Out-of-plane motion detection in encapsulated electrostatic MEMS gyroscopes: Principal parametric resonance

A great deal of study has been done on the dynamics of straight pipes conveying fluid. Relatively less effort has been directed towards the examination of the dynamics of curved pipes. In this paper, out-of-plane vibrations of a curved pipe due to the pulsating fluid flow are examined. The pipe is hanging horizontally and is supported at both ends. The main purpose of this paper is to investigate the nonlinear interaction between the in-plane and the out-of-plane vibrations analytically and experimentally. First, from the physical discussion of the equation for the spatial motion, the parametric excitation of the out-of-plane vibration and the forced excitation of the in-plane vibration most likely occur by the presence of pulsating fluid flow. Second, the complex amplitude equation of the out-of-plane pipe vibration in the case of the principal parametric resonance, is derived. The out-of-plane vibration is excited by the pulsating fluid flow and the nonlinear interaction between in-plane and out-of-plane vibrations. From the nonlinear analysis, it was clarified that the nonlinear interaction between in-plane and out-of-plane vibrations greatly affects the out-of-plane vibration. Third, the experiments were conducted with a silicon rubber pipe. The deflections of the pipe were measured with increasing the frequency of the pulsating flow gradually. In order to observe the principal parametric resonance, the frequency of the pulsating flow was determined as near twice the natural frequency of the out-of-plane vibration for the first mode. We confirm that the in-plane vibration affects the out-of-plane vibration, qualitatively.

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Ultrasound Sub-pixel Motion-tracking Method with Out-of-plane Motion Detection for Precise Vascular Imaging

Ultrasound in Medicine & Biology ◽

10.1016/j.ultrasmedbio.2019.11.005 ◽

2020 ◽

Vol 46 (3) ◽

pp. 782-795 ◽

Cited By ~ 1

Author(s):

Hideki Yoshikawa ◽

Taku Yamamoto ◽

Tomohiko Tanaka ◽

Ken-ichi Kawabata ◽

Shin Yoshizawa ◽

...

Keyword(s):

Motion Detection ◽

Motion Tracking ◽

Plane Motion ◽

Vascular Imaging ◽

Tracking Method ◽

Out Of Plane

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Design and Performance of MEMS Multifunction Optical Device Using a Combined In-Plane and Out-of-Plane Motion of Dual-Slope Mirror

Journal of Lightwave Technology ◽

10.1109/jlt.2010.2084290 ◽

2010 ◽

Cited By ~ 1

Author(s):

Q. H. Chen ◽

W. G. Wu ◽

Z. Q. Wang ◽

G. Z. Yan ◽

Y. L. Hao

Keyword(s):

Plane Motion ◽

Optical Device ◽

Out Of Plane ◽

And Performance

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An electrostatic MEMS spring actuator with large stroke and out-of-plane actuation

Journal of Micromechanics and Microengineering ◽

10.1088/0960-1317/21/11/115029 ◽

2011 ◽

Vol 21 (11) ◽

pp. 115029 ◽

Cited By ~ 13

Author(s):

Fangrong Hu ◽

Weiming Wang ◽

Jun Yao

Keyword(s):

Electrostatic Mems ◽

Out Of Plane

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Out-of-Plane Motion Effects in Microscopic Particle Image Velocimetry

Journal of Fluids Engineering ◽

10.1115/1.1598989 ◽

2003 ◽

Vol 125 (5) ◽

pp. 895-901 ◽

Cited By ~ 34

Author(s):

Michael G. Olsen ◽

Chris J. Bourdon

Keyword(s):

Particle Image Velocimetry ◽

Particle Image ◽

Laser Sheet ◽

Plane Motion ◽

Entire Volume ◽

Measurement Volume ◽

Microscopic Particle ◽

Image Velocimetry ◽

Out Of Plane ◽

Signal Peak

In microscopic particle image velocimetry (microPIV) experiments, the entire volume of a flowfield is illuminated, resulting in all of the particles in the field of view contributing to the image. Unlike in light-sheet PIV, where the depth of the measurement volume is simply the thickness of the laser sheet, in microPIV, the measurement volume depth is a function of the image forming optics of the microscope. In a flowfield with out-of-plane motion, the measurement volume (called the depth of correlation) is also a function of the magnitude of the out-of-plane motion within the measurement volume. Equations are presented describing the depth of correlation and its dependence on out-of-plane motion. The consequences of this dependence and suggestions for limiting its significance are also presented. Another result of the out-of-plane motion is that the height of the PIV signal peak in the correlation plane will decrease. Because the height of the noise peaks will not be affected by the out-of-plane motion, this could lead to erroneous velocity measurements. An equation is introduced that describes the effect of the out-of-plane motion on the signal peak height, and its implications are discussed. Finally, the derived analytical equations are compared to results calculated using synthetic PIV images, and the agreement between the two is seen to be excellent.

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