  Energy methods for constructing time-stepping algorithms are of increased
interest in application to nonlinear problems, since numerical stability can be
inferred from the conservation of the system energy. Alternatively, symplectic
integrators may be constructed that preserve the symplectic form of the system.
This methodology has been established for Hamiltonian systems, with numerous
applications in engineering problems. In this paper an extension of such
methods to non-conservative acoustic systems is presented. Discrete
conservation laws, equivalent to that of energy-conserving schemes, are derived
for systems with linear damping, incorporating the action of external forces.
Furthermore the evolution of the symplectic structure is analysed in the
continuous and the discrete case. Existing methods are examined and novel
methods are designed using a lumped oscillator as an elemental model. The
proposed methodology is extended to the case of distributed systems and
exemplified through a case study of a vibrating string bouncing against a rigid
obstacle.
