Nonlinear Dynamics Analysis of a Laminated Printed Wiring Board

[+] Author and Article Information
Xiaoling He

Bell Labs, Lucent Technology, Orlando, FL 32811e-mail: xiaolingh@hotmail.com

Robert E. Fulton

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332e-mail: robert.fulton@me.gatech.edu

J. Electron. Packag 124(2), 77-84 (May 02, 2002) (8 pages) doi:10.1115/1.1457454 History: Received May 30, 2000; Online May 02, 2002
Copyright © 2002 by ASME
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He, X., 2000, A theoretical Framework for the Dynamic Analysis of a Printed Wiring Board Under Mechanical and Thermal Loading, Ph.D. thesis, Georgia Institute of Technology, Atlanta.


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Printed wiring board in isotropic laminate (a=154 mm, b=154 mm, h=1.53 mm)
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Response under constant load (ω11=1588.55 Hz,Q11=0.27 N/cm2, Q11=2.4 N/cm2)
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First mode linear resonance (ω11=1588.52 Hz,Q11=0.24 N/cm2, t=10−3 s, 0.06 s)
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Linear and nonlinear compariso in maximum deflection (ω=k*ω11, k=[1,10]Q11=0.24, 2.4, 12 N/cm2)
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Nonlinear harmonic resonance (ω=2.2ω11,Q11=2.4 N/cm2)
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Nonlinear subharmonic response (ω11=1.588 Hz,k=1.2, 0.36, 3.6, Q11=0.24 N/cm2)
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High mode nonlinear harmonic response (ω12=3,970.81 Hz, ω88=101,093.17 Hz, Q12=0.24 N/cm2)
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Stress σx distribution at the top of copper layer
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Stress σxy distribution at the top of copper layer
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Mode shapes of PWB with Wmn=3.3 mm (m=n=1 and m=n=8)
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Response with initial deflection (ω11=1588.55 Hz,x(0)=1 mm, x(0)=5 mm)
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Response with initial velocity (ω11=1588.55 Hz,v(0)=1 m/s, v(0)=20 m/s)
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Nonlinear harmonic response—load effect (ω=ω11, Q11=0.12, 0.24 N/cm2)
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Velocity-deflection for t<0.05 s,t<0.1 s in the fundamental mode harmonic response (ω=0.36*ω11=0.24 N/cm2)
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Velocity-deflection for t<0.045 s in first mode harmonic response (ω=1.2*ω11, ω=3.6*ω11, Q11=0.24 N/cm2)



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