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Nonlinear Vibration Analysis of Membrane SAR Antenna Structure Adopting a Vector Form Intrinsic Finite Element

Published online by Cambridge University Press:  23 January 2015

R. Xu
Affiliation:
National University of Defense Technology, Hunan, China
D.-X. Li*
Affiliation:
National University of Defense Technology, Hunan, China
J.-P. Jiang
Affiliation:
National University of Defense Technology, Hunan, China
W. Liu
Affiliation:
National University of Defense Technology, Hunan, China
*
*Corresponding author ([email protected])
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Abstract

This study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to study the nonlinear vibration of the membrane SAR (Synthetic Aperture Radar) antenna structure. As the dynamic characteristic of the antenna is mainly determined by the support frame, it can be simplified as an axially loaded cantilever beam. The linear and geometrically nonlinear models of the axially loaded cantilever beam are established. The beam is modeled as discrete mass points which are connected by deformable elements through VFIFE method. A statics analysis is first presented to verify the VFIFE method. Then effects of the geometrical nonlinearity and axial load are investigated. It is believed that the presented study is valuable for better understanding the influences of the geometrical nonlinearity and axial load of the cantilever beam on the structural vibration characteristics.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFERENCES

1.Vo, T.P. and Lee, J., “Free Vibration of Axially Loaded Thin-Walled Composite Box Beams,” Composite Structures, 90, pp. 233241 (2009).Google Scholar
2.Vo, T.P. and Lee, J., “Free Vibration of Axially Loaded Thin-Walled Composite Timoshenko Beams,” Archive of Applied Mechanics, 81, pp. 11651180 (2011).CrossRefGoogle Scholar
3.Vo, T.P. and Huu-Tai, T., “Free Vibration of Axially Loaded Rectangular Composite Beams Using Refined Shear Deformation Theory,” Composite Structures, 94, pp. 33793387 (2012).CrossRefGoogle Scholar
4.Li, J. and Hua, H., “Free Vibration Analyses of Axi-ally Loaded Laminated Composite Beams Based on Higher-Order Shear Deformation Theory,” Meccanica, 46, pp. 12991317 (2011).Google Scholar
5.Li, X.F., “Free Vibration of Axially Loaded Shear Beams Carrying Elastically Restrained Lumped Tip Masses via Asymptotic Timoshenko Beam Theory,” Journal of Engineering Mechanics, 139, pp. 418428 (2013).Google Scholar
6.Calio, I. and Greco, A., “Free Vibrations of Timo-shenko Beam Columns on Pasternak Foundations,” Journal of Vibration and Control, 19, pp. 686696 (2013).Google Scholar
7.Belouettar, S.et al., “Active Control of Nonlinear Vibration of Sandwich Piezoelectric Beams: A Simplified Approach,” Computers & Structures, 86, pp. 386397 (2008).CrossRefGoogle Scholar
8.Azrar, L., Belouettar, S. and Wauer, J., “Nonlinear Vibration Analysis of Actively Loaded Sandwich Piezoelectric Beams with Geometric Imperfections,” Computers & Structures, 86, pp. 21822191 (2008).Google Scholar
9.Azrar, L., Benamar, R. and White, R.G., “A Semi-Analytical Approach to the Non-Linear Dynamics Response Problem of S-S and C-C Beams at Large Amplitudes. Part I: General Theory and Application to the Single Mode Approach to the Free and Forced Vibration Analysis,” Journal of Sound and Vibration, 224, pp. 183207 (1999).Google Scholar
10.Azrar, L., Benamar, R. and White, R.G., “A Semi-Analytical Approach to the Non-Linear Dynamics Response Problem of S-S and C-C Beams at Large Amplitudes. Part II: Multimode Approach to the Steady State Forced Periodic Response,” Journal of Sound and Vibration, 255, pp. 141 (2002).Google Scholar
11.Jacques, N., Daya, E.M. and Potier-Ferry, M., “Non-Linear Vibration of Viscoelastic Sandwich Beams by the Harmonic Balance and Finite Element Methods,” Journal of Sound and Vibration, 329, pp. 42514265 (2010).Google Scholar
12.Hemmatnezhad, M., Ansari, R. and Rahimi, G.H., “Large-Amplitude Free Vibrations of Functionally Graded Beams by Means of a Finite Element Formulation,” Applied Mathematical Modelling, 37, pp. 84958504 (2013).Google Scholar
13.Mahmoodi, S.N., Jalili, N. and Khadem, S.E., “An Experimental Investigation of Nonlinear Vibration and Frequency Response Analysis of Cantilever Viscoelastic Beams,” Journal of Sound and Vibration, 311, pp. 14091419 (2008).Google Scholar
14.Bayat, M., Pakar, I. and Bayat, M., “On the Large Amplitude Free Vibrations of Axially Loaded Euler-Bernoulli Beams,” Steel and Composite Structures, 14, pp. 7383 (2013).Google Scholar
15.Ting, E.C., Shih, C. and Wang, Y.K., “Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements,” Journal of Mechanics, 20, pp. 123132 (2004).Google Scholar
16.Ting, E.C., Shih, C. and Wang, Y.K., “Fundamentals of a Vector form Intrinsic Finite Element: Part I. Basic Procedure and a Plane Frame Element,” Journal of Mechanics, 20, pp. 113122 (2004).CrossRefGoogle Scholar
17.Shih, C., Wang, Y.K. and Ting, E.C., “Fundamentals of a Vector form Intrinsic Finite Element: Part III. Convected Material Frame and Examples,” Journal of Mechanics, 20, pp. 133143 (2004).Google Scholar
18.Wang, C.Y.et al., “Nonlinear Dynamic Analysis of Reticulated Space Truss Structures,” Journal of Mechanics, 22, pp. 199212 (2006).Google Scholar
19.Wang, C.-Y., Wang, R.-Z. and Tsai, K.-C., “Numerical Simulation of the Progressive Failure and Collapse of Structure Under Seismic and Impact Loading,” 4th International Conference on Earthquake Engineering, Taipei, Taiwan (2006).Google Scholar
20.Wu, T.Y., Wang, R.Z. and Wang, C.Y., “Large Deflection Analysis of Flexible Planar Frames,” Journal of the Chinese Institute of Engineers, 29, pp. 593606 (2006).Google Scholar
21.Wu, T.-Y., Tsai, W.-C. and Lee, J.-J., “Dynamic Elastic-Plastic and Large Deflection Analyses of Frame Structures Using Motion Analysis of Structures,” Thin-Walled Structures, 47, pp. 11771190 (2009).Google Scholar
22.Wu, T.Y., et al., “Motion Analysis of 3D Membrane Structures by a Vector form Intrinsic Finite Element,” Journal of the Chinese Institute of Engineers, 30, pp. 961976 (2007).Google Scholar
23.Wu, T.Y. and Ting, E.C., “Large Deflection Analysis of 3D Membrane Structures by a 4-Node Quadrilateral Intrinsic Element,” Thin-Walled Structures, 46, pp. 261275 (2008).CrossRefGoogle Scholar
24.Lien, K.H., et al., “Nonlinear Behavior of Steel Structures Considering the Cooling Phase of a Fire,” Journal of Constructional Steel Research, 65, pp. 17761786 (2009).CrossRefGoogle Scholar
25.Lien, K.H., et al., “Vector form Intrinsic Finite Element Analysis of Nonlinear Behavior of Steel Structures Exposed to Fire,” Engineering Structures, 32, pp. 8092 (2010).CrossRefGoogle Scholar
26.Lien, K.H., Chiou, Y.J. and Hsiao, P.A., “Vector Form Intrinsic Finite-Element Analysis of Steel Frames with Semirigid Joints,” Journal of Structural Engineering, 138, pp. 327336 (2012).Google Scholar
27.Wu, T.-Y., “Dynamic Nonlinear Analysis of Shell Structures Using a Vector form Intrinsic Finite Element,” Engineering Structures, 56, pp. 20282040 (2013).CrossRefGoogle Scholar