GBT-Based Vibration Analysis Using the Exact Element Method

Rui Bebiano, Moshe Eisenberger, Dinar Camotim, Rodrigo Gonçalves

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Generalized Beam Theory (GBT), intended to analyze the structural behavior of prismatic thin-walled members and structural systems, expresses the member deformed configuration as a combination of cross-section deformation modes multiplied by the corresponding longitudinal amplitude functions. The determination of the latter, often the most computer-intensive step of the analysis, is almost always performed by means of GBT-based “conventional” 1D (beam) finite elements. This paper presents the formulation, implementation and application of the so-called “exact element method” in the framework of GBT-based elastic free vibration analyses. This technique, originally proposed by Eisenberger (1990), uses the power series method to solve the governing differential equations and obtains the vibration eigenvalue problem from the boundary terms. A few illustrative numerical examples are presented, focusing mainly on the comparison between the combined accuracy and computational effort associated with the determination of vibration solutions with the exact and conventional GBT-based (finite) elements. This comparison shows that the GBT-based exact element method may lead to significant computational savings, particularly when the vibration modes exhibit large half-wave numbers.

Original languageEnglish
JournalInternational Journal of Structural Stability and Dynamics
Publication statusAccepted/In press - 1 Jan 2017


  • exact element method
  • free vibration
  • generalized beam theory (GBT)
  • power series solution
  • Thin-walled members


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