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Topological materials can host edge and corner states that are protected fromdisorder and material imperfections. In particular, the topological edge statesof mechanical structures present unmatched opportunities for achieving robustresponses in wave guiding, sensing, computation, and filtering. However,determining whether a mechanical structure is topologically nontrivial andfeatures topologically-protected modes has hitherto relied on theoreticalmodels. This strong requirement has limited the experimental and practicalsignificance of topological mechanics to laboratory demonstrations. Here, weintroduce and validate an experimental method to detect the topologicallyprotected zero modes of mechanical structures without resorting to any modelingstep. Our practical method is based on a simple electrostatic analogy:topological zero modes are akin to electric charges. To detect them, weidentify elementary mechanical molecules and measure their chiral polarization,a recently introduced marker of topology in chiral phases. Topological zeromodes are then identified as singularities of the polarization field. Ourmethod readily applies to any mechanical structure and effectively detects theedge and corner states of regular and higher-order topological insulators. Ourfindings extend the reach of chiral topological phases beyond designermaterials, and allow their direct experimental investigation.

Model-free characterization of topological edge and corner states in mechanical networks