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Classical continuum models are unable to capture the response of a microstructured solid when the scale effect is relevant. In vibration analysis, this limitation appears when the solid undergoes vibrations of wavelength that approaches the characteristic length of the microstructure. A discrete model may be formulated to account for this effect, but this comes at the expenses of high computational costs. For example, scale effects are relevant in strings employed in sensing applications which often rely on information gathered in the nonlinear dynamic regime. In this work, we study the dynamic behavior of a taut string modeled as a lattice of particles linked to first neighbors by linear springs. We develop an inertia gradient generalized continuum model of the chain, which undergoes nonlinear vibrations. Unlike the corresponding classical continuum model, enrichment of the kinetic energy density with the characteristic length of the microstructure permits the model to capture short-wavelength vibrations. Comparison of the response predicted by the continuum models highlights that the generalized model provides better estimations of the dynamic response of the considered microstructured string in the nonlinear regime and at short wavelengths. (C) 2019 Published by Elsevier Ltd.