Study on Vibration Suppression of Elastic Structures by Sloshing in Multiple Liquid-Filled Containers

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Vibrations of elastic structures which are suppressed by multiple liquid-filled containers have been investigated. Their results are summarized in the three categories as follows:(1) Vibration Suppression of Elastic Structures by Using Multiple Liquid Containers1) Vibrations of the elastic structures with a single degree of freedom, which are subjected to vertical sinusoidal excitation, can be suppressed by using two rectangular liquid tanks when the natural frequencies of the structure and sloshing in the two liquid tanks have the ratio of 1:1:1. However, if the tuning condition deviates slightly, then the Hopf bifurcation occurs. As a result, the steady-state solution becomes unstable and amplitude-modulated motion appears. This motion loses the effectiveness of tuned liquid dampers2) In a two-story elastic structure with two degrees of freedom which is subjected to horizontal sinusoidal excitation, the amplitude-modulated motion may appear when rectangular tanks are installed on eac … More h floor of the structure. As the excitation becomes larger or the liquid levels of the tanks increase, amplitude-modulated motion may appear.(2) Nonlinear Vibrations in Elastic Structures Containing a Single Liquid Tank1) When an elastic structure movable in the horizontal plane, containing a cylindrical liquid tank, is subjected to one-directional horizontal excitation, whirling motion may be caused by the swirl motion in the tank.2) In the same case as 1)of(1)mentioned above but with a single cylindrical liquid tank, the values of the system's parameters when bifurcation phenomena including Hopf bifurcation occur are shown.(3) Effectiveness of Multiple Dynamic Absorbers with Nonlinear Spring Characteristics1) It has already been known that using dynamic absorbers make the vibrations of the structure minimal at the tuning frequency but new two peaks appear on both sides of the tuning frequency. For example, if multiple dynamic absorbers with nonlinear softening spring characteristics are used, multiple steady-state solutions appear on the left side of the resonance curve. We call this phenomenon a multi-modal vibration which never appears in using a single nonlinear dynamic absorber. The multi-modal vibration has (2n-1) steady-state solutions for n nonlinear dynamic absorbers.2) The multi-modal vibration appears in the two excitation frequency intervals where it has constant amplitude and modulated amplitude. As the number of the nonlinear dynamic absorbers increases, the excitation frequency range of the multi-modal vibration becomes wider but that of the amplitude-modulated motion becomes narrower. Less