Circumferential Ridge Wave Propagation in Piezoelectric Tubes
碩士 === 國立交通大學 === 機械工程系所 === 95 === Flexural ridge wave propagation around a circular cylindrical tube has no exact solution up to the present. It is used to be solved numerically or using an empirical formula. This thesis investigates the dispersive properties of ridge waves traveling circumferenti...
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| Format: | Others |
| Language: | zh-TW |
| Published: |
2007
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| Online Access: | http://ndltd.ncl.edu.tw/handle/25569130026543325793 |
| Summary: | 碩士 === 國立交通大學 === 機械工程系所 === 95 === Flexural ridge wave propagation around a circular cylindrical tube has no exact solution up to the present. It is used to be solved numerically or using an empirical formula. This thesis investigates the dispersive properties of ridge waves traveling circumferentially around the piezoelectric tubes and their resonant modes. Based on separation of variables, the displacements of ridge wave are represented as the product of a cross-sectional coordinate depending function and the propagator along the circumference of tube. The dispersion equation of ridge waves is formulated by using Hamilton’s principle and so-called bi-dimensional finite element method. Dispersion curves of traveling waves and resonant frequencies corresponding to standing waves are solved numerically. Several applications are illustrated such as optimal design for ultrasonic motors and modal separation of structure among adjacent resonant frequencies.
The impedance curves of a free-free piezoelectric tube are measured by a network analyzer. The measured resonant frequencies are compared with the predicted dispersion curves of ridge waves. Validity of the present numerical approach has been verified. Geometric parameters and elastic constants of the piezoelectric tube are determined through an inverse scheme based on the measured resonant frequencies by using simplex method. A good accuracy in inversion for elastic constants can be strategically achieved by determining the geometric parameters first. Then it is followed by seeking the best likelihood of elastic constants. The number of local minima during inversion can be reduced if more measured resonant frequencies of higher order axial modes are included in the objective function.
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