Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

• Published in: Journal of sound and vibration Vol. 312; no. 3; pp. 442 - 460
• Main Authors: Virella, Juan C., Prato, Carlos A., Godoy, Luis A.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 06.05.2008; Elsevier
• Subjects: Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical models; Nonlinearity; Physics; Pressure distribution; Solid mechanics; Structural and continuum mechanics; Tanks; Two dimensional; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Walls; High strain; Eigenmode; Displacement(deformation); Surface wave; Acoustics; Modeling; Finite element method; Pressure effect; Hydroelasticity; Plane strain; Non linear effect; Vibrational mode; Storage tank; Liquid sloshing; Non linear wave
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2007.07.088

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.