Structural damage often manifests as small parameter variations that are difficult to identify using linear response indicators. This work presents a dynamical switching approach for structural damage detection based on nonlinear dynamics and in-mechanical computing principles. A lattice of nonlinear mechanical oscillators is attached to a primary structural system and act as a damage-sensitive sensing and computing layer for monitoring the primary system. The oscillator lattice is programmed to introduce multistability. The coupled system is designed so that damage-induced parameter variations shift the system across bifurcation boundaries, such that damage triggers transitions between distinct dynamical states. Damage features are encoded not only in the occurrence of switching, but also in the amplitude levels of the responses reached after switching. Nonlinear solution manifolds of the governing equations are computed using numerical continuation as damage parameters vary to identify critical thresholds that define switching boundaries in parameter space. Numerical optimization is used to program the embedded oscillator lattice by tailoring its structural parameters to shape the bifurcation structure of the coupled system [1,2], effectively implementing a mechanical logic operation for damage monitoring. In this framework, continuation analysis serves as both an analysis and design tool for in-mechanical computing architectures with inherent sensitivity to structural damage. Numerical studies on nonlinear structural models demonstrate damage-induced switching associated with folds bifurcations and stability changes of periodic solution branches, showing how the topology of nonlinear responses can be used to enhance detectability. This work establishes a connection between continuation-based analysis of nonlinear dynamical systems and in-mechanical computing for structural health monitoring, and shows how nonlinear solution manifolds can be exploited to design mechanical systems that process information through distributed in-mechanical computation with centralized observation of a limited set of oscillator responses. [1] Mélot A., Denimal E., Renson L., Multi-parametric optimization for controlling bifurcation structures, Proceedings of the Royal Society A, Vol. 480, 2024. [2] Mélot A., Denimal Goy E., Renson L., Control of isolated response curves through optimization of codimension-1 singularities, Computers & Structures, Vol. 299, 2024.