Analytic calculation of liquid sloshing force excited by uniform acceleration motion

ZHANG Haitao1,2,SUN Beibei2

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (12) : 158-163.

PDF(1336 KB)
PDF(1336 KB)
Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (12) : 158-163.

Analytic calculation of liquid sloshing force excited by uniform acceleration motion

  • ZHANG Haitao1,2,SUN Beibei2
Author information +
History +

Abstract

For forced sloshing in a rectangular tank moving in a constant acceleration, an analytic method was proposed to solve analytical approximate solutions of sloshing forces on the tank based on the nonlinear vibration theory. Nonlinearity of sloshing and the effects of acceleration and filling rate were also analyzed. The liquid pressure on the sidewall was mainly calculated by the analytical solutions of fluid velocity potential, while in partial regions of sidewalls, the liquid pressure was approximately predicted by linear distribution. The analytical approximate solutions of sloshing force on the sidewalls were obtained by the integrations of liquid pressure along the sidewall. The results show that nonlinear factors do not have a major impact on the sloshing force on the tank; nonlinear term of sloshing force is proportional to the cube of accelerated speed; the fluctuation of filling rate will change the natural frequency of linear sloshing, and then make an impact to the nonlinear term of sloshing force, the impact is in agreement with the tendency of natural frequency curve.   

Key words

sloshing force / nonlinearity / analytical approximate solutions / uniform acceleration motion

Cite this article

Download Citations
ZHANG Haitao1,2,SUN Beibei2. Analytic calculation of liquid sloshing force excited by uniform acceleration motion[J]. Journal of Vibration and Shock, 2020, 39(12): 158-163

References

[1] Abramson H N. The dynamic behavior of liquids in moving containers[R]. NASA Special Publication, 1966, SP-106.
[2] 刘奎, 康宁. 罐车转向时液体晃动的仿真分析[J]. 北京航空航天大学学报, 2009, 35(11): 1403-1407.
Liu Kui, Kang Ning. Simulation of liquid slosh in braking process of tank truck[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(7): 1403-1407. (in Chinese)
[3] Abid H M, Shah Q H, Faris W F. The structural integrity assessment of a partially filled tank pertaining to liquid sloshing upon sudden brake applications[J]. International Journal of Vehicle Systems Modelling and Testing, 2011, 6(3-4): 307-317.
[4] Dai J, Han M, Ang K K. Moving element analysis of partially filled freight trains subject to abrupt braking[J]. International Journal of Mechanical Sciences, 2019, 151: 85-94.
[5] 刘延柱,陈立群. 非线性振动[M]. 北京:高等教育出版社,2001.  
[6] Faltinsen O M, Timokha A N. Analytically approximate natural sloshing modes and frequencies in two-dimensional tanks[J]. European Journal of Mechanics, 2014, 47(5):176-187.
[7] Weidman P. Analytical solutions of first-mode sloshing in new containers[J]. Wave Motion, 2016, 63:170-178.
[8] Hasheminejad S M, Soleimani H. An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth[J]. Applied Mathematical Modelling, 2017, 48:338-352.      
[9] 张海涛, 孙蓓蓓. 容器匀加速运动状态下液体大幅晃动的解析计算[J]. 东南大学学报(自然科学版), 2018, 48(2):207-212.
Zhang Haitao, Sun Beibei. Analytic calculation of large-amplitude liquid sloshing in tank moving in uniform acceleration motion[J]. Journal of Southeast University (Natural Science Edition), 208, 48(2): 207-212. (in Chinese)
[10] 张海涛, 孙蓓蓓, 陈建栋. 基于自由液面预测的非线性液体晃动问题的数值模拟[J]. 东南大学学报(自然科学版), 2014, 44(2): 277-282.
Zhang Haitao, Sun Beibei, Chen Jiandong. Numerical simulation of nonlinear liquid sloshing problems based on forecast of free surface[J]. Journal of Southeast University (Natural Science Edition), 2014, 44(2): 277-282. (in Chinese)
[11] Frandsen J B. Sloshing motions in excited tanks[J]. Journal of Computational Physics, 2004, 196(1): 53-87.
[12] Dodge F T. The new dynamic behavior of liquids in moving containers[M]. San Antonio, Texas: Southwest Research Institute, 2000.
PDF(1336 KB)

726

Accesses

0

Citation

Detail

Sections
Recommended

/