Vibration of thick plates carrying concentrated masses

J. W. Nicholson, L. A. Bergman

Research output: Contribution to journalArticlepeer-review


The method for obtaining the natural frequencies and orthogonality relation for combined dynamical systems in which the Green functions of the vibrating subsystems are used is applied to a thick plate carrying concentrated masses. The effects of transverse shear and rotary inertia of each mass is accounted for. It is demonstrated that as the plate thickness goes to zero the results of thin plate analysis are obtained. The Green functions for both thin and thick vibrating plates are derived by modal analysis in the form of infinite series. The advantages and disadvantages of this representation are discussed. An example involving a simply supported isotropic square plate carrying a single concentrated mass at its center is provided.

Original languageEnglish (US)
Pages (from-to)357-369
Number of pages13
JournalJournal of Sound and Vibration
Issue number3
StatePublished - Dec 8 1985

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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