... + ( ∂ φ ∂ y ) 2 + ( ∂ φ ∂ z ) 2 } + g z + P ρ = - z ·· 0 z Fig. 2 Shapes of two predominant sloshing modes. ( a ) (1,0) mode, ( b ) (0,1) mode. where Q 1 = ν 0 + γ hw , and H 1 represents...

... nonlinear governing equation for the sloshing response of the floating roof has a cubic nonlinear stiffness term similar to the well known Duffing equation. It is shown that accounting for large deflections could substantially reduce the wave elevation for near resonance harmonic excitations. Evaluating...

...Takashi Ikeda Nonlinear vibrations of an elastic structure with two partially filled liquid tanks subjected to horizontal harmonic excitation are investigated. The natural frequencies of the structure and sloshing satisfy the tuning condition 1:1:1 when tuned liquid dampers are used. The equations...