Modal Analysis of Complex Structures via a Sub-Structuring Approach

Subject Areas : vibration and control

Vahid Heydari ¹ , Mohammd Ahmadi Balootaki ² , Mohammad Orak ³ , Mehdi Salehi ⁴

1 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Department of Mechanical Engineering, Shahid Nikbakht Faculty, University of Sistan and Baluchestan, Zahedan, Iran Faculty of Shahid Bahonar, Sistan and Baluchestan Branch, Technical and Vocational University (TVU), Zahedan, Iran.
3 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
4 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Received: 2020-04-05 Accepted : 2020-09-02 Published : 2021-03-01

Keywords: Modal Analysis, Component Mode Synthesis, Substructures, Singular-Value Decomposition Method, Free Interface Method,

Abstract :

In this paper, the problems arising from determining the modal properties of large and complex structures are investigated. For this purpose, the free interface component mode synthesis method has been used. In the following, Singular-Value Decomposition (SVD) is applied as a powerful mathematical tool to determine the appropriate coordinates to participate in the coupling process. Also, the effective error resources including modal shear error and the continuous systems overlapping error and their solution are introduced. Initially, a discrete system has been employed to investigate the free interface component mode synthesis method. Eventually, the studied main samples in this research are beam, plate and cylindrical shell. It is worth noting that the application of this method on the cylindrical shell has not been observed in previous researches.

References:

[1]     Ahmadi Balootaki, M., Gholamzadeh, A., and Salehi, M., Sensitivity Analysis of Operational Modal Approaches in Damping Identification and Implementation On an Industrial Sample, The Journal of Solid and Fluid Mechanics, Vol. 8, No. 3, 2018, pp. 177- 192.

[2]     Salcher, P., Christoph, A., Modeling of Dynamic Train–Bridge Interaction in High-Speed Railways, Acta Mechanica, Vol. 226, No. 8, 2015, pp. 2473-2495.

[3]     Klosterman, A. L., A Combined Experimental and Analytical Procedure for Improving Automotive System Dynamics, SAE Transactions, 1972, pp. 343-353.

[4]     Sainsbury, M. G., Ewins, D. J., Vibration Analysis of a Damped Machinery Foundation Structure Using the Dynamic Stiffness Coupling Technique, 1974, pp. 1000-1005.

[5]     Ewins, D. J., Silva, J. M. M., and Maleci, G., Vibration Analysis of a Helicopter Plus an Externally-Attached Structure, Shock and Vibration Information Center the Shock and Vibration Bull, 1980, pp. 50.

[6]     Weight, A., The Measurement of Mechanical Impedance and Its Use in Vibration Testing, The Shock and Vibration Bulletin, 1972, pp. 55.

[7]     Heer, E., Lutes, L. D., Application of the Mechanical Receptance Coupling Principle to Spacecrafr Systems, Shock and Vibration Bulletin, Vol. 38, No. 2, 1968.

[8]     Heer, E., Lutes, L. D., Receptance Coupling of Structural Components Near a Component Resonance Frequency, 1968.

[9]     Ewins, D. J., Modal Test Requirements for Coupled Structure Analysis Using Experimentally Derived Component Models, Combined Experimental/Analytical Modelling of Dynamic Structural Systems, 1985, pp. 31-48.

[10]  Gleeson, P. T., Identification of Spatial Models for The Vibration Analysis of Lightly Damped Structures, 1979.

[11]  Imregun, M., Structural Modification and Coupling Dynamic Analysis Using Measured FRF Data, In Proc. 5th Int. Modal Analysis Conf, Vol. 1136, 1987.

[12]  Przemieniecki, J. S., Matrix Structural Analysis of Substructures, AIAA Journal, Vol. 1, No. 1, 1963, pp. 138-147.

[13]  Hurty, W. C., Dynamic Analysis of Structural Systems Using Component Modes, AIAA Journal, Vol. 3, No. 4, 1965, pp. 678-685.

[14]  Craig, J. R., Roy, R., and Bampton, M. C. C., Coupling of Substructures for Dynamic Analyses, AIAA Journal, Vol. 6, No. 7, 1968, pp. 1313-1319.

[15]  Gladwell, G. M. L., Branch Mode Analysis of Vibrating Systems, Journal of Sound and Vibration, Vol. 1, No. 1, 1964, pp. 41-59.

[16]  Goldman, R. L., Vibration Analysis by Dynamic Partitioning, AIAA Journal, Vol. 7, No. 6, 1969, pp. 1152-1154.

[17]  Craig J, R. R., Methods of Component Mode Synthesis, Shock and Vibration, Vol. 4, No. 3, 1977, 199-210, DOI: 10.1155/1997/147513.

[18]  Nelson, F. C., A Review of Substructure Analysis of Vibrating Systems, Shock and Vibration Inform. Center the Shock and Vibration Digest, Vol. 11, No. 11, 1979.

[19]  Goldenberg, S., Shapiro, M., A Study of Modal Coupling Procedures for The Space Shuttle, NASA CR-112252, Vol. 1, 1972.

[20]  Hart, G. C., Hurty, W. C., and Collins, J. D., A Survey of Modal Synthesis Methods, SAE Transactions, 1971, pp. 2612-2618.

[21]  Hurty, W. C., Collins, J. D., and Hart, G. C., Dynamic Analysis of Large Structures by Modal Synthesis Techniques, Computers & Structures, Vol. 1, No. 4, 1971, pp. 535-563.

[22]  MacNeal, R. H., A Hybrid Method of Component Mode Synthesis, Computers & Structures, Vol. 1, No. 4, 1971, pp. 581-601.

[23]  Kuhar, E J., Stahle, C. V., Dynamic Transformation Method for Modal Synthesis, AIAA Journal, Vol. 12, No. 5, 1974, pp. 672-678.

[24]  Hintz, R. M., Analytical Methods in Component Modal Synthesis, AIAA Journal, Vol. 13, No. 8, 1975, pp. 1007-1016.

[25]  Benfield, W. A., Hruda, R. F., Vibration Analysis of Structures by Component Mode Substitution, AIAA journal, Vol. 9, No. 7, 1971, pp. 1255-1261.

[26]  Rubin, S., Improved Component-Mode Representation for Structural Dynamic Analysis, AIAA Journal, Vol. 13, No. 8, 1975, pp. 995-1006.

[27]  Bai, B., Bai, G., and Li, C., Application of Improved Hybrid Interface Substructural Component Modal Synthesis Method in Vibration Characteristics of Mistuned Blisk, Chinese Journal of Mechanical Engineering, Vol. 27, No. 6, 2014, pp. 1219-1231.

[28]  Shadmani, M., Tikani, R., and Ziaei-Rad, S., On Using a Distributed-Parameter Model for Modal Analysis of a Mistuned Bladed Disk Rotor and Extracting the Statistical Properties of Its In-Plane Natural Frequencies, Journal of Sound and Vibration, Vol. 438, 2019, pp. 324-343.

[29]  Gutierrez Salas, M., Petrie-Repar, P., Ronnie Bladh, H. M., and Vogt, D. M., Forced Response Analysis of a Mistuned Blisk Using Noncyclic Reduced-Order Models, Journal of Propulsion and Power, Vol. 34, No. 3, 2018, pp. 565-577.

[30]  Bai, B., Li, H., Zhang, W., and Cui, Y., Application of Extremum Response Surface Method-Based Improved Substructure Component Modal Synthesis in Mistuned Turbine Bladed Disk, Journal of Sound and Vibration, Vol. 472, 2020, pp. 115210.

[31]  Bai, B, Zhang, J., Cui, Y., and Li, H., Vibration Characteristics Investigation of Mistuned Blisks with Receptance Substructure Component Modal Synthesis Method, Journal of Mechanical Science and Technology, Vol. 34, No. 7, 2020, pp. 2715-2729.

[32]  Seshu, P., Substructuring and Component Mode Synthesis, Shock and Vibration, Vol. 4, No. 3, 1997, pp. 199-210.

[33]  Nestorović, T., Trajkov, M., and Patalong, M., Identification of Modal Parameters for Complex Structures by Experimental Modal Analysis Approach, Advances in Mechanical Engineering, Vol. 8, No. 5, 2016, pp. 1687814016649110.

[34]  Karpel, M., Ricci, S., Experimental Modal Analysis of Large Structures by Substructuring, Mechanical Systems and Signal Processing, Vol. 11, No. 2, 1997, pp. 245-256.

[35]  An, B. H., Lee, J. W., Improved Substructure Synthesis Method Using Experimental Modal Analysis Technique to Solve Analysis and Design Problems Based On Security Issues, Mechanical Systems and Signal Processing, Vol. 145, 2020, pp. 106934.

[36]  Yangui, M., Bouaziz, S., Taktak, M., and Haddar, M., Experimental Updating of a Segmented Wind Turbine Blade Numerical Model Using the Substructure Method, The Journal of Strain Analysis for Engineering Design, 2020, pp. 0309324720932786.

[37]  Hou, S. N., Review of Modal Synthesis Techniques and A New Approach, Shock and Vibration Bulletin, Vol. 40, No. 4, 1969, pp. 25-39.

[38]  Kordkheili, S. A. H., Massouleh, S. H. M., Kokabi, M. J., and Bahai, H., A Modal Coupling Procedure to Improve Residual Modal Effects Based On Experimentally Generated Data, Journal of Sound and Vibration, Vol. 331, No. 1, 2012, pp. 66-80.

[39]  Kim, J., Boo, S. H., and Lee, P. S., Considering the Higher-Order Effect of Residual Modes in the Craig–Bampton Method, AIAA Journal, 2018, pp. 403-412.