focus here.
Let us consider the membrane with a flexible boundary allowing some or
all of the boundary points to attain non-zero displacement from the plane.
Let the arc length differential of a section of the boundary in equilibrium be
denoted by ds. The reactive force on the section due to displacement