Nonlinear damped vibration of pre-stressed orthotropic membrane structure under impact loading. (English) Zbl 1359.74150
Summary: This paper is concerned with the nonlinear damped forced vibration problem of pre-stressed orthotropic membrane structure under impact loading. The governing equations of motion were derived based on the von Kármán large deflection theory and D’Alembert’s principle, and solved by using the Bubnov-Galerkin method and the Krylov-Bogolubov-Mitropolsky (KBM) perturbation method. The asymptotic analytical solutions of the frequency and lateral displacement of rectangular orthotropic membrane with fixed edges were obtained. In the computational example, the frequency results were compared and analyzed. Meanwhile, the vibration mode of the membrane and the displacement and time curves of each feature point on the membrane surface were analyzed. The results obtained herein provide a simple and convenient approach to calculate the frequency and lateral displacement of the nonlinear forced vibration of rectangular orthotropic membranes with low viscous damping under impact loading. In addition, the results provide some computational basis for the vibration control and dynamic design of membrane structures.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K15 | Membranes |
| 74M20 | Impact in solid mechanics |
References:
| [1] | C. Shin, J. T. Chung and W. Kim, J. Sound Vib. 286(5), 1091 (2005), DOI: 10.1016/j.jsv.2005.01.013. |
| [2] | H. Zhang and J. Shan, Initial form finding and free vibration properties study of membrane, 2006 Xi’an Int. Conf. Architecture and Technology, Proceedings-Architecture in Harmony, Xi’an (Architecture & Building Press, Beijing, China, 2006) pp. 316-320. |
| [3] | Y. L. Li, C. G. Wang and H. F. Tan, Research on free vibration of wrinkled membranes, Proc. 5th Int. Conf. Nonlinear Mechanics, Shanghai (Shanghai University Press, Shanghai, China, 2007) pp. 649-654. |
| [4] | J. J. Pan and M. Gu, J. Tongji Univ. (Nat. Sci.) 35(11), 1450 (2007). |
| [5] | S. Y. Reutskiy, CMES – Comput. Model. Eng. Sci. 51(2), 115 (2009). genRefLink(128, ’rf5’, ’000274366900002’); |
| [6] | F. Formosa, J. Sound Vib. 326(5), 794 (2009), DOI: 10.1016/j.jsv.2009.05.025. genRefLink(16, ’rf6’, ’10.1016 |
| [7] | P. B. Goncalves, R. M. Soares and D. Pamplona, J. Sound Vib. 327(2), 231 (2009). genRefLink(16, ’rf7’, ’10.1016 |
| [8] | Z. L. Zheng, Math. Prob. Eng. 2009, 634362 (2009). |
| [9] | C. J. Liu, Math. Prob. Eng. 2010, 561364 (2010). |
| [10] | X. T. He and S. L. Chen, J. Chongqing Jianzhu Univ. 25(6), 46 (2003). |
| [11] | X. T. He and S. L. Chen, Appl. Math. Mech. 27(4), 404 (2006). genRefLink(128, ’rf11’, ’A1974U799500004’); |
| [12] | I. V. Andrianov, J. Awrejcewicz and V. Chernetskyy, Math. Prob. Eng. 2006, 20598 (2006). |
| [13] | E. L. Jansen, Int. J. Solids Struct. 45(4), 1124 (2008), DOI: 10.1016/j.ijsolstr.2007.07.007. genRefLink(16, ’rf13’, ’10.1016 |
| [14] | H. R. Eipakchi, J. Mech. Mater. Struct. 5(1), 1 (2010), DOI: 10.2140/jomms.2010.5.1. genRefLink(16, ’rf14’, ’10.2140 |
| [15] | P. Kozic, G. Janevski and R. Pavlovic, J. Mech. Mater. Struct. 4(10), 1689 (2009). genRefLink(16, ’rf15’, ’10.2140 |
| [16] | M. A. Abdou, Int. J. Comput. Meth. 6(4), 569 (2009), DOI: 10.1142/S0219876209002005. [Abstract] genRefLink(128, ’rf16’, ’000273735200005’); |
| [17] | S. Fallahian, D. Hamidian and S. M. Seyedpoor, Int. J. Comput. Meth. 6(2), 229 (2009), DOI: 10.1142/S0219876209001826. [Abstract] genRefLink(128, ’rf17’, ’A1995QM61400005’); |
| [18] | G. Domairry and A. Aziz, Math. Prob. Eng. 2009, 603916 (2009), DOI: 10.1155/2009/603916. |
| [19] | F. Shakeri and M. Dehghan, Math. Comput. Model. 48(4), 486 (2008), DOI: 10.1016/j.mcm.2007.09.016. genRefLink(16, ’rf19’, ’10.1016 |
| [20] | Z. Z. Ganji, Topol. Meth. Nonlinear Anal. 31(2), 341 (2008). genRefLink(128, ’rf20’, ’000257574400015’); |
| [21] | X. J. Lu and H. X. Li, J. Mech. Design 131(11), 111006 (2009), DOI: 10.1115/1.3213529. genRefLink(16, ’rf21’, ’10.1115 |
| [22] | C. J. Liu, Int. J. Struct. Stability Dynam. 12(5), 1250035 (2012), DOI: 10.1142/S0219455412500356. [Abstract] |
| [23] | C. J. Liu, Math. Prob. Eng. 2011, 793798 (2011). |
| [24] | C. J. Liu, Int. J. Struct. Stability Dynamics 13(2), 1350018 (2013), DOI: 10.1142/S0219455413500181. [Abstract] |
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