Browse > Article
http://dx.doi.org/10.7734/COSEIK.2014.27.2.63

Density-based Topology Design Optimization of Piezoelectric Crystal Resonators  

Ha, Youn Doh (Dept. of Naval Architecture, Kunsan National Univ.)
Byun, Taeuk (Faculty of Co-op, Hoseo Univ.)
Cho, Seonho (National Creative Research Initiatives(NCRI) Center for Isogeometric Optimal Design, Seoul National Univ.)
Publication Information
Journal of the Computational Structural Engineering Institute of Korea / v.27, no.2, 2014 , pp. 63-70 More about this Journal
Abstract
Design sensitivity analysis and topology design optimization for a piezoelectric crystal resonator are developed. The piezoelectric crystal resonator is deformed mechanically when subjected to electric charge on the electrodes, or vice versa. The Mindlin plate theory with higher-order interpolations along thickness direction is employed for analyzing the thickness-shear vibrations of the crystal resonator. Thin electrode plates are masked on the top and bottom layers of the crystal plate in order to enforce to vibrate it or detect electric signals. Although the electrode is very thin, its weight and shape could change the performance of the resonators. Thus, the design variables are the bulk material densities corresponding to the mass of masking electrode plates. An optimization problem is formulated to find the optimal topology of electrodes, maximizing the thickness-shear contribution of strain energy at the desired motion and restricting the allowable volume and area of masking plates. The necessary design gradients for the thickness-shear frequency(eigenvalue) and the corresponding mode shape(eigenvector) are computed very efficiently and accurately using the analytical design sensitivity analysis method using the eigenvector expansion concept. Through some demonstrative numerical examples, the design sensitivity analysis method is verified to be very efficient and accurate by comparing with the finite difference method. It is also observed that the optimal electrode design yields an improved mode shape and thickness-shear energy.
Keywords
piezoelectric material; crystal resonator; eigenvalue analysis; topology design optimization;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Bottom, V.E. (1982) Introduction to Quartz Crystal unit Design, Van Nostrand Reinhold Co., New Work.
2 Cady, W.G. (1946) Piezoelectricity, McGraw-Hill, New Work.
3 Lee, P.C.Y., Syngellakis, S., Hou, J.P. (1987) A Two-dimensional Theory for High-frequency Vibrations of Piezoelectric Crystal Plates with or Without Electrodes, Journal of Applied Physics, 61(4), pp.1249-1262.   DOI
4 Mindlin, R.D. (1963) High Frequency Vibrations of Plated, Crystal Plates, Progress in Applied Mechanics, Macmillan, New York, pp.73-84.
5 Mindlin, R.D. (1984) Frequencies of Piezoelectrically Forced Vibrations of Electroded, Doubly Rotated, Quarz Plates, International Journal of Solids and Structures, 20(2), pp.141-157.   DOI   ScienceOn
6 Nelson, R.B. (1986) Simplified Calculation of Eigenvector Derivative, AIAA Journal, 14(9), pp.823-832.
7 Tiersten, H.F. (1969) Linear Piezoelectic Plate Vibrations, Plenum Press, New York.
8 Wang, J., Yong, Y.K., Imai, T. (1999) Finite Element Analysis of Piezoelectric Vibrations of Quartz Plate Resonators with Higher-order Plate Theory, International Journal of Solids and Structures, 36, pp.2303-2319.   DOI   ScienceOn
9 Kim, M.-G., Kim, J.-H., Cho, S. (2010) Topology Design Optimization of Heat Conduction Problems using Adjoint Sensitivity Analysis Method, Computational Structural Engineering Institute of Korea, 23(6), pp.683-691.   과학기술학회마을