Analytical Solution for Dynamic Response of Underground Rectangular Fluid Tank Subjected to Arbitrary Dynamic Loads
Publication: Journal of Engineering Mechanics
Volume 146, Issue 8
Abstract
In this paper, the dynamic response of underground rectangular fluid tank resting on an elastic foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The dynamic responses investigated are deflection, bending moment, and shear force of the tank. The underground rectangular tank is assumed to be a frame composed of horizontal and vertical beams resting on an elastic foundation. The mechanical resistance of elastic foundation is modeled using spring elements that account for soil resistance due to compressive strains in the soil. The fluid in the tank is assumed as inviscid and irrotational, and the influence of free-surface wave is ignored. An analytical solution of free vibration modes of empty tank (dry modes) is derived at first, and then the free vibration modes of fluid tank infilled with water (wet modes) can be obtained by the dry modes. Based on the wet modes, the explicit formulations of dynamic responses of the tank are finally obtained by the modal superposition method. The solutions for several cases, such as empty tank and fully filled fluid tank subjected to harmonic loads, are also discussed. Further parametric analysis is carried out to investigate the influence of the soil–structure relative stiffness ratio on dynamic responses of the fully filled fluid tank.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The research has been supported by the National Key Research and Development Plan of China (Nos. 2018YFC0809602, 2018YFC1504305, and 2017YFC1500703), the National Natural Science Foundation of China (Nos. 41922059, 51678438, and 51978431), the Shanghai Committee of Science and Technology (Nos. 18DZ1205103 and 17DZ1203804), and the Fundamental Research Funds for the Central Universities of China.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 8 • August 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Aug 20, 2019
Accepted: Mar 13, 2020
Published online: May 28, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 28, 2020
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