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Research Papers

Modeling the Effects of the PCB Motion on the Response of Microstructures Under Mechanical Shock

[+] Author and Article Information
Abdallah H. Ramini, Ronald Miles

Department of Mechanical Engineering,  State University of New York at Binghamton, Binghamton, NY 13902

Mohammad I. Younis

Department of Mechanical Engineering,  State University of New York at Binghamton, Binghamton, NY 13902myounis@binghamton.edu

J. Vib. Acoust 133(6), 061019 (Nov 28, 2011) (9 pages) doi:10.1115/1.4005219 History: Received April 13, 2010; Revised September 18, 2011; Published November 28, 2011; Online November 28, 2011

Microelectromechanical systems (MEMS) are often used in portable electronic devices that are vulnerable to mechanical shock or impact, such as that induced due to accidental drops on the ground. This work presents a modeling and simulation effort to investigate the effect of the vibration of a printed circuit board (PCB) on the dynamics of MEMS microstructures when subjected to shock. Two models are investigated. In the first model, the PCB is modeled as an Euler-Bernoulli beam to which a lumped model of a MEMS device is attached. In the second model, a special case of a cantilever microbeam is studied and modeled as a distributed-parameter system, which is attached to the PCB. These lumped-distributed and distributed-distributed models are discretized into ordinary differential equations, using the Galerkin method, which are then integrated numerically over time to simulate the dynamic response. Results of the two models are compared against each other for the case of a cantilever microbeam and also compared to the predictions of a finite-element model using the software ANSYS. The influence of the higher order vibration modes of the PCB, the location of the MEMS device on the PCB, the electrostatic forces, damping, and shock pulse duration are presented. It is found that neglecting the effects of the higher order modes of the PCB and the location of the MEMS device can cause incorrect predictions of the response of the microstructure and may lead to failure of the device. It is noted also that, for some PCB designs, the response of the microstructure can be amplified significantly causing early dynamic pull-in and hence possibly failure of the device.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

A schematic of a half-sine pulse used to model an actual shock load

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Figure 2

A schematic diagram for the beam-lumped model

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Figure 3

A schematic diagram for the beam-beam model

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Figure 4

A comparison between the beam-beam model and the beam-lumped model for the case study of a cantilever beam when subjected to shock of amplitude = 200 g with Tshock  = 5 ms

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Figure 5

The response of a cantilever beam, placed at the center of the PCB (a = L/2), generated using the dynamic FE model (*), the beam-beam model (solid) for Tshock  = 0.1 ms and fMEMS  = 8.6 kHz and fn1  = 64 Hz

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Figure 6

The response of a cantilever beam, placed at the center of the PCB (a = L/2), generated using the dynamic FE model (*), the beam-beam model (solid) for Tshock  = 5 ms, fMEMS  = 8.6 kHz, and fn1  = 64 Hz

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Figure 7

(a) The response of the microbeam with PCB under electrostatic load only with VDC  = 1.0 V. (b) The response of the microbeam with PCB under only shock load of amplitude 14 g and Tshock  = 5 ms. (c) The response of the microbeam without PCB under only shock load of amplitude 14 g and Tshock  = 5 ms. (d) The response of the microbeam without PCB under the combined effect of the electrostatic force and shock. In the figure, ζMEMS  = 0.1 and modal damping of the PCB = 0.001.

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Figure 8

The response of the combined shock and the electrostatic forces showing dynamic pull-in

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Figure 9

The pull-in voltage versus the shock amplitude when fMEMS  = 8.6 kHz and fn1  = 2.8 kHz

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Figure 10

Shock-response spectrum of the microbeam including the PCB effect when fMEMS  = 8.6 kHz and fn1  = 2.8 kHz under shock of amplitude 100 g

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Figure 11

(a) The microbeam response under VDC  = 1.04 V and shock pulse of amplitude 50 g and Tshock  = TMEMS without the PCB effect. (b) The microbeam response under VDC  = 1.04 V and shock pulse of amplitude 50 g and Tshock  = TMEMS with the PCB effect. The modal damping of the microbeam is assumed ζMEMS = 0.001.

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Figure 12

The pull-in voltage instability threshold versus the shock amplitude comparing the case when the microbeam is subjected to shock directly to the case when it is placed on a poor-designed PCB

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Figure 13

A shock response spectrum of the microbeam including the PCB effect when fMEMS  = fn1  = 8.6 kHz under shock amplitude 100 g

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Figure 14

The maximum displacement of the cantilever beam when subjected to shock amplitude 50 g with fMEMS fn1  =  8.8 kHz. The PCB’s natural frequencies are fn1  = 8.8 kHz, fn3  = 79 kHz, and fn5  = 219 kHz.

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Figure 15

The maximum displacement of the cantilever beam when subjected to shock of amplitude 150 g with fMEMS ≈ fn3 . The PCB’s natural frequencies are fn1  = 1 kHz, fn3  = 9 kHz, fn5  = 25.3 kHz, and fn7  = 50 kHz.

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Figure 16

The maximum displacement of the cantilever beam when subjected to shock amplitude 150 g with fMEMS  = fn5  =  8.6 kHz. The PCB’s natural frequencies are fn1  = 342 Hz, fn3  =  3 kHz, and fn5  = 8.6 kHz.

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Figure 17

The effect of ζ3 on the maximum displacement of the cantilever beam when subjected to shock of amplitude 50 g with fMEMS ≈ fn3 . The PCB’s natural frequencies are fn1  = 1 kHz, fn3  = 9 kHz, fn5  = 25.3 kHz, and fn7  = 50 kHz.

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