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Abstract We study the elastodynamics of a periodic metastructure incorporating a defect pair that enforces a parity-time (PT) symmetry due to judiciously engineered imaginary impedance elements—one having energy amplification (gain) and the other having an equivalent attenuation (loss) mechanism. We show that their presence affects the initial band structure of the periodic Hermitian metastructure and leads to the formation of numerous exceptional points (EPs) which are mainly located at the band edges where the local density of modes is higher. The spatial location of the PT-symmetric defect serves as an additional control over the number of emerging EPs in the corresponding spectra as well as the critical non-Hermitian (gain/loss) strength required to create the first EP—a specific defect location minimizes the critical non-Hermitian strength. We use both finite element and coupled-mode-theory-based models to investigate these metastructures and use a time-independent second-order perturbation theory to further demonstrate the influence of the size of the metastructure and the PT-symmetric defect location on the minimum non-Hermitian strength required to create the first EP in a band. Our findings motivate feasible designs for the experimental realization of EPs in elastodynamic metastructures. 

Abstract We introduce a class of parity-time symmetric elastodynamic metamaterials (Ed-MetaMater) whose Hermitian counterpart exhibits unfolding (fractal) spectral symmetries. Our study reveals a scale-free formation of exceptional points in those Ed-MetaMaters whose density is dictated by the fractal dimension of their Hermitian spectra. We demonstrate this scale-free EP-formation in a quasi-periodic Aubry-Harper Ed-MetaMater, a geometric H-tree-fractal Ed-MetaMater, and an aperiodic Fibonacci Ed-MetaMater—each having a specific fractal spectrum—using finite element models and establish a universal route for EP-formation via a coupled mode theory model with controllable fractal spectrum. This universality may enable the rational design of novel Ed-MetaMater for hypersensitive sensing and elastic wave control.