Interval type-2 fuzzy hydroelastic Ritz–Koopman optimization of a partially filled cylindrical tank for robust sloshing-induced vibro-acoustic suppression

Abstract

Partially filled storage and transport tanks often radiate objectionable low-frequency sound because liquid sloshing, flexible shell modes, and uncertain damping interact in the same operating band. This paper develops a compact hydroelastic vibro-acoustic design method for a vertical cylindrical tank equipped with internal porous annular baffles and external viscoelastic rings. The fluid is represented by Bessel-based sloshing modes, the shell by a Ritz expansion, and the nonlinear free-surface contribution by a cubic Koopman–Galerkin lifting. Interval type-2 fuzzy sets describe epistemic uncertainty in fill height, fluid density, shell stiffness, loss factor, and baffle clogging. A deterministic design and a proposed fuzzy robust design are compared over alpha-plane uncertainty scenarios using peak sound power, band-averaged sound power, wall acceleration, and wave-height constraints. The proposed design reduces the 95th-percentile peak sound power from 57.84 dB in the uncontrolled tank to 48.55 dB, decreases the 95th-percentile band-averaged acoustic level from 28.47 dB to 26.73 dB, and lowers the 95th-percentile wall-acceleration level from 130.48 dB to 120.34 dB. Relative to the deterministic optimum, the robust design has a 0.216 dB higher nominal peak and a 0.173 dB higher 95th-percentile peak. Still, it lowers the 95th-percentile band mean by 1.059 dB and wall acceleration by 0.613 dB. The contribution is the integrated reduced-order design workflow; physical validation remains necessary.