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Lines of exceptional points are robust in the 3-dimensional non-Hermitianparameter space without requiring any symmetry. However, when more elaborateexceptional structures are considered, the role of symmetry becomes critical.One such case is the exceptional chain (EC), which is formed by theintersection or osculation of multiple exceptional lines (ELs). In this study,we investigate a non-Hermitian classical mechanical system and reveal that asymmetry intrinsic to second-order dynamical equations, in combination with thesource-free principle of ELs, guarantees the emergence of ECs. This symmetrycan be understood as a non-Hermitian generalized latent symmetry, which isabsent in prevailing formalisms rooted in first-order Schr\"odinger-likeequations and has largely been overlooked so far. We experimentally confirm andcharacterize the ECs using an active mechanical oscillator system. Moreover, bymeasuring eigenvalue braiding around the ELs meeting at a chain point, wedemonstrate the source-free principle of directed ELs that underlies themechanism for EC formation. Our work not only enriches the diversity ofnon-Hermitian degeneracies, but also highlights the new potential fornon-Hermitian physics in second-order dynamical systems.

Experimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems