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Research Papers

A Double Degree Freedom Mass-Spring-Damper-Foam Collision Model for High Porosity Metallic Foams

[+] Author and Article Information
Binchao Li

 State Key Laboratory of Mechanical Structure Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, Chinalibinchaomail@gmail.com

Guiping Zhao

 State Key Laboratory of Mechanical Structure Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, Chinazhaogp@mail.xjtu.edu.cn

Tian Jian Lu1

 State Key Laboratory of Mechanical Structure Strength and Vibration, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, Chinatjlu@mail.xjtu.edu.cn

1

Corresponding author.

J. Appl. Mech 79(5), 051021 (Jul 02, 2012) (13 pages) doi:10.1115/1.4006451 History: Received July 07, 2011; Revised February 23, 2012; Posted March 26, 2012; Published July 02, 2012; Online July 02, 2012

A theoretical study on the vibration isolation and energy absorption capability of high porosity closed-cell aluminum foams subjected to impact loading is presented. A double degree of freedom (DDF) spring-damper-foam collision model (mimicking important equipment and/or personnel) is established to explore the physical mechanisms of shock attenuation when the system as a whole is dropped from a given height and collides with hard ground. For validation, the finite element method is employed to simulate directly the dynamic responses of the whole system. The effects of key system parameters including spring stiffness, damping ratio, mass ratio, initial impact velocity and foam thickness on the mass of the foam cushion and peak acceleration of the protected structure are quantified. The DDF model is subsequently employed to minimize the weight of the foam cushion against impact energy subjected to different design constraints; the corresponding optimal geometrical dimensions of the foam cushion are also obtained.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 4

Comparison between DDF model of High-case and FE simulation for (a) velocity attenuation of M1 and M2 , (b) impact acceleration of M2 and (c) energy dissipated separately via foam, damper and friction

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Figure 5

Energy absorption of the foam estimated by DDF model in both Low-case and High-case is plotted as a function of nominal strain

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Figure 6

Acceleration predicted by DDF model compared with that predicted by SDF foam protection model (Eq. 19)

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Figure 7

Comparison between DDF model and SDF mass-spring-damper model: (a) impact attenuation of M2 ; (b) energy absorbed by damper

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Figure 8

Peak acceleration of inner object plotted as a function of foam mass ratio m2 for selected values of (a) spring stiffness (ζ=0.2, α=15), (b) damping ratio (ωn/ωn0=1, α=15), and (c) mass ratio between M1 and M2 (ωn/ωn0=1, ζ=0.2)

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Figure 9

Peak acceleration of inner object plotted as a function of foam mass ratio for selected values of (a) initial velocity (Hf = 75 mm) and (b) foam thickness (Vinitial = 4.5 m/s)

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Figure 10

Minimum weight of foam cushion plotted as a function of impact energy influenced by both the allowable acceleration and critical stress

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Figure 11

Optimal thickness of foam cushion plotted as a function of impact energy for selected constraint conditions

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Figure 12

Foam cylinder of unit area with additional mass M impacting rigid ground at initial velocity Vinitial

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Figure 13

Rate-independent, rigid, perfectly-plastic, locking idealization of quasi-static stress-strain curve of aluminum foam

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Figure 14

Allowable impact velocity Vinitial max and inertia effects coefficient κmax plotted as functions of mass ratio

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Figure 2

Finite element (FE) model of double degree freedom (DDF) spring-damper-foam system colliding with rigid ground at low velocity

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Figure 3

Comparison between DDF model of Low-case and FE simulation for (a) velocity attenuation of M1 and M2 , (b) impact acceleration of M2 , (c) foam stress and (d) energy dissipated separately via foam, damper and friction

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Figure 1

(a) Landing of a re-entry space capsule and (b) DDF spring-damper-foam collision model

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