  In structural dynamics, energy dissipative mechanisms with non-viscous
damping are characterized by their dependence on the time-history of the
response velocity, mathematically represented by convolution integrals
involving hereditary functions. Combination of damping parameters in the
dissipative model can lead the system to be overdamped in some (or all) modes.
In the domain of the damping parameters, the thresholds between induced
oscillatory and non--oscillatory motion are called critical damping surfaces
(or manifolds, since we can have a lot of parameters). In this paper a general
method to obtain critical damping surfaces for nonviscously damped systems is
proposed. The approach is based on transforming the algebraic equations which
defined implicitly the critical curves into a system of differential equations.
The derivations are validated with three numerical methods covering single and
multiple degree of freedom systems.
