On the vibration of a Point-Supported linear distributed system

L. A. Bergman, D. Michael McFarland

Research output: Contribution to journalArticlepeer-review


The vibration of a constrained dynamical system, consisting of an Euler-Bernoulli beam with homogeneous boundary conditions, supported in its interior by arbitrarily located pin supports and translational and torsional linear springs, is studied. A generalized differential equation is obtained by the method of separation of variables and is solved in terms of the Green’s function and its derivatives of the unconstrained beam. System natural frequencies and modes are obtained, and the orthogonality relation for the natural modes is derived. A general solution for the forced response is given. Finally, two pertinent problems from the literature are examined, and results obtained are compared with those of a small, dedicated finite element formulation to assess the relative accuracy and efficiency of each.

Original languageEnglish (US)
Pages (from-to)485-492
Number of pages8
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Issue number4
StatePublished - Oct 1988

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


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