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Research Papers

Design and Numerical Analysis of Vibration Isolators With Quasi-Zero-Stiffness Characteristics Using Bistable Foldable Structures

[+] Author and Article Information
Sachiko Ishida

Senior Assistant Professor
Mem. ASME
Department of Mechanical Engineering,
School of Science and Technology,
Meiji University,
1-1-1, Higashimita,
Kawasaki, Kanagawa 2148571, Japan
e-mail: sishida@meiji.ac.jp

Hiroshi Uchida

Professor
Department of Mechanical Systems Engineering,
Faculty of Engineering,
Fukuyama University,
1, Sanzo, Gakuen-cho,
Fukuyama, Hiroshima 7290292, Japan
e-mail: uchidah@fume.fukuyama-u.ac.jp

Haruo Shimosaka

Professor
Department of Mechanical Engineering,
School of Science and Technology,
Meiji University,
1-1-1, Higashimita,
Kawasaki, Kanagawa 2148571, Japan
e-mail: hshimos@meiji.ac.jp

Ichiro Hagiwara

Professor
Fellow ASME
Meiji Institute for Advanced Study of
Mathematical Sciences,
Meiji University,
4-21-1, Nakano,
Tokyo 1648525, Japan
e-mail: ihagi@meiji.ac.jp

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 10, 2015; final manuscript received January 5, 2017; published online April 24, 2017. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 139(3), 031015 (Apr 24, 2017) (8 pages) Paper No: VIB-15-1373; doi: 10.1115/1.4036096 History: Received September 10, 2015; Revised January 05, 2017

In this paper, a novel vibration isolator based on a foldable cylinder with a torsional buckling pattern, which is also called Kresling's pattern, is proposed, and the performance of the proposed isolator in terms of preventing structural vibration is numerically evaluated. It is known that foldable cylinders with a torsional buckling pattern provide bistable folding motions under specific conditions. For simplification, a foldable cylinder with a torsional buckling pattern is modeled using horizontal, longitudinal, and diagonal truss elements connected by rotational joints and enforced by rigid frames, which are also called Rahmen, while maintaining the bistability of the structure. Additional linear springs are incorporated into the structure in order to obtain a nonlinear spring with quasi-zero-stiffness characteristics. It is numerically established that: (i) the resonance of the combined structure is effectively suppressed and (ii) the structure decreases the vibration response even at high frequencies when it is used around the equilibrium position at which the spring stiffness is quasi-zero.

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References

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Figures

Grahic Jump Location
Fig. 1

Folding motions of the cylindrical model based on torsional buckling: (a) initial spatial state, (b) folding/expanding state, (c) folded state, and (d) developed pattern for the structure. The figure has been extracted from Ref. [21].

Grahic Jump Location
Fig. 2

Two-layered computational models: (a) foldable truss structure, consisting of horizontal, longitudinal, and diagonal bar elements connected by ball joints, used in the previous study [21] and (b) foldable truss structure with rigid frames, to be used in the present study

Grahic Jump Location
Fig. 3

Computed folding motions of the two-layered structure with rigid frames: (a) initial state, (b) intermediate state during the folding process, and (c) intermediate state during the folding process. Further, (d)–(f) show the top views of (a)–(c), respectively. The rigid frames are not visualized in the figure: (a) height = 0.0775 m, (b) height = 0.0387 m, (c) height = 0 m, (d) height = 0.0775 m, (e) height = 0.0387 m, and (f) height = 0 m.

Grahic Jump Location
Fig. 4

Computed mechanical characteristics of the two-layered structure: (a) strain of bar elements through folding/deploying processes: a horizontal element (upper), a longitudinal element (middle), and a diagonal element (bottom), (b) vertical force–displacement graph, and (c) stiffness–displacement graph

Grahic Jump Location
Fig. 5

Computed folding motions of the three-layered structure with rigid frames: (a) initial state, (b) intermediate state during the folding process, and (c) intermediate state during the folding process, where the upper layer is perfectly folded but the lower layer cannot be folded. The rigid frames are not visualized in the figure: (a) height = 0.155 m, (b) height = 0.116 m, and (c) height = 0.0775 m.

Grahic Jump Location
Fig. 6

Two-layered and three-layered computational models with linear springs: (a) two-layered model with rigid frames connected by a linear spring, (b) side view of the two-layered model, and (c) side view of the three-layered model with two independent linear springs

Grahic Jump Location
Fig. 7

Computed mechanical characteristics of the two-layered combined structure: (a) strain of bar elements through folding/deploying processes: a horizontal element (upper), alongitudinal element (middle), and a diagonal element (bottom), (b) total force–displacement graph, and (c) stiffness–displacement graph

Grahic Jump Location
Fig. 8

Computed folding motions of three-layered structure with rigid frames and linear spring: (a) initial state, (b) intermediate state during the folding process, where the stiffness is quasi-zero, and (c), (d) intermediate states where all the layers are folded uniformly. The rigid frames and linear spring are not visualized in the figure: (a) height = 0.155 m, (b) height = 0.12 m, (c) height = 0.06 m, and (d) height = 0.02 m.

Grahic Jump Location
Fig. 9

Computed mechanical characteristics of three-layered combined structure: (a) strain of bar elements through folding/deploying processes: a horizontal element (upper), a longitudinal element (middle), and a diagonal element (bottom), (b) total force–displacement graph, and (c) stiffness–displacement graph

Grahic Jump Location
Fig. 10

Simulation model for vibration excitation to the foldable isolator and linear spring

Grahic Jump Location
Fig. 11

Vibration characteristics of the foldable isolator and linear spring under 1-mm and 5-mm standard deviation of the vibration amplitude. Spectra were obtained by averaging 5000 data segments under the conditions of fast Fourier transform size = 216 and sampling period = 0.0005 s.

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