Geometric assessment of hydrodynamic response in liquid tanks under band-limited stochastic excitation using finite element modeling

Traditionally, liquid storage tanks were designed with regular geometries, such as rectangular or cylindrical shapes. However, due to spatial limitations and geometric constraints in modern engineering applications, the use of irregularly shaped liquid tanks has become increasingly necessary and unavoidable. Although the hydrodynamic behavior of regularly shaped tanks is well understood, it remains a subject of debate for tanks with irregular geometries. The present paper investigated the impact of the tank geometry on the overall hydrodynamic performance. The hydrodynamic response of various shape tanks (trapezoidal tank, and chamfered bottom tank) is compared with the response of conventional rectangular tanks. For an effective comparison, the liquid quantity inside all shape tanks is kept equal. A finite element model based on linearized sloshing wave theory capable of quantifying the impulsive and convective components of the hydrodynamic response is employed in the present study. The accuracy of the proposed finite element model has been validated against existing experimental, analytical, and numerical results, demonstrating excellent agreement. Depending upon the tank geometry the quadrilateral and triangular finite elements were chosen to discretize the computational domain. Dynamic analysis is conducted under both harmonic excitation and stochastic excitation characterized by band-limited white noise. The present study demonstrates that the frequency band-width of the stochastic external excitation is a more critical factor influencing the sloshing response than the total input energy. It is observed that the convective and impulsive components of the hydrodynamic response in liquid storage tanks are significantly influenced by both the characteristics of the external excitation and the tank geometry. Furthermore, this study demonstrates that chamfered-bottom tanks with wall inclinations between 15°–45° exhibit lower hydrodynamic force demands under stochastic excitation, highlighting their enhanced performance and suitability for real-world engineering applications.