Dry-friction-induced self-excitation of a rectangular liquid-filled tank

A comprehensive review of variable-length pendulums is presented. An attempt at a unique evaluation of current trends in this field is carried out in accordance with mathematical modeling, dynamical analysis, and original computer simulations. Perspectives of future trends are also noted on the basis of various concepts and possible theoretical and engineering applications. Some important physical concepts are verified using dedicated numerical procedures and assessed based on dynamical analysis. At the end of the review, it is concluded that many variable-length pendulums are very demanding in the modeling and analysis of parametric dynamical systems, but basic knowledge about constant-length pendulums can be used as a good starting point in providing much accurate mathematical description of physical processes. Finally, an extended model for a variable-length pendulum’s mechanical application being derived from the Swinging Atwood Machine is proposed. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. The results of original numerical simulations show that the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. It can also be applied in simple mechatronic and robotic systems.

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“…In [48], a water plant-related problem was used with dry friction, which added to the excitement of the water-filled container, see Fig. 25.…”

Section: Load Oscillationsmentioning

confidence: 99%

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

Yakubu

Olejnik

Awrejcewicz

2022

Arch Computat Methods Eng

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“…for cuboids [15], cylinders of various orientations [1,15,16] or cones [17]). Many authors deal with cylindrical tanks [18][19][20][21][22] or rectangular tanks [23][24][25][26][27], but also equivalent models for spherical tanks [10], tilted cylinders [28], or prismatic-walled containers [29] have been derived. Moreover, many works consider just a single (most dominant) sloshing mode.…”

Section: Introductionmentioning

confidence: 99%

Rapid sloshing-free transport of liquids in arbitrarily shaped containers

Toth,

Scharner,

Schirrer

et al. 2024

Preprint

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We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneu-vers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulummodel to represent the sloshing dynamics and suggest a novel parameter identification scheme suitablefor arbitrary container shapes and any number of sloshing modes. By computing natural modes andfluid reaction forces and torques for imposed harmonic container motions via a finite element model,we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We alsoprovide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameterestimates. The proposed feed forward control method uses a virtual tray pendulum on which we placethe container (in the form of its equivalent pendulum model). Designing the virtual tray such thatthe fluid’s dominant sloshing mode becomes uncontrollable for displacements of the tray pendulumpivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property ofthe resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in highermodes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed methodis demonstrated through extensive simulations and experimental results using a Martini cocktail glass,whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept.

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Rapid sloshing-free transport of liquids in arbitrarily shaped containers

Toth,

Scharner,

Schirrer

et al. 2024

Acta Mech

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We present a model-based feedforward control strategy suitable for designing swift rest-to-rest maneuvers for liquids in arbitrarily shaped containers. We employ the commonly used equivalent pendulum model to represent the sloshing dynamics and suggest a novel parameter identification scheme suitable for arbitrary container shapes and any number of sloshing modes. By computing natural modes and fluid reaction forces and torques for imposed harmonic container motions via a finite element model, we obtain data for the identification scheme. A fitting procedure then yields highly accurate parameters for a physical pendulum model, where each pendulum represents one sloshing mode. We also provide a thorough analysis of parameter identifiability and guidelines for obtaining robust parameter estimates. The proposed feedforward control method uses a virtual tray pendulum on which we place the container (in the form of its equivalent pendulum model). Designing the virtual tray such that the fluid’s dominant sloshing mode cannot be excited by horizontally moving the tray pendulum pivot effectively zeros out any sloshing motion in this mode. We then exploit the flatness property of the resulting system to design rest-to-rest maneuvers where any residual sloshing motion (in higher modes) can be exactly stopped at the end of the maneuver. The effectiveness of the proposed method is demonstrated through extensive simulations and experimental results using a Martini cocktail glass, whose shape is challenging in terms of sloshing. The experimental results show the successful, accurate suppression of sloshing, validating the efficacy of the proposed concept.

show abstract

Dry-friction-induced self-excitation of a rectangular liquid-filled tank

Cited by 6 publications

References 43 publications

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

Rapid sloshing-free transport of liquids in arbitrarily shaped containers

Rapid sloshing-free transport of liquids in arbitrarily shaped containers

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