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In this article, an exact strain gradient (SG) continuum model to capture the broadband bandgap characteristics of the prestressed diatomic lattice (PDL) with local/nonlocal interactions has been proposed. By considering the periodicity of wave motion, the wavelength-dependent Taylor expansion is established, leading to a desirable prediction when the wavelength is close to the lattice scale. For PDL, the dispersion curves of the proposed continuum model are always consistent with those of discrete model in the first Brillouin zone. The proposed SG continuum model is used to investigate the effects of structural parameters, orders of SG continua and various nonlocal interactions on bandgap properties of PDL.HighlightsContinuum modelling of prestressed acoustic diatomic lattices.Perfect agreements achieved between dispersion diagrams by discrete and proposed continuum models.Effects of prestress, nonlocal interactions, mass and stiffness ratios on band gap structures analyzed.Proper strain gradient (SG) orders determined to guarantee a satisfactory accuracy. Continuum modelling of prestressed acoustic diatomic lattices. Perfect agreements achieved between dispersion diagrams by discrete and proposed continuum models. Effects of prestress, nonlocal interactions, mass and stiffness ratios on band gap structures analyzed. Proper strain gradient (SG) orders determined to guarantee a satisfactory accuracy.

Exact strain gradient modelling of prestressed nonlocal diatomic lattice metamaterials