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Equivalent mechanical model of rectangular container attached to a pendulum compared to experimental data and analytical solution

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Abstract

A tuned liquid damper (TLD) is a passive control device that transfers kinetic energy from the main structure to a liquid sloshing in a tank. The mechanical description of a sloshing liquid contained in a tank requires an intricate mathematical formulation. An alternative technique describes the TLD dynamic behavior as an equivalent mechanical model comprising a series of pendulums or mass–spring systems attached to the tank walls. To validate this approach, this paper compares the discrete model to experimental results and an analytical solution for a rectangular container attached to a pendulum (pendulum-slosh problem). At first, the fundamental oscillation period of the discrete model, representing a rectangular tank, is compared to experimental data and a classic analytical solution. Finally, we compare the pendulum-slosh problem modeled as a discrete model with the analytical solution and experimental results.

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Acknowledgments

This work was supported by the Brazilian Coordination for the Improvement of Higher Education Personnel (CAPES) – Finance Code 001, Brazilian Council for Scientific and Technological Development (CNPq) and Research Support Foundation of the Federal District (FAPDF). The second author acknowledges the Group of Dynamics of Systems (UnB-FT/EnM/GDS) for its support to make possible the present experiments.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Brasília, Darcy Ribeiro Campus, Asa Norte, Brasília, DF, 70910-900, Brazil

    Marcus V. G. de Morais

  2. Department of Civil Engineering, University of Brasília, Darcy Ribeiro Campus, Asa Norte, Brasília, DF, 70910-900, Brazil

    Alejandro A. O. Lopez & Lineu J. Pedroso

  3. PPG, Graduate Program in Engineering Material Integrity, University of Brasilia (UnB), Campus of Gama (FGA), Gama (Brasília), 72444-240, Brazil

    Marcus V. G. de Morais & Juliano F. Martins

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  1. Marcus V. G. de Morais
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  2. Alejandro A. O. Lopez
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  3. Juliano F. Martins
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  4. Lineu J. Pedroso
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Correspondence to Marcus V. G. de Morais.

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Technical Editor: Thiago Ritto.

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Appendix A: Curve Fitting Toolbox

Appendix A: Curve Fitting Toolbox

Figure 11 shows an example of dynamic parameter identification performed by the Curve Fitting Toolbox (CFTOOL/MATLAB). This illustration presents the liquid’s dynamic level motion in a rectangular container observed by motion capture, as shown in Fig. 5.

Fig. 11
figure 11

Example of identification of modal parameters by the Curve Fitting Toolbox (MATLAB)

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de Morais, M.V.G., Lopez, A.A.O., Martins, J.F. et al. Equivalent mechanical model of rectangular container attached to a pendulum compared to experimental data and analytical solution. J Braz. Soc. Mech. Sci. Eng. 42, 143 (2020). https://doi.org/10.1007/s40430-020-2232-7

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  • DOI: https://doi.org/10.1007/s40430-020-2232-7

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