  This work deals with the modeling of nonsmooth vibro-impact motion of a
continuous structure against a rigid distributed obstacle. Galerkin's approach
is used to approximate the solutions of the governing partial differential
equations of the structure, which results in a system of ordinary differential
equations (ODEs). When these ODEs are subjected to unilateral constraints and
velocity jump conditions, one must use an event detection algorithm to
calculate the time of impact accurately. Event detection in the presence of
multiple simultaneous impacts is a computationally demanding task. Ivanov
proposed a nonsmooth transformation for a vibro-impacting
multi-degree-of-freedom system subjected to a single unilateral constraint.
This transformation eliminates the unilateral constraints from the problem and,
therefore, no event detection is required during numerical integration. Ivanov
used his transformation to make analytical calculations for the stability and
bifurcations of vibro-impacting motions; however, he did not explore its
application for simulating distributed collisions in spatially continuous
structures. We adopt Ivanov's transformation to deal with multiple unilateral
constraints in spatially continuous structures. Also, imposing the velocity
jump conditions exactly in the modal coordinates is nontrivial and challenging.
Therefore, in this work we use a modal-physical transformation to convert the
system from modal to physical coordinates on a spatially discretized grid. We
then apply Ivanov's transformation on the physical system to simulate the
vibro-impact motion of the structure. The developed method is demonstrated by
modeling the distributed collision of a nonlinear string against a rigid
distributed surface. For validation, we compare our results with the well-known
penalty approach.
