A beam with arbitrarily placed lateral dampers: Evolution of complex modes with damping

Y. Chen, D. M. McFarland, B. F. Spencer, Lawrence Bergman

Research output: Contribution to journalArticlepeer-review


Free vibration of a beam with multiple arbitrarily placed lateral viscous dampers is investigated to gain insight into the intrinsic dynamic features of non-proportional damped systems. In terms of virtual boundary condition method, complex modes of a damper-beam system are achieved, and the solution is also suitable for the beams that have different boundary conditions. The features of the wave numbers satisfying the frequency equation were discussed in theory. The orthogonality analysis conducted in this paper provides two orthogonality conditions for complex modes. Pseudoundamped natural frequencies, damping ratios and complex modes are surveyed via numerical study. The analysis on the evolution of complex modes shows that the increasing damping would lead to over damped modes, and the mode shape that corresponds to the small one of a pair of real-valued natural frequencies is close to the static deformation shape of a beam subjected to static forces located at the positions of the dampers. For the rest modes that would never be over damped with increasing damping, the mode shapes and corresponding psuedoundamped natural frequencies will converge to that of a beam with rolling supports located at where dampers are placed. The exact solution of free vibration of a multiple-span beam is presented in addition.

Original languageEnglish (US)
Pages (from-to)379-392
Number of pages14
JournalJVC/Journal of Vibration and Control
Issue number2
StatePublished - Jan 1 2018


  • Damper-beam system
  • complex domain
  • evolution of complex modes
  • exact solution
  • free vibration

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'A beam with arbitrarily placed lateral dampers: Evolution of complex modes with damping'. Together they form a unique fingerprint.

Cite this