Sign-engineered interactions enable dynamic frustration and topology in a passive elastic lattice

The sign and strength of interactions between coupled elements govern collective phenomena ranging from wave localization to topological phases and frustration. Whereas active systems can tune interaction signs through external driving, passive systems are typically limited to fixed structures where reversing signs requires changes to lattice connectivity or global symmetry. Here we demonstrate, both theoretically and experimentally, that local anisotropy enables continuous Hamiltonian sign engineering in central-force elastic lattices. Rotating anisotropic confinement projects interactions onto local degrees of freedom, decomposing the two-dimensional dynamics into spectrally separated one-dimensional Hamiltonians with continuously tunable effective couplings—from positive to negative—via rotation alone, without altering the force law or lattice connectivity. Implemented in a zigzag magnetoelastic lattice, this mechanism enables the concurrent emergence of frequency-selective wave frustration and topological band inversion in a single passive system. These results establish local anisotropy as a general tool for Hamiltonian engineering and offer a classical analogue to phonon-mediated interaction design in quantum many-body platforms. Controlling the sign of mechanical interactions in passive lattices normally requires redesigning lattice connectivity. Here, rotating anisotropic cantilevers in a zigzag magnetoelastic lattice continuously tunes interaction signs, producing simultaneous wave frustration and topological edge states in a single static structure.