Abstract
Recent focus has been given to analytically predicting amplitude-dependent dispersion in periodic structures with weak stiffness nonlinearity. These dispersion relationships may inform devices such as amplitude-dependent filters, waveguides, and diodes. However, attention is generally restricted to either spatially uniform nonlinearity or mutually exclusive distributions of hardening or softening stiffness. This study investigates dispersion in lattices with spatial modulations in stiffness nonlinearity. Special attention is given to modulations consisting of both hardening and softening nonlinear terms. A multiple scales perturbation analysis reveals that patterns of hardening and softening stiffness enable both lifting and lowering of a passband’s frequencies. In such cases, passbands contain discrete frequency and wavenumber pairs that prevent amplitude-dependent dispersion shifting. Numerical integration of the lattice equations of motion are carried out to confirm the analytically predicted dispersion behavior. A design of experiment is proposed in which strength and sign of nonlinearity can be tuned with the initial angle of additively manufactured grounding springs. [Work supported by the Office of Naval Research.]
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