Negative stiffness behaviors emerging in elastic instabilities of prismatic tensegrities under torsional loading

Zhang, Li-Yuan; Xu, Guang-Kui

doi:10.1016/j.ijmecsci.2015.09.009

Cited by 33 publications

(11 citation statements)

References 35 publications

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“…The proposed structural approach can also model moving bridges thanks to the cables that can be rolled or pulled to control the structural shape. Tensegrity statics has been studied in many works [7,[11][12][13], and the minimal mass and optimization problem has been applied in many fields like: acoustics dos Santos, et al [14][15][16][17][18][19], biomechanics [20][21][22], form finding [19,[23][24][25][26], stability of Tbar tensegrity structures [27]. The simplest form of the tensegrity dynamics was obtained by Skelton [28], where a matrix form was introduced, devoid of transcendental functions.…”

Section: Introductionmentioning

confidence: 99%

On the Dynamics of Tensegrity Bridges

Carpentieri¹,

Skelton²

2017

J Aerosp Eng Mech

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This paper describes the nonlinear dynamics of planar tensegrity bridges designed for minimal mass. The three-dimensional bridge benefits by the planar analysis in the most important manner relating to topology of material. We start with the minimal mass bridge, counting both structural mass and deck mass, and then derive the nonlinear dynamics to study dynamic behavior of the minimal mass bridge. Suggested design criteria include static and dynamic response. The minimal mass tensegrity has an optimal complexity (number of elements), and we show how the dynamic response influences the best choice of complexity, in comparison with the optimal complexity of the static design. The structures are first designed with minimal mass criteria, accounting for equilibrium and static stability conditions, and subsequently, we investigate the dynamics of such structures subject to constraints on displacements and loads perturbations. We employ an efficient approach to rigid body dynamics in matrix form, modified to include cable masses. We also show how to pass from the matrix to vector form of the dynamics. The equations of motion are derived analytically using Newtonian methods, and include damping and bar length constraints. Prestress of cables is added to tune stiffness. We show an application for artificial gravity space habitats.

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Section: Introductionmentioning

confidence: 99%

On the Dynamics of Tensegrity Bridges

Carpentieri¹,

Skelton²

2017

J Aerosp Eng Mech

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“…In the figure, the normalized stiffness is defined as k * h =kh/kh0, k * c =kc/kc0 and k * m =km/km0 with kh0, kc0 and km0 being the effective stiffness at the tensegrity configuration (u = 0, = 0). For a stable structure, k * h and k * m should always be greater than zero (Zhang and Xu, 2015;Zhang, et al, 2016) and therefore, the deep blue regions (k * m <0) in Fig. 2a represent unstable PTS configurations which will not be studied in this research.…”

Section: Theoretical Model Of Tunable Prismatic Tensegrity Structurementioning

confidence: 99%

Wave propagation in tunable lightweight tensegrity metastructure

Wang

Liu

Zhu

et al. 2018

Sci Rep

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Lightweight metastructures are designed consisting of prismatic tensegrity building blocks which have excellent strength-to-weight ratio and also enable unique compression-torsion coupling. A theoretical model with a coupled axial-torsional stiffness is first developed to study the band structures of the proposed lightweight metastructures. Then, various unit cell designs are investigated for bandgap generations at desired frequency ranges. Broadband full-wave attenuation is found in the tensegrity metastructure with special opposite-chirality. Furthermore, tunable stiffness in the prismatic tensegrity structure is investigated and ‘small-on-large’ tunability is achieved in the metastructure by harnessing the geometrically nonlinear deformation through an external control torque. Prestress adjustment is also investigated for fine tuning of the band structure. Finally, frequency response tests on the finite metastructures are preformed to validate their wave attenuation ability as well as their wave propagation tunability. The proposed tensegrity metastructures could be very useful in various engineering applications where lightweight and tunable structures with broadband vibration suspension and wave attenuation ability are in high demand.

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“…16 have provided a useful insight into the analysis and design of nonlinear vibration isolators by exploiting potential nonlinear benefits of the time delay in vibration control. Zang and Xu 17 explored the negative stiffness behaviors of prismatic tensegrities emerging in their instability responses under torsion. Fulcher et al.…”

Section: Introductionmentioning

confidence: 99%

A 6-DOF micro-vibration isolation platform based on the quasi-zero-stiffness isolator

Tang

Yang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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Micro-vibrations generated by rotating machinery could influence the working performance of the precise instruments equipped in industrial facilities, aircraft, ships, etc. Isolation systems are thus essential for preventing the high-sensitive instruments from being disturbed. In this work, a 6 degrees-of-freedom (DOF) micro-vibration isolation platform is proposed based on the quasi-zero-stiffness (QZS) isolator. The structure of the isolation platform is a conventional Stewart mechanism equipped with the QZS isolators in each leg. To analyze the stiffness of the leg, the static analysis is carried out. Afterwards, the stiffness of the platform in six directions are also discussed. Moreover, the dynamical equations of the isolation platform are formulated by the Lagrange Equation. Finally, the dynamic response of the proposed model is investigated and compared with the linear case whose stiffness of the leg is linear. The results show that the newly designed QZS platform in this work has a good isolation performance, which can attenuate the external vibrations significantly within a broad frequency band. Parametric analysis shows that the structure parameters, damping and excitation amplitude have a great influence on the isolation performance of the QZS platform. Delightfully, the result of indicates that, (a) the newly designed QZS platform is able to provide an excellent isolation performance in all the six DOFs, which advances the dynamic study of multi-dimensional QZS vibration isolation; (b) The multi-dimensional vibration isolation platform is innovatively designed using geometric nonlinear technology, there is no influence of the magnetic sources to the precision instruments when compared with the previous designs; (c) the regulation mechanism of the structure parameters of the QZS isolation platform on the dynamic transmission characteristics of the system is revealed, which indicates that the platform is particularly suitable for micro-vibration isolation whose vibration magnitude and frequency are quite low.

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Negative stiffness behaviors emerging in elastic instabilities of prismatic tensegrities under torsional loading

Cited by 33 publications

References 35 publications

On the Dynamics of Tensegrity Bridges

On the Dynamics of Tensegrity Bridges

Wave propagation in tunable lightweight tensegrity metastructure

A 6-DOF micro-vibration isolation platform based on the quasi-zero-stiffness isolator

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