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RESEARCH PAPERS

# Three-Dimensional Modeling and Simulation of a Falling Electronic Device

[+] Author and Article Information
Hua Shan

Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019hshan@uta.edu

Jianzhong Su

Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019su@uta.edu

Jiansen Zhu

Nokia Research Center, 6000 Connection Drive, Irving, TX 75039jiansen.zhu@nokia.com

Leon Xu

Nokia Research Center, 6000 Connection Drive, Irving, TX 75039leon.xu@nokia.com

J. Comput. Nonlinear Dynam 2(1), 22-31 (Aug 04, 2006) (10 pages) doi:10.1115/1.2389039 History: Received August 02, 2005; Revised August 04, 2006

## Abstract

This article focuses on a realistic mathematical model for multiple impacts of a rigid body to a viscoelastic ground and its comparison to theoretic results. The methodology is used to study impact on an electronic device. When an electronic device drops to the floor at an uneven level, the rapid successions of impact sequence are important for their shock response to internal structure of the devices. A three-dimensional, continuous contact, computational impact model has been developed to simulate a sequence of multiple impacts of a falling rigid body with the ground. The model simulates the impact procedure explicitly and thus is capable of providing detailed information regarding impact load, impact contact surface, and the status of the body during the impact. For the purposes of model verification, we demonstrate the numerical simulation of a falling rod problem, in which the numerical results are in good agreement with the analytic solutions based on discrete contact dynamics impact models. It is indicated by the numerical experiments that simultaneous impacts occurred to multiple locations of the body and that subsequent impacts might be larger than initial ones due to different angles of impact. The differential equation-based computational model is shown to be realistic and efficient in simulating impact sequence and laid a foundation for detailed finite element analysis of the interior impact response of an electronic device.

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## Figures

Figure 1

Rigid body and coordinate systems

Figure 2

Distributed viscoelastic foundation

Figure 3

Impact contact region for a triangular surface element

Figure 4

Impact contact region for a quadrilateral surface element

Figure 5

Falling rod colliding with massive horizontal surface

Figure 6

Meshes at the surface of the falling rod.

Figure 7

Comparisons between simulation and analytical results of Brach (4) and Wang and Mason (8) for the first collision of the rigid rod with ground. Mass m=1, length L=1, radius rd=0.01, initial angular velocity ω=0, pre-impact normal velocity vn=−1, ground stiffness kG=1011, ground damping coefficient cG=0, no friction. (a) Post-impact normal velocity of center of mass as a function of the initial angle; (b) post-impact angular velocity as a function of the initial angle; (c) normal impact impulse as a function of the initial angle; (d) energy loss as a function of the initial angle.

Figure 8

Comparisons between simulation and analytical results of Brach (4) and Wang and Mason (8) for the first impact of the rigid rod in the second test case. Mass m=1, length L=1, radius rd=0.01, initial impact contact θ=45°, initial angular velocity ω=0, pre-impact normal velocity vn=−1, ground stiffness kG=1011, ground damping coefficient cG=0. (a) Post-impact tangential velocity at center of mass as a function of impulse ratio; (b) post-impact angular velocity as a function of impulse ratio; (c) normal impact impulse as a function of impulse ratio; (d) energy loss as a function of impulse ratio.

Figure 9

Numerical results of the continuous contact computational impact model showing the normal impact force and relative tangential velocity as functions of time during the first impact of the rigid rod with the ground. All parameters are the same as in Fig. 8. The tangential/normal impulse ratio μi=0.1, 0.3, 0.5, and 0.6–1.0.

Figure 10

Dropping the cell phone

Figure 11

Simplified cell phone model

Figure 12

Numerical results for multiple collisions of the model cell phone with the ground. Initial contact angle θ=10deg, initial angular velocity ω=0, initial elevation of center of mass zc∣t=0=1, ground stiffness kG=108, ground damping coefficient cG=107, static friction coefficient μs=0.075, and sliding friction coefficient μk=0.075. (a) Normal impact contact force as a function of time; (b) total energy, kinetic energy and potential energy as a function of time.

Figure 13

Numerical results for multiple collisions of the model cell phone with the ground. Initial contact angle θ=2deg, initial angular velocity ω=0, initial elevation of center of mass zc∣t=0=1, ground stiffness kG=108, ground damping coefficient cG=107, friction coefficient μk=0.075. (a) Normal impact contact force as a function of time; (b) total energy, kinetic energy, and potential energy as a function of time.

Figure 14

Views of multiple collisions of the model cell phone with the ground. Initial drop Euler angle: ϕ0=45deg, θ0=20deg, ψ0=45deg. Initial angular velocity ω=0, initial elevation of center of mass zc∣t=0=1, ground stiffness kG=108, ground damping coefficient cG=2×107, static friction coefficient μs=0.075, and sliding friction coefficient μk=0.075.

Figure 15

Numerical results for multiple collisions of the model cell phone with the ground. Initial drop Euler angle: ϕ0=45°, θ0=20°, ψ0=45°. Initial angular velocity ω=0, initial elevation of center of mass zc∣t=0=1, ground stiffness kG=108, ground damping coefficient cG=2×107, friction coefficient μk=0.075. (a) Normal impact contact force as a function of time; (b) total energy, kinetic energy and potential energy as a function of time.

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