Dynamic response of liquid-filled rectangular tank with elastic appendages under pitching excitation. (English) Zbl 1173.74338
Summary: Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin’s method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.
Keywords:
liquid-filled rectangular tank; elastic appendage; nonlinear dynamics; natural frequency; pitchReferences:
| [1] | Moiseev N N, Rumyantesev V V. Dynamics of liquid-filled rigid body[M]. Han zipeng (transl). Beijing: Aerospace Press, 1992 (in Chinese). |
| [2] | Abramson H N. The dynamic behavior of liquids in moving containers[R]. NASA: SP106, 1966. · Zbl 0152.37602 |
| [3] | Odd M Faltinsen. A nonlinear theory of sloshing in rectangular tanks[J]. Journal of Ship Research, 1974, 18(4):224–241. |
| [4] | Odd M Faltinsen, Olav F Rognebakke, Ivan A Lukovsky, Alexander N Timokha. Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth[J]. J Fluid Mech, 2000, 407:201–234. · Zbl 0990.76006 · doi:10.1017/S0022112099007569 |
| [5] | Odd M Faltinsen, Alexander N Timokha. Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth[J]. J Fluid Mech, 2002, 470:319–357. · Zbl 1163.76325 · doi:10.1017/S0022112002002112 |
| [6] | Wang Zhaolin, Liu Yanzhu. Dynamics of liquid-filled system[M]. Beijing: Science Press, 2002 (in Chinese). |
| [7] | Yin Lizhong. Study on large sloshing of liquid and dynamics of the liquid-solid coupling system[D]. Ph D Dissertation. Harbin: Harbin Institute of Technology, 1999 (in Chinese). |
| [8] | Gou Xingyu, Yin Lizhong, Ma Xingrui, Huang Huaide. Forced sloshing of liquid in a narrow rectangular container[J]. Mechanics and Practice, 1998, 20:20–22 (in Chinese). |
| [9] | Yin Lizhong, Liu Min, Wang Benli, Zou Jingxiang. Study on dynamic response of the liquid-solid coupling system with the liquid in a rectangular container under horizontal excitation[J]. Journal of Vibration Engineering, 2000, 13:433–437 (in Chinese). |
| [10] | Ma Xingrui, et al. Dynamics of spacecraft-developments and applications of some problems[M]. Beijing: Science Press, 2001 (in Chinese). |
| [11] | Chen Ke, Li Junfeng, Wang Tianshu. Nonlinear dynamics modeling and analysis of liquid sloshing in rectangular tank[J]. Acta Mechanica Sinica, 2005, 37(3):339–344 (in Chinese). |
| [12] | Zeng Jianghong. Dynamics of spinning system with partially liquid-filled tanks and numerical study of three-dimensional nonlinear liquid sloshing[D]. Ph D Dissertation. Beijing: Tsinghua University, 1996 (in Chinese). |
| [13] | Xu Gang. Numerical study on fluid-structure interaction between large-scale thin-walled structures and viscous fluid with large sloshing[D]. Ph D Dissertation. Beijing: Tsinghua University, 2003 (in Chinese). |
| [14] | Yue Baozeng, Liu Yanzhu, Wang Zhaolin. ALE finite element method for three-dimensional large amplitude liquid sloshing using fractional step method[J]. Chinese Journal of Applied Mechanics, 2001, 18(1):110–115 (in Chinese). |
| [15] | Yue Baozeng. Three dimensional large amplitude liquid sloshing under pitching excitation[J]. Acta Mechanica Sinica, 2005, 37(2):199–203 (in Chinese). |
| [16] | Li Yuchun, Lou Menglin. BEM simulation of nonlinear sloshing for aqueduct fluid[J]. Earthquake Engineering and Engineering Vibration, 2000, 20(2):51–56 (in Chinese). |
| [17] | Li Junfeng, Wang Zhaolin. Attitude dynamics of a spacecraft with deploying flexible appendages[J]. Journal of Tsinghua University (Sci & Tech), 1996, 36(10):35–40 (in Chinese). |
| [18] | Kalaycioglu S, Misra A K. Approximate solutions for vibration of deploying appendages[J]. J Guid Cont Dyn, 1991, 14(2):287–293. · doi:10.2514/3.20639 |
| [19] | Jia Yinghong, Xu Shijie. Variable structure control for liquid-filled flexible multi-body spacecraft[J]. Journal of Astronautics, 2002, 23(3):18–23 (in Chinese). |
| [20] | Jia Yinghong, Xu Shijie, Jing Wuxing. Dynamics and variable structure control of a spacecraft with elastic appendages[J]. Journal of Harbin Institute of Technology, 2003, 35(1):1–4 (in Chinese). |
| [21] | Li Tiecheng, Wang Zhaolin, Li Junfeng, Yue Baozeng. On the generation of dynamical equations and dynamical boundary conditions of a rigid-fluid-elastic coupled system[J]. Chinese Journal of Applied Mechanics, 1998, 15(2):127–131 (in Chinese). · doi:10.3901/CJME.2002.supp.127 |
| [22] | Cheng Xuduo, Wang Zhaolin, Li Junfeng. Study on attitude dynamics of a liquid-filled spacecraft with elastic appendages[J]. Chinese Journal of Space Science, 2000, 20(3):271–277 (in Chinese). |
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