Rosa Matheus I N, Pal Raj Kumar, Arruda José R F, Ruzzene Massimo
School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
Phys Rev Lett. 2019 Jul 19;123(3):034301. doi: 10.1103/PhysRevLett.123.034301.
Spatial stiffness modulations defined by the sampling of a two-dimensional surface provide one-dimensional elastic lattices with topological properties that are usually attributed to two-dimensional crystals. The cyclic modulation of the stiffness defines a family of lattices whose Bloch eigenmodes accumulate a phase quantified by integer valued Chern numbers. Nontrivial gaps are spanned by edge modes in finite lattices whose location is determined by the phase of the stiffness modulation. These observations drive the implementation of a topological pump in the form of an array of continuous elastic beams coupled through a distributed stiffness. Adiabatic stiffness modulations along the beams' length lead to the transition of localized states from one boundary, to the bulk and, finally, to the opposite boundary. The first demonstration of topological pumping in a continuous elastic system opens new possibilities for its implementation on elastic substrates supporting surface acoustic waves, or to structural components designed to steer waves or isolate vibrations.
通过对二维表面进行采样定义的空间刚度调制为一维弹性晶格提供了通常归因于二维晶体的拓扑特性。刚度的周期性调制定义了一族晶格，其布洛赫本征模积累了由整数值陈数量化的相位。有限晶格中的边缘模跨越非平凡能隙，其位置由刚度调制的相位决定。这些观察结果推动了以通过分布式刚度耦合的连续弹性梁阵列形式实现拓扑泵。沿梁长度的绝热刚度调制导致局域态从一个边界转移到体中，最后转移到相对的边界。在连续弹性系统中首次证明拓扑泵浦为在支持表面声波的弹性基板上实现它，或为设计用于引导波或隔离振动的结构部件开辟了新的可能性。
