Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Vibration serviceability of footbridges under human-induced excitation : a literature review

SUMMARY: This paper proposes the use of a novel type of passive vibration control system to reduce vibrations in civil engineering structures subject to base excitation. The new system is based on the inerter, a device that was initially developed for high-performance suspensions in Formula 1 racing cars. The principal advantage of the inerter is that a high level of vibration isolation can be achieved with low amounts of added mass. This feature makes it an attractive potential alternative to traditional tuned mass dampers (TMDs). In this paper, the inerter system is modelled inside a multi-storey building and is located on braces between adjacent storeys. Numerical results show that an excellent level of vibration reduction is achieved, potentially offering improvement over TMDs. The inerter-based system is compared to a TMD system by using a range of base excitation inputs, including an earthquake signal, to demonstrate how the performance could potentially be improved by using an inerter instead of a TMD. © 2013 John Wiley & Sons, Ltd.

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Using an inerter-based device for structural vibration suppression

The dynamic characteristics and effectiveness of multiple mass dampers (MMDs), a collection of several mass dampers with distributed natural frequencies, under random loading are investigated in this paper. The MMD attached in a parallel configuration modifies the transfer function of the damper-building system by flattening the peaks observed in a typical single tuned mass damper-building transfer function. The MMD parameters considered here include the frequency range of MMDs, damping ratio of individual dampers, and the number of dampers. Uniform and variable frequency increments in a specified frequency range and mass variation alone, and in combination, are considered. The secondary inertial effect can be represented by conventional mass dampers or liquid sloshing or oscillating liquid column dampers. A parameter study is conducted to delineate the influence of several parameters on the effectiveness and robustness of MMDs in comparison with a single tuned mass damper (TMD). The random loads considered here include wind and seismic excitations. It is demonstrated that the MMD configuration is more effective in controlling the motion of the primary system. It offers the advantages of portability and ease of installation (because of the reduced size of an individual damper) which makes it attractive not only for new installation, but also for temporary use during construction or for retrofitting existing structures.

Performance of Multiple Mass Dampers Under Random Loading

Multiple Tuned Mass Dampers (MTMD) consist of a large number of small oscillators with natural frequencies distributed around the natural frequency of a controlled mode of the structure. In the present paper, the modal characteristics and efficiency of the MTMD are studied analytically. Perturbation solutions for the modal properties of the MTMD–structure system are obtained and the modal characteristics are discussed. An explicit formula to estimate the effectiveness of the MTMD subjected to harmonic forces is also derived. It is shown that the MTMD is efficient when at least one of the oscillators is strongly coupled with the structure in any mode. Based on this observation, a critical bandwidth of the natural frequencies of the MTMD to make the system multiply tuned is derived in a simple form, and furthermore a robustness criterion for the frequency tuning under a given bandwidth is proposed. It is shown that, when properly designed, the MTMD can be much more stable (robust) than a conventional single TMD while maintaining more or less the same efficiency. Numerical studies verify the accuracy of the perturbation solutions and the proposed formulas.

Dynamic characterization of multiple tuned mass dampers and some design formulas

Modal properties of tuned mass damper (TMD)-structure two-degree-of-freedom (2DOF) linear systems are studied employing a perturbation technique. Using the perturbation solutions, formulas relevant to designing the TMD for various types of loading are obtained; they are expressed as a function of mass ratio, tuning ratio, damping ratio of the TMD and damping ratio of the structure. Equivalent additional dampings of the structure due to the TMD are derived for random and harmonic forces. Matched expressions of equivalent damping, which are valid for detuned, i.e. non-optimal, conditions are also presented. The stability boundary of TMD-structure systems subject to linear self-excited forces is derived in a closed form. Using the perturbation solutions, procedures for optimizing the TMD parameters for various types of loading are explained and the optimal values are derived. The formulas obtained in this study can be used with good accuracy for mass ratios less than 0.02.

Design formulas for tuned mass dampers based on a perturbation technique

Analytical results are developed for vibration control of structures with one or more Tuned Mass Dampers (TMDs). The input is a harmonic load with a range of possible frequencies. The control objective is to reduce the maximum amplitude of the structural response. Perturbation theory is used with three sets of small parameters: the ratio of TMD and structural modal masses, the damping of the system, and the differences between the structural and loading frequencies. It is shown analytically that for structures with widely spaced natural frequencies, the response can be approximated accurately by the response of the well-known single-mode structure/TMD system. For structures with p closely spaced natural frequencies, more general analytical results are developed to describe the coupling between the motions of the p modes of the structure and the multiple TMDs. The results show that at least p TMDs with properly placed attachments to the structure are necessary to control the response. If fewer TMDs are used, the maximum frequency response has a lower bound which is independent of the properties of the TMDs. The TMD placement is shown to be always important, regardless of the spacing of the structure's natural frequencies. The results are illustrated for both lumped-mass and continuous structures.

Masato Abe

Papers

Dynamic characterization of multiple tuned mass dampers and some design formulas

Design formulas for tuned mass dampers based on a perturbation technique

Tuned mass dampers for structures with closely spaced natural frequencies

Image analysis of human-induced lateral vibration of a pedestrian bridge

A 3D contact-friction model for pounding at bridges during earthquakes