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Research Papers

Viscoelastic Characteristics of Mechanically Assembled Three-Dimensional Structures Formed by Compressive Buckling

[+] Author and Article Information
Haibo Li

State Key Laboratory of Ocean Engineering,
School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China;
Department of Civil and Environmental Engineering;
Department of Mechanical Engineering;
Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208

Xi Wang

State Key Laboratory of Ocean Engineering,
School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

Feng Zhu

Department of Civil and Environmental Engineering;
Department of Mechanical Engineering;
Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208;
School of Logistics Engineering,
Wuhan University of Technology,
Wuhan 430063, China

Xin Ning

Department of Materials Science and Engineering,
Frederick Seitz Materials Research Laboratory,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Heling Wang

Department of Civil and Environmental Engineering;
Department of Mechanical Engineering;
Department of Materials Science and Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: heling.wang@northwestern.edu

John A. Rogers

Department of Materials Science and Engineering;
Department of Biomedical Engineering;
Department of Chemistry;
Department of Mechanical Engineering;
Department of Electrical Engineering and Computer Science;
Department of Neurological Surgery,
Center for Bio-Integrated Electronics,
Simpson Querrey Institute for BioNanotechnology,
McCormick School of Engineering and
Feinberg School of Medicine,
Northwestern University,
Evanston, IL 60208

Yihui Zhang

Center for Flexible Electronics Technology and
Center for Mechanics and Materials,
Beijing 100084, China;
AML, Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China

Yonggang Huang

Department of Civil and Environmental Engineering;
Department of Mechanical Engineering;
Department of Materials Science and Engineering;
Center for Bio-Integrated Electronics,
Northwestern University,
Evanston, IL 60208

1Present address: Department of Aerospace Engineering, The Pennsylvania State University, University Park, PA 16802

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 9, 2018; final manuscript received August 5, 2018; published online August 31, 2018. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 85(12), 121002 (Aug 31, 2018) (10 pages) Paper No: JAM-18-1393; doi: 10.1115/1.4041163 History: Received July 09, 2018; Revised August 05, 2018

Vibrational microplatforms that exploit complex three-dimensional (3D) architectures assembled via the controlled compressive buckling technique represent promising candidates in 3D micro-electromechanical systems (MEMS), with a wide range of applications such as oscillators, actuators, energy harvesters, etc. However, the accuracy and efficiency of such 3D MEMS might be significantly reduced by the viscoelastic damping effect that arises from material viscosity. Therefore, a clear understanding and characterization of such effects are essential to progress in this area. Here, we present a study on the viscoelastic damping effect in complex 3D structures via an analytical model and finite element analysis (FEA). By adopting the Kelvin–Voigt model to characterize the material viscoelasticity, an analytical solution is derived for the vibration of a buckled ribbon. This solution then yields a scaling law for the half-band width or the quality factor of vibration that can be extended to other classes of complex 3D structures, as validated by FEA. The scaling law reveals the dependence of the half-band width on the geometries of 3D structures and the compressive strain. The results could serve as guidelines to design novel 3D vibrational microplatforms for applications in MEMS and other areas of technology.

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Banks, H. T. , and Inman, D. , 1991, “ On Damping Mechanisms in Beams,” ASME J. Appl. Mech., 58(3), pp. 716–723. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Illustration of (a) a straight ribbon attached to a prestrained substrate at selected bonding sites, (b) the compressive post-buckling induced by the contraction of the elastomer, (c) the external load, and (d) the first-order vibration mode. Two phases corresponding to the largest vibration amplitudes are shown, i.e., up line: phase 0 deg, down line: phase 180 deg.

Grahic Jump Location
Fig. 2

Finite element analysis validations of the analytical model for the first-order vibration mode: (a) transverse vibrational displacement as a function of position, (b) the nondimensional half-band width ξ̂ as a function of the compressive strain εcompre, and (c) a comparison of the nondimensional velocity responses of the buckled ribbon with and without the viscoelastic damping effect

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Fig. 3

The nondimensional half-band width of three 3D structures and their 2D precursors

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Fig. 4

Extension of the scaling law to representative 3D structures, with validations by FEA: (a) tent, (b) helix, and (c) table

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Fig. 5

Extension of the scaling law to 3D table structures with different central circle radii, with validations by FEA: (a) illustration of the precursor and geometries, (b)–(g) the nondimensional half-band width ξ̂ as a function of the compressive strain, for different normalized central circle radii (r/L = 0.07, 0.10, 0.125, 0.15, 0.175, and 0.50) of the 2D precursor, and (h) parameters α and β that characterize the scaling law of the nondimensional half-band width, as a function of r/L

Grahic Jump Location
Fig. 6

Extension of the scaling law to 3D helical structures with different top angles, with validations by FEA: (a) illustration of the precursor and geometries, (b)–(g) the nondimensional half-band width ξ̂ as a function of the compressive strain, for different top angles (θ = 0 deg, 20 deg, 120 deg, 150 deg, 170 deg, and 180 deg) of the 2D precursor, and (h) parameters α and β that characterize the scaling law of the nondimensional half-band width, as a function of θ

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