On the existence of normal modes of damped discrete-continuous systems

H. T. Banks, Zheng Hua Luo, L. A. Bergman, D. J. Inman

Research output: Contribution to journalArticlepeer-review


In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.

Original languageEnglish (US)
Pages (from-to)980-989
Number of pages10
JournalJournal of Applied Mechanics, Transactions ASME
Issue number4
StatePublished - Dec 1998

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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