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摘要
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Dissipation alone can produce counterintuitive topological wave transport that is otherwise absent in a non-dissipative system. This work demonstrates the influence of dissipation on degeneracies that arise in the context of elastic wave transport. The conditions on the parameters necessary to observe non-Hermitian degeneracies in the Bloch spectrum are precisely derived. It will be shown-contrary to the expectation from singularity theory of a linear eigenvalue problem-that a proportionally damped system with commutative damping does not exhibit non-Hermitian degeneracies. The necessity of a non-commutative and non-proportional dissipation model to observe non-Hermitian degeneracies (or exceptional points) is emphasized. Non-proportional dissipation is used to induce a non-Hermitian degeneracy in a local resonance sub-Bragg bandgap of a linear chain, without using negative damping. While Bloch waves are chosen to illustrate the influence of dissipation, the results readily extend to waves in non-periodic media as well as other wave and vibration transport problems.
Keyword:
CLASSICAL NORMAL-MODES
EXCEPTIONAL POINTS
WAVE-PROPAGATION
SELF-PROPULSION
IDENTIFICATION
PHYSICS
MOTION
PHASE
期刊
IF:
3.6
论文数:
10.4W
被引数:
17.8W
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