zbMATH — the first resource for mathematics

Nonlinear breathing vibrations and chaos of a circular truss antenna with 1:2 internal resonance. (English) Zbl 1343.78014

78A50 Antennas, waveguides in optics and electromagnetic theory
74K25 Shells
74H45 Vibrations in dynamical problems in solid mechanics
74H65 Chaotic behavior of solutions to dynamical problems in solid mechanics
Full Text: DOI
[1] Amabili, M. [2003] ” Theory and experiments for large-amplitude vibrations of empty and fluid-filled circular cylindrical shells with imperfections,” J. Sound Vibr.262, 921-975. genRefLink(16, ’S0218127416500772BIB001’, ’10.1016%252FS0022-460X%252802%252901051-9’); genRefLink(128, ’S0218127416500772BIB001’, ’000182617500009’);
[2] Awrejcewicz, J., Krysko, V. A., Papkova, I. V. & Krysko, A. V. [2012a] ” Routes to chaos in continuous mechanical systems. Part 1: Mathematical models and solution methods,” Chaos Solit. Fract.45, 687-708. genRefLink(16, ’S0218127416500772BIB002’, ’10.1016%252Fj.chaos.2012.01.016’); genRefLink(128, ’S0218127416500772BIB002’, ’000304213300001’); · Zbl 1414.74013
[3] Awrejcewicz, J., Krysko, A. V., Papkova, I. V. & Krysko, V. A. [2012b] ” Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents, hyper, hyper-hyper and spatial-temporal chaos,” Chaos Solit. Fract.45, 721-736. genRefLink(16, ’S0218127416500772BIB003’, ’10.1016%252Fj.chaos.2012.02.002’); genRefLink(128, ’S0218127416500772BIB003’, ’000304213300003’); · Zbl 1414.74013
[4] Burgardt, B. & Cartaud, P. [1999] ” Continuum modeling of beamlike lattice trusses using averaging methods,” Comput. Struct.73, 267-279. genRefLink(16, ’S0218127416500772BIB004’, ’10.1016%252FS0045-7949%252898%252900274-0’); genRefLink(128, ’S0218127416500772BIB004’, ’000082842100019’);
[5] Chen, J. J., Zeng, Y. G. & Sun, H. A. [1996] ” Dynamic reliability analysis of antenna reflector accuracy under wind excitation,” Comput. Struct.59, 819-822. genRefLink(16, ’S0218127416500772BIB005’, ’10.1016%252F0045-7949%252895%252900339-8’); genRefLink(128, ’S0218127416500772BIB005’, ’A1996UE43900005’);
[6] Chen, J. E., Zhang, W., Guo, X. Y. & Sun, M. [2013] ” Theoretical and experimental studies on nonlinear oscillations of symmetric cross-ply composite laminated plates,” Nonlin. Dyn.73, 1697-1714. genRefLink(16, ’S0218127416500772BIB006’, ’10.1007%252Fs11071-013-0896-6’); genRefLink(128, ’S0218127416500772BIB006’, ’000322014200041’);
[7] Dai, L., Guan, F. L. & Guest, J. K. [2014] ” Structural optimization and model fabrication of a double-ring deployable antenna truss,” Acta Astronautica94, 843-851. genRefLink(16, ’S0218127416500772BIB007’, ’10.1016%252Fj.actaastro.2013.10.002’); genRefLink(128, ’S0218127416500772BIB007’, ’000328663500032’);
[8] Gan, W. W. & Pellegrino, S. [2006] ” Numerical approach to the kinematic analysis of deployable structures forming a closed loop,” Proc. Instit. Mech. Engin., Part C: J. Mech. Engin. Sci.220, 1045-1056. genRefLink(16, ’S0218127416500772BIB008’, ’10.1243%252F09544062JMES245’); genRefLink(128, ’S0218127416500772BIB008’, ’000241142200010’);
[9] Gasbarri, P., Monti, R., Campolo, G. & Toglia, C. [2012] ” Control-oriented modelization of a satellite with large flexible appendages and use of worst-case analysis to verify robustness to model uncertainties of attitude control,” Acta Astronautica81, 214-226. genRefLink(16, ’S0218127416500772BIB009’, ’10.1016%252Fj.actaastro.2012.07.016’); genRefLink(128, ’S0218127416500772BIB009’, ’000309568900022’);
[10] Ghosh, A. K. & Kumar, M. R. [1997] ” Dynamic analysis of supporting structure of mobile antenna,” Comput. Struct.63, 633-637. genRefLink(16, ’S0218127416500772BIB010’, ’10.1016%252FS0045-7949%252895%252900099-2’); genRefLink(128, ’S0218127416500772BIB010’, ’A1997WN25300024’);
[11] Gonçalves, P., Silva, F. A., Rega, G. & Lenci, S. [2011] ” Global dynamics and integrity of a two-dof model of a parametrically excited cylindrical shell,” Nonlin. Dyn.63, 61-82. genRefLink(16, ’S0218127416500772BIB011’, ’10.1007%252Fs11071-010-9785-4’); genRefLink(128, ’S0218127416500772BIB011’, ’000285102200005’); · Zbl 1215.74049
[12] Gonella, S. & Ruzzene, M. [2008] ” Homogenization and equivalent in-plane properties of two-dimensional periodic lattices,” Int. J. Solids Struct.45, 2897-2915. genRefLink(16, ’S0218127416500772BIB012’, ’10.1016%252Fj.ijsolstr.2008.01.002’); genRefLink(128, ’S0218127416500772BIB012’, ’000255323900008’); · Zbl 1169.74529
[13] Hao, Y. X., Zhang, W. & Yang, J. [2012] ” Nonlinear dynamics of cantilever FGM cylindrical shell under 1:2 internal resonance relations,” Mech. Adv. Mater. Struct.20, 819-833. genRefLink(16, ’S0218127416500772BIB013’, ’10.1080%252F15376494.2012.676717’); genRefLink(128, ’S0218127416500772BIB013’, ’000321172800004’);
[14] Hohe, J. & Becker, W. [1999] ” Effective elastic properties of triangular grid structures,” Compos. Struct.45, 131-145. genRefLink(16, ’S0218127416500772BIB014’, ’10.1016%252FS0263-8223%252899%252900016-1’); genRefLink(128, ’S0218127416500772BIB014’, ’000080923300005’);
[15] Jansen, E. L. [2008] ” The effect of static loading and imperfections on the nonlinear vibrations of laminated cylindrical shells,” J. Sound Vibr.315, 1035-1046. genRefLink(16, ’S0218127416500772BIB015’, ’10.1016%252Fj.jsv.2008.02.004’); genRefLink(128, ’S0218127416500772BIB015’, ’000257517000015’);
[16] Kattan, P. I. [2008] MATLAB Guide to Finite Elements (Springer, Berlin, Heidelberg, NY). genRefLink(16, ’S0218127416500772BIB016’, ’10.1007%252F978-3-540-70698-4’); · Zbl 1114.74001
[17] Kurylov, Y. & Amabili, M. [2011] ” Nonlinear vibrations of clamped-free circular cylindrical shells,” J. Sound Vibr.330, 5363-5381. genRefLink(16, ’S0218127416500772BIB017’, ’10.1016%252Fj.jsv.2011.05.037’); genRefLink(128, ’S0218127416500772BIB017’, ’000293928400012’);
[18] Lee, U. [1998] ” Equivalent continuum representation of lattice beams: Spectral element approach,” Engin. Struct.20, 587-592. genRefLink(16, ’S0218127416500772BIB018’, ’10.1016%252FS0141-0296%252897%252900063-1’); genRefLink(128, ’S0218127416500772BIB018’, ’000072482500003’);
[19] Li, T. J. & Wang, Y. [2009] ” Deployment dynamic analysis of deployable antennas considering thermal effect,” Aerosp. Sci. Technol.13, 210-215. genRefLink(16, ’S0218127416500772BIB019’, ’10.1016%252Fj.ast.2009.04.005’); genRefLink(128, ’S0218127416500772BIB019’, ’000268362500008’);
[20] Lombardo, M. & Askes, H. [2012] ” Higher-order gradient continuum modelling of periodic lattice materials,” Comput. Mater. Sci.52, 204-208. genRefLink(16, ’S0218127416500772BIB020’, ’10.1016%252Fj.commatsci.2011.05.025’); genRefLink(128, ’S0218127416500772BIB020’, ’000297779700035’);
[21] Mitsugi, J., Ando, K., Senbokuya, Y. & Meguro, A. [2000] ” Deployment analysis of large space antenna using flexible multibody dynamics simulation,” Acta Astronautica47, 19-26. genRefLink(16, ’S0218127416500772BIB021’, ’10.1016%252FS0094-5765%252800%252900014-X’); genRefLink(128, ’S0218127416500772BIB021’, ’000088589700003’);
[22] Moreau, G. & Caillerie, D. [1998] ” Continuum modeling of lattice structures in large displacement application to buckling analysis,” Comput. Struct.68, 181-189. genRefLink(16, ’S0218127416500772BIB022’, ’10.1016%252FS0045-7949%252898%252900041-8’); genRefLink(128, ’S0218127416500772BIB022’, ’000074928500014’);
[23] Morterolle, S., Mauriin, B., Quirant, J. & Dupuy, C. [2012] ” Numerical form-finding of geotensoid tension truss for mesh reflector,” Acta Astronautica76, 151-163. genRefLink(16, ’S0218127416500772BIB023’, ’10.1016%252Fj.actaastro.2012.02.025’);
[24] Na, K. S. & Kim, J. H. [2006] ” Deployment of a multi-link flexible structure,” J. Sound Vibr.20, 298-313. genRefLink(16, ’S0218127416500772BIB024’, ’10.1016%252Fj.jsv.2005.11.018’);
[25] Nayfeh, A. H. & Mook, D. T. [1979] Nonlinear Oscillations (Wiley, NY).
[26] Nayfeh, A. H. & Hefzy, M. S. [1982] ” Effective constitutive relations for large repetitive frame-like structures,” Int. J. Solids Struct.18, 975-987. genRefLink(16, ’S0218127416500772BIB026’, ’10.1016%252F0020-7683%252882%252990087-7’); genRefLink(128, ’S0218127416500772BIB026’, ’A1982PP93400005’); · Zbl 0488.73002
[27] Noor, A. K. & Russell, W. C. [1986] ” Anisotropic continuum models for beamlike lattice trusses,” Comput. Meth. Appl. Mech. Engin.57, 257-277. genRefLink(16, ’S0218127416500772BIB027’, ’10.1016%252F0045-7825%252886%252990141-6’); genRefLink(128, ’S0218127416500772BIB027’, ’A1986E175600001’);
[28] Nosier, A. & Reddy, J. N. [1991] ” A study of non-linear dynamic equations of higher-order deformation plate theories,” Int. J. Non-Lin. Mech.26, 233-249. genRefLink(16, ’S0218127416500772BIB028’, ’10.1016%252F0020-7462%252891%252990054-W’); genRefLink(128, ’S0218127416500772BIB028’, ’A1991FC23500007’);
[29] Pellicano, F. [2009] ” Dynamic stability and sensitivity to geometric imperfections of strongly compressed circular cylindrical shells under dynamic axial loads,” Commun. Nonlin. Sci. Numer. Simul.14, 3449-3462. genRefLink(16, ’S0218127416500772BIB029’, ’10.1016%252Fj.cnsns.2009.01.018’); genRefLink(128, ’S0218127416500772BIB029’, ’000264840600029’); · Zbl 1221.74054
[30] Qing, Z., Su, J. & Jiang, D. Z. [2014] ” Anisotropic mechanical properties of diamond lattice composites structures,” Compos. Struct.39, 23-30.
[31] Reddy, J. N. [2004] Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (CRC Press). · Zbl 1075.74001
[32] Salehian, A. & Inman, D. J. [2010] ” Micropolar continuous modeling and frequency response validation of a lattice structure,” J. Vibr. Acoust.132, 011010-1-7. genRefLink(16, ’S0218127416500772BIB032’, ’10.1115%252F1.4000472’);
[33] Sennett, R. [1994] Matrix Analysis of Structures (Prentice Hall).
[34] Shen, H. S. [2012] ” Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium,” Compos. Struct.94, 1144-1154. genRefLink(16, ’S0218127416500772BIB034’, ’10.1016%252Fj.compstruct.2011.11.012’); genRefLink(128, ’S0218127416500772BIB034’, ’000299594900034’);
[35] Su, W. Z. & Liu, S. T. [2014] ” Vibration analysis of periodic cellular solids based on an effective couple-stress continuum model,” Int. J. Solids Struct.51, 2676-2686. genRefLink(16, ’S0218127416500772BIB035’, ’10.1016%252Fj.ijsolstr.2014.03.043’); genRefLink(128, ’S0218127416500772BIB035’, ’000337262300010’);
[36] Sun, C. T. & Liebbe, S. W. [1990] ” Global-local approach to solving vibration of large truss structures,” AIAA J.28, 303-308. genRefLink(16, ’S0218127416500772BIB036’, ’10.2514%252F3.10389’); · Zbl 0697.73050
[37] Tanaka, H. & Natori, M. C. [2004] ” Shape control of space antennas consisting of cable networks,” Acta Astronautica55, 519-527. genRefLink(16, ’S0218127416500772BIB037’, ’10.1016%252Fj.actaastro.2004.05.014’); genRefLink(128, ’S0218127416500772BIB037’, ’000223574300035’);
[38] Tollenaere, H. & Caillerie, D. [1998] ” Continuous modeling of lattice structures by homogenization,” Adv. Engin. Softw.29, 699-705. genRefLink(16, ’S0218127416500772BIB038’, ’10.1016%252FS0965-9978%252898%252900034-9’); genRefLink(128, ’S0218127416500772BIB038’, ’000075496600018’);
[39] Touzé, C., Amabili, M. & Thomas, O. [2008] ” Reduced-order models for large-amplitude vibrations of shells including in-plane inertia,” Comput. Meth. Appl. Mech. Engin.197, 2030-2045. genRefLink(16, ’S0218127416500772BIB039’, ’10.1016%252Fj.cma.2008.01.002’); genRefLink(128, ’S0218127416500772BIB039’, ’000254931400013’); · Zbl 1194.74148
[40] Wang, Q. T., Tian, Q. & Hu, H. Y. [2014] ” Dynamic simulation of frictional contacts of thin beams during large overall motions via absolute nodal coordinate formulation,” Nonlin. Dyn.77, 1411-1425. genRefLink(16, ’S0218127416500772BIB040’, ’10.1007%252Fs11071-014-1387-0’); genRefLink(128, ’S0218127416500772BIB040’, ’000340564600024’);
[41] Zhang, W. & Zhao, M. H. [2012] ” Nonlinear vibrations of a composite laminated cantilever rectangular plate with one-to-one internal resonance,” Nonlin. Dyn.70, 295-313. genRefLink(16, ’S0218127416500772BIB041’, ’10.1007%252Fs11071-012-0455-6’); genRefLink(128, ’S0218127416500772BIB041’, ’000309940000025’); · Zbl 1267.93115
[42] Zhang, W., Hao, Y. X. & Yang, J. [2012] ” Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges,” Compos. Struct.94, 1075-1086. genRefLink(16, ’S0218127416500772BIB042’, ’10.1016%252Fj.compstruct.2011.11.004’); genRefLink(128, ’S0218127416500772BIB042’, ’000299594900028’);
[43] Zhang, W., Zhou, R. & Zu, J. [2013] ” Nonlinear vibrations of a shell-shaped workpiece during high-speed milling process,” Nonlin. Dyn.72, 1-21. genRefLink(16, ’S0218127416500772BIB043’, ’10.1007%252Fs11071-012-0586-9’); · Zbl 1284.74073
[44] Zhang, W., Chen, J. & Yang, Y. D. [2015] ”Nonlinear dynamical analysis of circular mesh antenna subjected to thermal excitation,” to be submitted.
[45] Ziegler, E., Accorsi, M. & Bennett, M. [2004] ” Continuum plate model for lattice block material,” Mech. Mater.36, 753-766. genRefLink(16, ’S0218127416500772BIB045’, ’10.1016%252Fj.mechmat.2003.06.002’); genRefLink(128, ’S0218127416500772BIB045’, ’000220987200008’);
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.