Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation
Abstract
:1. Introduction
2. Equations of Motion of Hemispherical Resonator with First–Third Harmonics of Mass Imperfection
2.1. Basic Structure of HRG
2.2. Establishment of Coordinate Systems of Hemispherical Resonator
2.3. Deformation Energy of Hemispherical Resonator
2.4. Second-Order Vibration Mode Function
2.5. Kinetic Energy of Hemispherical Resonator
2.6. Equations of Motion of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection
3. Effect of Linear Vibration on Standing Wave of Imperfect Hemispherical Resonator
3.1. Effect of Vertical Linear Vibration on Standing Wave of Imperfect Hemispherical Resonator
3.2. Effect of Horizonal Linear Vibration on Standing Wave of Imperfect Hemispherical Resonator
4. Identification of Location of First–Third Harmonics of Mass Imperfection by Linear Vibration
4.1. Identification for Location of the Second Harmonic of Mass Imperfection by Vertical Vibration
4.2. Calibration for Locations of the First and Third Harmonics of Mass Imperfection by Horizontal Vibration
5. Numerical Simulation Results
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol | Name | Value | Symbol | Name | Value |
---|---|---|---|---|---|
ρ0 | Average density | 2500 kg/m3 | l | Length of supporting column | 60 mm |
E | Young’s modulus | 76.7 GPa | r1 | Radius of supporting column | 6 mm |
μ | Poisson’s ratio | 0.17 | R | Radius of mid-surface | 25 mm |
Qf | Quality factor | 106 | R3 | Inner corner radius | 3 mm |
h | Thickness | 1 mm | R4 | Outer corner radius | 3 mm |
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Huo, Y.; Ren, S.; Wei, Z.; Yi, G. Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation. Sensors 2020, 20, 5454. https://doi.org/10.3390/s20195454
Huo Y, Ren S, Wei Z, Yi G. Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation. Sensors. 2020; 20(19):5454. https://doi.org/10.3390/s20195454
Chicago/Turabian StyleHuo, Yan, Shunqing Ren, Zhennan Wei, and Guoxing Yi. 2020. "Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation" Sensors 20, no. 19: 5454. https://doi.org/10.3390/s20195454
APA StyleHuo, Y., Ren, S., Wei, Z., & Yi, G. (2020). Standing Wave Binding of Hemispherical Resonator Containing First–Third Harmonics of Mass Imperfection under Linear Vibration Excitation. Sensors, 20(19), 5454. https://doi.org/10.3390/s20195454