| Popis: |
Reciprocity is a fundamental physical principle of wave motion, which maintains the symmetric property of wave transmission between a source and a receiver. Although widely used in many applicable techniques of quality evaluation, this principle restricts the sophisticated wave control, such as one-way propagation and directional wave scattering. A passive method of breaking reciprocity, achieved by the combination of characteristic bilinear property and necessary spatial asymmetry, is proposed and discussed in this work. The bilinear stiffness is unique among nonlinear mechanisms in that it is independent of amplitude but sensitive to the sign of the wave motion. Spatial asymmetric setup is versatile and flexible, depending on the amount of bilinearity applied and the spatial dimension, one or two as considered here. Our nonreciprocal designs start with a fundamental candidate, a discrete two-degree-of-freedom bilinear spring-mass chain structure, demonstrating nonreciprocity in both static and dynamic conditions. Then a sequence of modulated nonreciprocal models are proposed and their properties examined: expansion of the fundamental bilinear spring and mass structure to a unidimensional long-chain system is shown to display one-way wave propagation; the further simplification of the fundamental structure results in a compact diode-like structure; a two-dimensional monatomic lattice is able to demonstrate directional and nonreciprocal wave scattering. Some problems frequently seen in nonreciprocal or nonlinear designs are discussed and solved: the mathematical tools of solving bilinear partial differential equations are introduced, and a novel set-base design method using machine learning algorithms with lower computational effort is proposed. |
