A Discrete Model for Transverse Vibration of a Cantilever Beam Carrying Multi Lumped Masses: Analogy with the Continuous Model

Eddanguir, Ahmed; Benamar, Rhali

doi:10.1007/978-3-642-37143-1_11

Cited by 6 publications

(7 citation statements)

References 2 publications

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“…The ski was modelled as a set of 25 equally spaced, elastically connected lumped masses [25] free to move in a direction aligned with the ski reference frame z-axis, s z , and free to move in torsion about the ski reference frame x-axis, s x . A reduced node count model is shown in Fig.…”

Section: Ski Modelmentioning

confidence: 99%

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Effect of edged snow contact on the vibration of alpine skis

et al. 2021

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When skiing, excessive ski vibrations can affect comfort, control and performance. Through the years, much efforts have been invested in understanding and reducing these ski vibrations. However, the vibration response of skis is still poorly understood as most laboratory measurements do not correlate with the on-snow response. This paper aims to understand the differences between ski vibrations measured in a laboratory setting and the actual in-use response. To that end, a miniature custom data-logging system was developed to measure the on-snow vibration response of an alpine ski during a turn and its associated operational deflection shapes. The operational deflection shapes of two fore-body resonant frequencies (22 Hz and 66 Hz) and one aft-body resonant frequency (37 Hz) were measured using that system and their frequencies agree with previously documented on-snow measurements. These operational deflection shapes also show that the ski's first three resonances are coupled in bending and torsion, and that the ski fore-body and aft-body are coupled in torsion. New tools were also developed to facilitate quantitative vibration testing of skis, including a custom test bench for controlled skidding and a ski simulation that include a simple snow interaction model. The operational deflection shapes obtained with these tools showed differences in resonance frequencies and amplitudes. Nevertheless, the results showed good overall agreement with on-snow measurements and confirmed that the observed vibration response and deflection shapes were the result of coupling between bending and torsion caused by the ski being on edge.

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Section: Ski Modelmentioning

confidence: 99%

“…The system's equations of motion are arranged into matrix form using an extension of Eddanguir's method [25] to include the torsional DOFs:…”

Section: Ski Modelmentioning

confidence: 99%

Effect of edged snow contact on the vibration of alpine skis

et al. 2021

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“…in which R and T are the radius and thickness of the member; θ is the angle between the member and the horizontal direction. The stiffness matrix and mass matrix are based on the discrete system for a multi-degree-of-freedom system made of n masses as shown in the Appendix (Eddanguir and Benamar, 2013). Table 1 tabulates the material properties of the steel used in the tower and jacket of the offshore wind turbine.…”

Section: Main Structural Modelmentioning

confidence: 99%

Vibration suppression of offshore wind turbine foundations using tuned liquid column dampers and tuned mass dampers

2019

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Highly dynamic nature of the applied loads on flexible and lightly damped offshore wind turbine (OWT) foundations affects the lifetime and serviceability of the system. In this study, the excessive vibration responses of OWTs are minimized using tuned mass dampers (TMD) and tuned liquid column dampers (TLCD). Due to high efficiency of TLCDs and TMDs for certain loading conditions, a combined TLCD-TMD is also utilized to improve the overall performance in a wide range of loading conditions. First, a parametric study was performed that highlights the sensitivity of these structural control devices. The effect of two devices on fixed offshore wind turbine foundations for the benchmark 5MW NREL turbine in various loading patterns was investigated. Then, the model was subjected to stochastically generated wind loading in operational, parked, startup, and shutdown conditions. The results suggest that the standard deviation of the dynamic responses can be greatly reduced with all structural control devices. However, TMDs are more efficient in operational conditions, whereas TLCDs show better performances in parked conditions. This highlights the possibility and efficiency of a combined TLCD-TMD system in which the dynamic responses are minimized efficiently in a wider selection of loading conditions.

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“…Therefore, the stiffness and mass matrices can be written with Eqs. (5)-(6) to achieve the elementary parameters for a discrete beam, as proposed by Eddanguir and Benamar (2013). As an alternative, the Finite Element Method (FEM) is often used for more complex problems, with arbitrary geometries and complex material behavior.…”

Section: Mechanical Subsystem Modelingmentioning

confidence: 99%

Modular modeling approach for FDM printed structures and piezo disks for metamaterial design

Rodrigues

Silva

Oliveira

2019

Lat. Am. j. solids struct.

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Research in metamaterials has recently gained interest in the field of noise and vibration control. The ability of creating band gap zones with minimum added mass is the main feature behind its success. In addition, the use of 3D printed parts, particularly the Fused Deposition Modeling (FDM), offers a practical solution for manufacturing parts with intricate shapes that are challenging for standard manufacturing processes, which is the case of many structural metamaterials. The combination of this concept with smart materials can further improve performance, providing the means to overcome typical issues. From a design perspective, the problem with coupling rises, as both the mechanical and electrical responses relies on the load circuit and on the mechanical properties of the smart elements. Therefore, the modeling of such structures is a rather complex task, for it involves multiphysical simulations of systems with complex geometries and typically a high number of degrees of freedom. Hence, this paper presents a direct approach for modeling and simulating smart metamaterials using a state-space formulation, which allows the modular coupling of electromechanical resonators manufactured by FDM. The numerical results are compared to experimental data obtained with unit cells prototypes embedded with piezoelectric elements and connected with a tunable shunt electric circuit. The good agreement between test and simulated data validates the design procedure.

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A Discrete Model for Transverse Vibration of a Cantilever Beam Carrying Multi Lumped Masses: Analogy with the Continuous Model

Cited by 6 publications

References 2 publications

Effect of edged snow contact on the vibration of alpine skis

Effect of edged snow contact on the vibration of alpine skis

Vibration suppression of offshore wind turbine foundations using tuned liquid column dampers and tuned mass dampers

Modular modeling approach for FDM printed structures and piezo disks for metamaterial design

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