Waves in a vibrating solid with boundary damping

The use of modal analysis for second order hyperbolic partial differential equations is well established. This is supported by a general theory when the associated eigenvalue problem is symmetric (or selfadjoint). The situation is different for the nonselfadjoint case and the usefulness of modal analysis is questioned. We show that modal analysis is useful for the wave equation with boundary damping but also show that sometimes more can be achieved by considering wave motion.