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Research Papers

Analytical Solution for Electronic Assemblies Under Vibration

[+] Author and Article Information
Mohammad A. Gharaibeh

Mechanical Engineering Department,
Thomas J. Watson School of Engineering and Applied Sciences,
Binghamton University,
State University of New York,
4400 Vestal Parkway East,
Binghamton, NY 13902-6000
e-mail: mgharai1@binghamton.edu

Quang T. Su

Mechanical Engineering Department,
Thomas J. Watson School of Engineering and Applied Sciences,
Binghamton University,
State University of New York,
4400 Vestal Parkway East,
Binghamton, NY 13902-6000
e-mail: qsu@binghamton.edu

James M. Pitarresi

Mechanical Engineering Department,
Thomas J. Watson School of Engineering and Applied Sciences,
Binghamton University,
State University of New York,
4400 Vestal Parkway East,
Binghamton, NY 13902-6000
e-mail: jmp@binghamton.edu

1Corresponding author.

Contributed by the Electronic and Photonic Packaging Division of ASME for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received October 11, 2015; final manuscript received December 30, 2015; published online March 10, 2016. Assoc. Editor: Eric Wong.

J. Electron. Packag 138(1), 011003 (Mar 10, 2016) (10 pages) Paper No: EP-15-1113; doi: 10.1115/1.4032497 History: Received October 11, 2015; Revised December 30, 2015

An analytical solution using Ritz method for the electronic assembly vibration problem has been presented in detail. In this solution, a special treatment for plate-mounted-on-standoffs boundary conditions scheme was required, and hence described. Also, a simple equation for estimating ball grid array (BGA) solder joint axial stiffness was developed. The results of the analytical solution were validated with modal analysis measurements and finite element (FE) models data in terms of natural frequencies and mode shapes. Then, the analytical solution was used to estimate the most critical solder joint deformations and stresses. Finally, the so developed solution provided an effective tool to examine the effect of several geometric and material configurations of electronic package structure on the fatigue performance of electronic products under mechanical vibration loadings.

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References

Figures

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Fig. 1

Test vehicle description

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Fig. 2

Modal analysis experiment

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Fig. 3

FE model: (a) assembly and (b) solder joint mesh

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Fig. 4

Two parallel plate configuration

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Fig. 5

SDOF system: (a) conservative and (b) nonconservative

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Fig. 6

A comparison between (a) FEA and (b) least square fit mode shapes

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Fig. 7

Comparison between FEA and least square fit mode shapes across the PCB diagonal line

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Fig. 8

BGA solder joint configuration

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Fig. 9

Effect of (a) solder ball width and (b) standoff height on BGA solder axial stiffness

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Fig. 10

Assembly's first mode shapes from (a) experiment, (b) FEA model, and (c) analytical solution

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Fig. 11

Outermost solder joint axial deflection response

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Fig. 12

BGA configuration showing the smallest area in the solder

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Fig. 13

Effect of PCB stiffness: (a) elastic modulus E1 and (b) thickness h1 on solder nominal stresses

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Fig. 14

Effect of solder ball (a) diameter and (b) height on solder nominal stresses

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