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Research Papers

Shock Isolation in Finite-Length Dimer Chains With Linear, Cubic, and Hertzian Spring Interactions

[+] Author and Article Information
Eric Smith

School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: eric.smith@gatech.edu

Aldo Ferri

Fellow ASME
School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: al.ferri@me.gatech.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 6, 2014; final manuscript received September 30, 2015; published online November 4, 2015. Assoc. Editor: Paul C.-P. Chao.

J. Vib. Acoust 138(1), 011012 (Nov 04, 2015) (8 pages) Paper No: VIB-14-1071; doi: 10.1115/1.4031741 History: Received March 06, 2014; Revised September 30, 2015

This paper investigates the use of finite 1:1 dimer chains to mitigate the transmission of shock disturbances. Dimer chains consist of alternating light and heavy masses with interconnecting compliance. Changing the mass ratio has provided interesting results in previous research. In particular, in the case of Hertzian contacts with zero-preload, certain mass ratios have revealed minimal levels of transmitted force. This paper examines this phenomenon from the perspective of utilizing it in practical isolation systems. The zero-preload Hertzian contact case is contrasted with chains connected by linear or cubic springs. Through numerical simulations, tradeoffs are examined between displacement and transmitted force. Parametric studies are conducted to examine how isolation performance changes with mass ratio, stiffness, and different chain lengths.

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Figures

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Fig. 1

Dynamic isolation mount

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Fig. 5

Impulse response of a linear chain with N = 21, and ε = 0.7

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Fig. 4

Wall force versus first mass displacement; comparison of linear and Hertzian springs for various chain lengths, N, and mass ratios, ε

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Fig. 3

Twenty-one mass, Hertzian, cubic, and linear system comparison; various values of mass ratio, ε

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Fig. 2

Wall force (N) versus mass ratio; Hertzian, cubic, and linear springs, N = 21

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Fig. 16

Max wall force versus the maximum displacement of mass 1. Linear spring case. Various values of ε and chain length, N. Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N.

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Fig. 6

Impulse response and transfer functions for linear chain with N = 21 and ε = 0.7. (a) Displacement and (b) wall force. Same parameter values as Fig. 5, but over a longer time span.

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Fig. 7

Wall force versus mass ratio for an N = 9 mass system; comparison of simulation results with upper bound

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Fig. 8

Energy evolution for linear system with mass ratio ε = 1.0; N = 9, Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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Fig. 9

Energy evolution for linear system with mass ratio ε = 0.1; N = 9, Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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Fig. 10

Energy evolution for nonlinear system with mass ratio ε = 1.0; N = 9, Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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Fig. 11

Energy evolution for nonlinear system with mass ratio ε = 0.465; N = 9, Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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Fig. 14

Max wall force versus the maximum displacement of mass 1. Hertzian chain of 21 masses, ε = 0.5; linear chain of nine masses, ε = 0.3. Varying stiffness.

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Fig. 15

Max wall force versus the maximum displacement of mass 1. Hertzian contact with zero preload. Various values of ε and chain length, N. Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N.

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Fig. 12

Wall force versus mass ratio for varying Hertzian chains; Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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Fig. 13

First mass displacement versus mass ratio for varying Hertzian chains; Mtot = 21 kg, Δ1 = 5 mm for a static load of 1 N

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