On the vibration of a point-supported linear distributed system

L. A. Bergman, D. Michael McFarland

Research output: Contribution to journalArticle

Abstract

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, Acoustics, Stress, and Reliability in Design
Volume110
Issue number4
StatePublished - Oct 1988

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Green's function
Natural frequencies
Dynamical systems
Differential equations
Boundary conditions
Derivatives
Euler-Bernoulli beams
vibration
orthogonality
dynamical systems
resonant frequencies
differential equations
Green's functions
boundary conditions
formulations

ASJC Scopus subject areas

  • Engineering(all)

Cite this

On the vibration of a point-supported linear distributed system. / Bergman, L. A.; McFarland, D. Michael.

In: Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 110, No. 4, 10.1988, p. 485-492.

Research output: Contribution to journalArticle

Bergman, L. A. ; McFarland, D. Michael. / On the vibration of a point-supported linear distributed system. In: Journal of Vibration, Acoustics, Stress, and Reliability in Design. 1988 ; Vol. 110, No. 4. pp. 485-492.
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