Research Papers: Design Automation

Architectural Synthesis and Analysis of Dual-Cellular Fluidic Flexible Matrix Composites for Multifunctional Metastructures

[+] Author and Article Information
Suyi Li

Department of Mechanical Engineering,
University of Michigan,
2271 G. G. Brown Laboratory,
2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: wilsonli@umich.edu

K. W. Wang

Stephen P. Timoshenko Collegiate
ASME Fellow
Department of Mechanical Engineering,
University of Michigan,
2236 G. G. Brown Laboratory,
2350 Hayward Street,
Ann Arbor, MI 48109
e-mail: kwwang@umich.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 24, 2014; final manuscript received December 13, 2014; published online February 16, 2015. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 137(4), 041402 (Apr 01, 2015) (11 pages) Paper No: MD-14-1253; doi: 10.1115/1.4029516 History: Received April 24, 2014; Revised December 13, 2014; Online February 16, 2015

Recently, a cellular structure concept based on fluidic flexible matrix composites (F2MCs) was investigated for its potential of concurrently achieving multiple adaptive functions. Such structure consists of two fluidically connected F2MC cells, and it has been proven capable of dynamic actuation with enhanced authority, variable stiffness, and vibration absorption. The purpose of the research presented in this paper is to develop comprehensive design and synthesis tools to exploit the rich functionality and versatility of this F2MC based system. To achieve this goal, two progressive research topics are addressed: The first is to survey unique architectures based on rigorous mathematical principles. Four generic types of architectures are identified for the dual-cellular structure based on fluidic and mechanical constraints between the two cells. The system governing equations of motion are derived and experimentally tested for these architectures, and it is found that the overall structural dynamics are related to the F2MC cell stiffness, internal pressure difference, and static flow volume between the two cells according to the architectural layout. The second research topic is to derive a comprehensive synthesis procedure to assign the F2MC designs so that the cellular structure can simultaneously reach a set of different performance targets. Synthesis case studies demonstrate the range of performance of the F2MC based cellular structure with respect to different architectures. The outcome of this investigation could provide valuable insights and design methodologies to foster the adoption of F2MC to advance the state of art of a variety of engineering applications. It also lays the foundation for a large-scale “metastructure,” where many pairs of fluidically connected F2MC can be employed as modules to achieve synergetic global performance.

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Fig. 6

Admissible constraints onto each type of system variables

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Fig. 5

Performance parametric space Ω, reproduced from Ref. [20]

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Fig. 4

The free body diagram of a F2MC cell within the structure. Positive vk corresponds to the net fluid flow direction as indicated by the arrow, and positive fk corresponds to a tension force.

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Fig. 3

The dynamic functions of the dual F2MC string structure. (a) Schematic diagram of the structure; (b) vibration absorption, the vertical axis is the ratio of end mass motion over input force; and (c) dynamic actuation with enhanced authority compared to a single cell, the vertical axis is the ratio of actuation stroke over pumping input.

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Fig. 2

The static functions of a single F2MC. (a) Neutral state, (b) active actuation by pumping, and (c) semipassive variable stiffness by opening and closing the end valves.

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Fig. 1

A schematic diagram of F2MC construction. There are three groups of important design variables: φ, ai/ao, and E1/E2.

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Fig. 7

Architectures of the dual-cellular structure. A combination of two constraints from Fig. 6 leads to a unique architecture.

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Fig. 8

Two different designs that belong to (BD) type of architrave. (a) An antagonist pair connected to a rotational inertia and (b) an adaptive lattice unit.

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Fig. 11

Test results for (BD) architecture. The end mass are (i) 0.97 × 103, (ii) 1.40 × 103, and (iii) 1.83 × 103. The Port inertance are (a) 2.59 × 103, (b) 3.46 × 103, and (c) 5.85 × 103. The bulk modulus is estimated to be 32 MPa (Cf = 0.42).

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Fig. 12

Test results for (BC) architecture. The end mass are (i) 390, (ii) 820, and (iii) 1250. The port inertance are (a) 1.08 × 103, (b) 1.41 × 103, and (c) 1.74 × 103. The bulk modulus is estimated to be 50 MPa (Cf = 0.27).

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Fig. 9

(AD) and (BD) linkage mechanism setup. (a) The computer aided design (CAD) model of the linkage design, (b)–(d) finished prototype. A closed valve (10) makes (AD) architecture; an open valve (10) makes (BD) architecture. Legend: (1) F2MC tube #1; (2) F2MC tube #2; (3) mount collar; (4) shafts; (5) acrylic linkage; (6) ball bearing; (7) end mass plates; (8) shaker; (9) external flow port; (10,11) end valves; and (12) screw rods for extra linkage rigidity.

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Fig. 10

Test results for (AD) architecture. The test results are the solid line and analytical predictions are the dashed line. Each plot is the result from different combinations of normalized end mass and flow port. The values of the end mass are (i) 0.97 × 103, (ii) 1.40 × 103, and (iii) 1.83 × 103. The port inertance values are (a) 3.46 × 103, (b) 8.79 × 103, and (c) 5.85 × 103. The bulk modulus is estimated to be 65 MPa (Cf = 0.21).

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Fig. 13

The flow chart of the comprehensive synthesis procedure. Note that steps 7 and 8 are skipped if the architecture is of (AC) or (AD) type.

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Fig. 14

A sample synthesis result for cell #1 of (BC) architecture

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Fig. 15

Combination of variable stiffness and actuation authority based on the same spectral data target as in Fig. 14. The Nd values for the four architectures: (AC) 862 (AD) 3369 (BC) 3013 (BD) 6910.

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Fig. 17

Illustration of extending the dual-cellular unit into a larger-scale metastructure. In this system, several pairs of fluidically connected, (AD) type of unit is assembled together into an active lattice.

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Fig. 16

Heat map summarizing the results of a performance survey. Note that the temperature scale of the first row is in logarithm scale.



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