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Research Papers

Modeling Impacts Between a Continuous System and a Rigid Obstacle Using Coefficient of Restitution

[+] Author and Article Information
Chandrika P. Vyasarayani1

Systems Design Engineeering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadacpvyasar@engmail.uwaterloo.ca

John McPhee

Systems Design Engineeering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadamcphee@real.uwaterloo.ca

Stephen Birkett

Systems Design Engineeering, University of Waterloo, Waterloo, ON, N2L 3G1, Canadasbirkett@real.uwaterloo.ca

1

Corresponding author.

J. Appl. Mech 77(2), 021008 (Dec 10, 2009) (7 pages) doi:10.1115/1.3173667 History: Received July 04, 2008; Revised April 13, 2009; Published December 10, 2009; Online December 10, 2009

In this work, we discuss the limitations of the existing collocation-based coefficient of restitution method for simulating impacts in continuous systems. We propose a new method for modeling the impact dynamics of continuous systems based on the unit impulse response. The developed method allows one to relate modal velocity initial conditions before and after impact without requiring the integration of the system equations of motion during impact. The proposed method has been used to model the impact of a pinned-pinned beam with a rigid obstacle. Numerical simulations are presented to illustrate the inability of the collocation-based coefficient of restitution method to predict an accurate and energy-consistent response. We also compare the results obtained by unit impulse-based coefficient of restitution method with a penalty approach.

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Figures

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Figure 1

Schematic of the physical system

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Figure 2

Illustration of collocation method

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Figure 3

Impact modeled using finite impulse

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Figure 4

Response at the impact location: (a) displacement and (b) magnified view at first impact

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Figure 5

Velocity at impact location

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Figure 6

Phase plot at impact location

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Figure 7

Energy of the mechanical system

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Figure 8

Pre- and post-impact velocity distributions

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Figure 9

Displacement at the impact location: (a) free vibration and (b) forced vibration

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Figure 10

Velocity at the impact location: (a) free vibration and (b) forced vibration

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Figure 11

Phase plot at the impact location: (a) free vibration and (b) forced vibration

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Figure 12

Energy in the mechanical system in free vibration

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Figure 13

Comparison of computational efficiency

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