Non-reciprocal wave transmission in a bilinear spring-mass system

Zhaocheng Lu, Andrew N. Norris

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Significant amplitude-independent and passive non-reciprocal wave motion can be achieved in a one-dimensional (1D) discrete chain of masses and springs with bilinear elastic stiffness. Some fundamental asymmetric spatial modulations of the bilinear spring stiffness are first examined for their non-reciprocal properties. These are combined as building blocks into more complex configurations with the objective of maximizing nonreciprocal wave behavior. The non-reciprocal property is demonstrated by the significant difference between the transmitted pulse displacement amplitudes and energies for incidence from opposite directions. Extreme non-reciprocity is realized when almost-zero transmission is achieved for the propagation from one direction with a noticeable transmitted pulse for incidence from the other. These models provide the basis for a class of simple 1D non-reciprocal designs and can serve as the building blocks for more complex and higher dimensional non-reciprocal wave systems.

Original languageEnglish (US)
Article number021006-1
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Issue number2
StatePublished - Apr 2020

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


  • Amplitude-independent
  • Bilinear stiffness
  • Non-linear vibration
  • Non-reciprocity
  • One-way propagation
  • Passive
  • Vibration isolation


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