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On Regularization in Design for Reliability for Nonlinear Planar Beam-Type Resonators

[+] Author and Article Information
Astitva Tripathi

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: astitva.tripathi@gmail.com

Anil K. Bajaj

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: bajaj@purdue.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 5, 2016; final manuscript received April 19, 2017; published online May 30, 2017. Assoc. Editor: Hanna Cho.

J. Vib. Acoust 139(4), 040907 (May 30, 2017) (11 pages) Paper No: VIB-16-1576; doi: 10.1115/1.4036624 History: Received December 05, 2016; Revised April 19, 2017

Robustness is a highly desirable quality in microelectromechanical systems (MEMS). Sensors and resonators operating on nonlinear dynamic principles such as internal resonances are no exception to this, and in addition, when nonlinear dynamic phenomena are used to enhance device sensitivity, their requirements for robustness may even be greater. This work discusses two aspects as they relate to the robustness and performance of nonlinear resonators. In the first aspect, different resonator designs are compared to find which among them have a better capacity to deliver reliable and reproducible performance in face of variations from the nominal design due to manufacturing process uncertainties/tolerances. The second aspect attempts to identify the inherent topological features that, if present in a resonator, enhance its robustness. Thus, the first part of this work is concerned with uncertainty analysis of several candidate nonlinear resonators operating under the principle of 1:2 internal resonance and obtained via a hierarchical optimization method introduced by the authors. The second part discusses specific changes to the computational design process that can be made so as to enhance the robustness and reliability of the candidate resonators.

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Figures

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Fig. 1

Some of the starting base structures for the optimization process (all dimensions are in meters)

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Fig. 2

Optimized candidate structures obtained for 1:2 internal resonance using the base structures from Fig. 1 (all dimensions are in meters)

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Fig. 3

Representative responses structures undergoing 1:2 internal resonances using Eq. (11) and Λi = 1, i = 1, 2, and 3 for (a) zero internal mistuning, σ1 = 0, and (b) some internal mistuning, σ1 = 2

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Fig. 4

Mode 1 amplitude excited via internal resonance for candidate structures shown in Fig. 2 when subjected to the same level of excitation. The solid line represents the stable branch, and the dotted line represents the unstable branch.

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Fig. 5

Response surface of the frequency ratio (ω2/ω1) for structure 1 shown in Fig. 2(a) with respect to lengths l2 and l3

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Fig. 6

Histograms of the frequency ratio (ω2/ω1) of the candidate structures shown in Fig. 2 obtained using the sampling of the MARS-based response surfaces. The y-axis represents the number of devices (out of the total samples) exhibiting the frequency ratio.

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Fig. 7

Mode 1 amplitude at zero external mistuning of the structures shown in Fig. 2 for nominal nonlinear parameters. The horizontal dotted (red) line indicates the failure criterion amplitude.

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Fig. 8

Mode 1 amplitude at σ2 = 0 for the structures shown in Fig. 2 for variation in internal mistuning σ1 and nonlinear coefficients Λis. The horizontal dotted (red) line indicates the failure criterion amplitude.

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Fig. 9

Mode 1 amplitude at σ2 = 0 for the candidate structures after regularization for variation in internal mistuning σ1 and nonlinear coefficients Λis. The horizontal dotted (red) line indicates the failure criterion amplitude.

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