The Vibration of Partially Filled Cylindrical Tank Subjected to Variable Acceleration


In this study, the vibration of a cylindrical tank partially filled with liquid under motion modeled as mass lumped is investigated. A three-dimensional quasi-static model of a partially-filled tank of circular cross-section is developed and integrated into a comprehensive three-dimensional vehicle model to study its dynamic performance as a function of acceleration, and the fill volume. The liquid load movement occurring in the roll and pitch planes of the tank is derived as a function of the longitudinal acceleration, and then the corresponding shifted load is expressed in terms of center of mass coordinates and mass moments of inertia of the liquid bulk, assuming negligible influence of fundamental slosh frequency and viscous effects. The vibration characteristics of the partially filled tank vehicle are evaluated in terms of load shift, forces and moments induced by the cargo movement, and dynamic load transfer in the longitudinal direction. The semi analytical response is obtained by means of SimuLink? Matlab Software. The effects of longitudinal acceleration of the tank system on the liquid surface inclination and consequently shifting of centroids and moment of inertia are illustrated.

Share and Cite:

O. Badran, M. Gaith and A. Al-Solihat, "The Vibration of Partially Filled Cylindrical Tank Subjected to Variable Acceleration," Engineering, Vol. 4 No. 9, 2012, pp. 540-547. doi: 10.4236/eng.2012.49069.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] G. Popov, S. Sankar, T. S. Sankar and G. H. Vatistas, “Liquid Sloshing in Rectangular Road Containers,” Computers in Fluids, Vol. 21, No. 4, 1992, pp. 551-569. doi:10.1016/0045-7930(92)90006-H
[2] A. S. Veletsos and J. Y. Yang, “Dynamics of Fixed Base Liquid Storage Tanks,” Proceedings of US-Japan Seminar on Earthquake Engineering Research with Emphasis on Lifeline Systems, Japan Society for Promotion of Earthquake Engineering, Tokyo, 8-12 November 1976, pp. 317-341.
[3] A. S. Veletsos and J. Y. Yang, “Earthquake Response of Liquid Storage Tanks,” Advances in Civil Engineering through Engineering Mechanics, ASCE, Raleigh, 23-25 May 1977, pp. 1-24.
[4] M. A. Haroun and G. W. Housner, “Seismic Design of Liquid Storage Tanks,” Journal of Technical Councils of ASCE, Vol. 107, No. 1, 1981, pp. 191-207.
[5] M. A. Haroun and G. W. Housner, “Earthquake Response of Deformable Liquid Storage Tanks,” Journal of Applied Mechanics, Vol. 48, No. 2, 1981, pp. 411-418. doi:10.1115/1.3157631
[6] A. S. Veletsos, “Seismic Effects in Flexible Liquid Storage Tanks,” Proceedings of the International Association for Earthquake Engineering Fifth World Conference, Rome, 25-29 June 1974, pp. 630-639.
[7] F. G. Rammerstorfer, K. Scharf, F. D. Fischer and R. Seeber, “Collapse of Earthquake Excited Tanks,” Journal of Mechanical Research, Vol. 25, No. 2, 1988, pp. 129143.
[8] F. Welt and V. J. Modi, “Vibration Damping Through Liquid Sloshing, Part1: A Nonlinear Analyses,” Transactions of the ASME, Journal Vibration and Acoustics, Vol. 114, No. 1, 1992, pp. 10-16. doi:10.1115/1.2930223
[9] S. K. Jain and P. S. Medhekar, “Proposed Provisions for a Seismic Design of Liquid Storage Tanks: Part I—Codal Provisions,” Journal of Structural Engineering, Vol. 20, No. 3, 1993, pp. 119-128.
[10] S. K. Jain and P. S. Medhekar, “Proposed Provisions for A Seismic Design of Liquid Storage Tanks: Part II— Commentary and Examples,” Journal of Structural Engineering, Vol. 20, No. 4, 1993, pp. 167-175.
[11] W. Chen and M. A. Haroun, “Dynamic Coupling between Flexible Tanks and Seismically Induced Nonlinear Liquid Sloshing,” Fluid Transients ASME, FED, Vol. 291, 1994.
[12] H. Takahara, K. Kimura and M. Sakata, “Frequency Response of Sloshing in a Circular Cylindrical Tank Subjected to Pitching Excitation,” Proceedings of Asia Pacific Vibration Conference, Kuala Lumpur, 27 November-1 December 1995, pp. 703-708.
[13] H. J. Kyeong and C. L. Seong, “Fourier Series Expansion Method for Free Vibration Analysis of Either a Partially Liquid-Filled or a Partially Liquid-Surrounded Circular Cylindrical Shell,” Computers & Structures, Vol. 58, No. 5, 1995, pp. 931-946.
[14] H. J. Kyeong and C. L. Seong, “Hydroelastic Vibration of a Liquid-Filled Circular Cylindrical Shell,” Computers & Structures, Vol. 66, No. 2-3, 1998, pp. 173-185. doi:10.1016/S0045-7949(97)00086-2
[15] J. S. Chang and W. J. Chiou, “Natural Frequencies and Critical Velocities of Fixed-Fixed Laminated Circular Cylindrical Shells Conveying Fluids,” Computer & Structures, Vol. 57, No. 5, 1995, pp. 929-939. doi:10.1016/0045-7949(94)00352-4
[16] J. G. Anderson, “Liquid Sloshing in Containers, Its Utilization and Control,” Ph.D. Thesis, Victoria University, Melbourne, 2000.
[17] M. F. Garrido, “On the Sloshing of Liquids in Parallelepiped—Shaped Containers,” European Journal of Physics, Vol. 24, No. 3, 2003, pp. 277-288.
[18] C. W. S. To and B. Wang, “An Axisymmetric Thin Shell Finite Element for Vibration Analysis,” Computers & Structures, Vol. 40, No. 3, 1991, pp. 555-568. doi:10.1016/0045-7949(91)90226-C
[19] B. S. Subhash and S. K. Bhattacharyya, “Finite Element Analysis of Fluid-Structure Interaction Effect on Liquid Retaining Structures Due to Sloshing,” Computers & Structures, Vol. 59, No. 6, 1996, pp. 1165-1171. doi:10.1016/0045-7949(95)00271-5
[20] M. Amabili, “Eigenvalue Problems for Vibrating Structures Coupled with Quiescent Fluids with Free Surface,” Journal of Sound and Vibration, Vol. 231, No. 1, 2000, pp. 79-97. doi:10.1006/jsvi.1999.2678
[21] C. Z. Wang and B. C. Khao, “Finite Element Analyses of Two-Dimensional Nonlinear Problem in Random Excitations,” Ocean Engineering, Vol. 32, No. 2, 2004, pp. 107113. doi:10.1016/j.oceaneng.2004.08.001
[22] K. B. Vamsi, and N. Ganesan, “Polynomial Approach for Calculating Added Mass for Fluid-Filled Cylindrical Shells,” Journal of Sound and Vibration, Vol. 291, No. 3-5, 2006, pp. 1221-1228. doi:10.1016/j.jsv.2005.06.031
[23] K. H. Jeong and K. J. Kim, “Free Vibration of a Circular Cylindrical Shell Filled with Bounded Compressible Fluid,” Journal of Sound and Vibration, Vol. 217, No. 2, 1998, pp. 197-221. doi:10.1006/jsvi.1998.1741
[24] S. Strandberg, Strandberg Engineering Laboratories, Inc. Greensboro, 2005.
[25] R. Ranganathan, “Analysis of Fluid in Partially Filled Tanks and Their Impact on the Directional Response of Tank Vehicles,” SAE, 1993, Article ID: 932942.
[26] S. Rakheja, R. Ranganathan and S. Sankar, “Field Testing and Validation of a Directional Dynamics Model of a Tank Truck,” International Journal of Vehicle Design, Vol. 13, No. 3, 1992, pp. 251-275.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.