Damped DQE Model Updating of a Three-Story Frame Using Experimental Data

Document Type: Research Paper

Authors

Mechanical Engineering Department, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

In this paper, following a two-stage methodology, the differential quadrature element (DQE) model of a three-story frame structure is updated for the vibration analysis. In the first stage, the mass and stiffness matrices are updated using the experimental natural frequencies. Then, having the updated mass and stiffness matrices, the structural damping matrix is updated to minimize the error between the experimental and numerical damping ratios. Note that two different damping models are used, including a diagonal matrix with unknown diagonal elements and a general damping model. Since the structural joints of the frames are not completely rigid in practice, several parameters are used to model the flexibility of these joints. The optimum values of the material and geometrical design parameters are obtained by updating the DQE model using the experimental modal parameters obtained through modal testing. Considering the robustness of the evolutionary optimization algorithms in the model updating practice, a combination of particle swarm optimization and artificial bee colony algorithm, that benefits from the advantages of both approaches, is utilized. By updating the DQE model, the effectiveness of the evolutionary optimization algorithms, especially in a high-dimensional optimization problem, e.g., finding the optimum general damping matrix, is studied. The results show that, considering the geometrical lengths of the frame as the design parameters, the natural frequencies of the updated model match better with the experimental ones. In addition, using the general damping matrix, the errors of the damping ratios significantly are decreased.

Keywords

Main Subjects

[1] C.N. Chen, The two-dimensional frame model of the differential quadrature element method, Computers & Structures, Vol. 62, No. 3, pp. 555-571, 1997.
[2] R. Bellman, B. Kashef, J. Casti, Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations, Journal of Computational Physics, Vol. 10, No. 1, pp. 40-52, 1972.
[3] C.N. Chen, The DQEM analysis of vibration of frame structures having nonprismatic members considering warping torsion, International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 2, No. 3, pp. 235-255, 2001.
[4] C.N. Chen, DQEM analysis of out-of-plane vibration of nonprismatic curved beam structures considering the effect of shear deformation, Advances in Engineering Software, Vol. 39, No. 6, pp. 466-472, 2008.
[5] M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.
[6] M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[7] X. Wang, Y. Wang, Free vibration analysis of multiple-stepped beams by the differential quadrature element method, Applied Mathematics and Computation, Vol. 219, No. 11, pp. 5802-5810, 2013.
[8] S. Asemi, A. Farajpour, H. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[9] M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.
[10] M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, Journal of Solid Mechanics, Vol. 7, No. 3, pp. 299-311, 2015.
[11] M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, No. 8, pp. 2207-2232, 2016.
[12] A. Pouretemad, K. Torabi, H. Afshari, DQEM analysis of free transverse vibration of rotating non-uniform nanobeams in the presence of cracks based on the nonlocal Timoshenko beam theory, SN Applied Sciences, Vol. 1, No. 9, pp. 1092, 2019.
[13] J. E. Mottershead, M. Friswell, Model updating in structural dynamics: a survey, Journal of Sound and Vibration, Vol. 167, No. 2, pp. 347-375, 1993.
[14] D. M. Hamby, A review of techniques for parameter sensitivity analysis of environmental models, Environmental Monitoring and Assessment, Vol. 32, No. 2, pp. 135-154, 1994.
[15] J. Mottershead, M. Friswell, G. Ng, J. Brandon, Geometric parameters for finite element model updating of joints and constraints, Mechanical Systems and Signal Processing, Vol. 10, No. 2, pp. 171-182, 1996.
[16] Y. Xiang, Y. Peng, Y. Zhong, Z. Chen, X. Lu, X. Zhong, A particle swarm inspired multi-elitist artificial bee colony algorithm for real-parameter optimization, Computational Optimization and Applications, Vol. 57, No. 2, pp. 493-516, 2014.
[17] J. Kennedy, R. Eberhart, Particle swarm optimization, in Proceeding of the IEEE International Conference on Neural Networks, 1995.
[18] D. Karaboga, An idea based on honey bee swarm for numerical optimization, Technical report-tr06, Erciyes university, 2005.
[19] N. Maia, J. Silva, A. Ribeiro, On a general model for damping, Journal of Sound and Vibration, Vol. 218, No. 5, pp. 749-767, 1998.
[20] S. Adhikari, Damping models for structural vibration, PhD Thesis, University of Cambridge, 2000.
[21] V. Arora, S. Singh, T. Kundra, On the use of damped updated FE model for dynamic design, Mechanical Systems and Signal Processing, Vol. 23, No. 3, pp. 580-587, 2009.
[22] V. Arora, Structural damping identification method using normal FRFs, International Journal of Solids and Structures, Vol. 51, No. 1, pp. 133-143, 2014.
[23] L. Fatahi, S. Moradi, Differential quadrature element model updating of frame structures, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 228, No. 7, pp. 1094-1107, 2014.
[24] P. Rizos, N. Aspragathos, A. Dimarogonas, Identification of crack location and magnitude in a cantilever beam from the vibration modes, Journal of Sound and Vibration, Vol. 138, No. 3, pp. 381-388, 1990.
[25] N. Imamovic, Validation of large structural dynamics models using modal test data, PhD Thesis, Department of Mechanical Engineering, Imperial College, 1998.
[26] D. C. Kammer, Sensor placement for on-orbit modal identification and correlation of large space structures, Journal of Guidance, Control, and Dynamics, Vol. 14, No. 2, pp. 251-259, 1991.
[27] S. Omkar, J. Senthilnath, R. Khandelwal, G. N. Naik, S. Gopalakrishnan, Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures, Applied Soft Computing, Vol. 11, No. 1, pp. 489-499, 2011.
[28] Z. Ding, R. Yao, J. Li, Z. Lu, Structural damage identification based on modified artificial bee colony algorithm using modal data, Inverse Problems in Science and Engineering, Vol. 26, No. 3, pp. 422-442, 2018.
[29] D. J. Downing, R. Gardner, F. Hoffman, An examination of response-surface methodologies for uncertainty analysis in assessment models, Technometrics, Vol. 27, No. 2, pp. 151-163, 1985.
[30] L. Bauer, D. Hamby, Relative sensitivities of existing and novel model parameters in atmospheric tritium dose estimates, Radiation Protection Dosimetry, Vol. 37, No. 4, pp. 253-260, 1991.
[31] J. Myers, A. Well, Research Design and Statistical Analysis (2nd edn), Lawrence Erlbaum, 2003.
 

Volume 51, Issue 2
December 2020
Pages 432-442
  • Receive Date: 02 September 2020
  • Revise Date: 08 September 2020
  • Accept Date: 09 September 2020