, Volume 50, Issue 6, pp 1509–1525 | Cite as

The application of the geometric offset method to the rigid joint modeling in the differential quadrature element model updating of frame structures

  • Laleh Fatahi
  • Shapour Moradi
  • Afshin Ghanbarzadeh


The following paper deals with the differential quadrature element (DQE) model updating of frame structures when the linear vibration behavior is of interest. To model the rigid L and T joints of the frame, a geometric offset method is employed to define a rigid region around each joint. The kinematic constraints due to the rigid joints, the equilibrium of axial and transverse forces, and the bending moments acting on the joint are utilized to model the joints in the DQE model of the frame. Then, to update the DQE model using the experimental natural frequencies, a minimization problem is defined to reduce an objective function based on the residuals between a measurement set obtained from modal testing on the frame and the corresponding DQE model predictions. Using the proposed approach, the DQE model of a three-story steel frame for in-plane vibrations is updated. To do so, several parameters of the model including the Young’s modulus, the density, the geometric offsets and mass parameters of the joints, and the stiffness of the rotational spring used to model the foundation are considered as the design parameters. The optimum values of the design parameters are then found by employing the particle swarm inspired multi-elitist artificial bee colony algorithm. The results of the model updating indicate a good coincidence of the modal parameters of the updated DQE and the experimental models. The sensitivity analysis also reveals that the highest eigenvalue sensitivities are to the joints’ parameters.


Frame Rigid joint Vibrations Differential quadrature element method Model updating Particle swarm inspired multi-elitist artificial bee colony 



The authors would like to thank Yi Xiang, a researcher from the Guangdong Baiyun University of China for providing the MATLAB code of the PS-MEABC algorithm.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Laleh Fatahi
    • 1
  • Shapour Moradi
    • 1
  • Afshin Ghanbarzadeh
    • 1
  1. 1.Mechanical Engineering DepartmentShahid Chamran UniversityAhvazIran

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