  The aim of this paper is to explore the relationship between invariant cones
and nonlinear normal modes in piecewise linear mechanical systems. As a key
result, we extend the invariant cone concept, originally established for
homogeneous piecewise linear systems, to a class of inhomogeneous continuous
piecewise linear systems. The inhomogeneous terms can be constant and/or
time-dependent, modeling nonsmooth mechanical systems with a clearance gap and
external harmonic forcing, respectively. Using an augmented state vector, a
modified invariant cone problem is formulated and solved to compute the
nonlinear normal modes, understood as periodic solutions of the underlying
conservative dynamics. An important contribution is that the invariant cones of
the underlying homogeneous system can be regarded as a singularity in the
theory of nonlinear normal modes of continuous piecewise linear systems. In
addition, we use a similar methodology to take external harmonic forcing into
account. We illustrate our approach using numerical examples. The resulting
backbone curves and frequency response diagrams are compared to the results
obtained using the shooting method and brute force time integration.
