Mode-splitting and quasi-degeneracies in circular plate vibration problems: The example of free vibrations of the stator of a traveling wave ultrasonic motor

2012 ◽  
Vol 331 (26) ◽  
pp. 5788-5802 ◽  
Author(s):  
Ashwin Kumar ◽  
Charles M. Krousgrill
Keyword(s):  
Circular Plate ◽  
Traveling Wave ◽  
Ultrasonic Motor ◽  
Free Vibrations ◽  
Plate Vibration ◽  
Mode Splitting ◽  
Vibration Problems

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

Power Harvesting from the Vibration-Induced by the Piezoelectric Stator of Traveling Wave Rotary Ultrasonic Motor

2011 ◽  
Vol 317-319 ◽  
pp. 616-620 ◽  
Author(s):  
Guang Qing Wang ◽  
Zhong Wei Zhao
Keyword(s):  
Energy Conversion ◽  
Analytical Model ◽  
Traveling Wave ◽  
Mechanical Energy ◽  
Ultrasonic Motor ◽  
Maximum Output ◽  
Induced Voltage ◽  
Power Harvesting ◽  
Conversion Model ◽  
The Relationship

In this article, a novel electro-mechanical energy conversion model of power harvesting from the vibration-induced the piezoelectric stator of the traveling wave rotary ultrasonic motor was proposed. Based on the curvature basis approach, the relationship between the deduced voltage and the mechanical stain induced by piezoelectric polarization was formulated. In addition to the relationships between the maximum induced voltages at the resonance frequency, the conversion energy density and the dimensions of the piezoelectric stator were also derived. The analytical model shows that the vibration-induced voltage is proportional to the exciting electrical voltage magnitude and square of height of the piezoelectric ceramic (PZT) but is inversely proportional to the permittivity of PZT and the damping coefficient of the stator. Some simulations and experimental results demonstrate that the maximum output voltage coincides with the energy conversion analytical model.

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