Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-28T01:02:32.791Z Has data issue: false hasContentIssue false
  • English
  • Français

Vibration Analysis for Piezoceramic Circular Plates with V-Notches. Part 1: Theory

Published online by Cambridge University Press:  12 August 2014

C.-H. Huang  and
Y.-Y. Chen
C.-H. Huang*
Affiliation:
Department of Mechanical Engineering, Chien Hsin University of Science and Technology, Taoyuan County, Taiwan
Y.-Y. Chen
Affiliation:
Department of Mechanical Engineering, Chien Hsin University of Science and Technology, Taoyuan County, Taiwan
*
*chhuang@uch.edu.tw
Get access

Abstract

In this paper the transverse vibration characteristics of piezoceramic circular plates with V-notches are investigated theoretically through use of the Ritz's method incorporated with the defined equivalent constants. The Ritz's method is employed with two sets of admissible displacement functions, algebraic-trigonometric polynomials and corner functions, to guarantee convergence sufficiently and represent the stress singularity, respectively. Moreover, the equivalent constants derived by comparing the characteristic equations of transverse vibration between isotropic and piezoceramic disks are applied to suspend the electrical field consideration regarding the piezoelectricity. With the aid of theoretical analysis, the non-dimensional frequency parameters of transverse vibration modes for completely free V-notching circular plates are exhibited; in addition, the frequency variations depending on various notch angles and depths are explored. Numerical calculations using the finite element method (FEM) are performed and the results are compared with the theoretical analysis. It is shown that the resonant frequencies predicted by theoretical analysis and calculated by FEM are in good agreement.

Keywords

VibrationPiezoceramic plateEquivalent constants
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 6 , December 2014 , pp. 603 - 609
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Tiersten, H. F., Linear Piezoelectric Plate Vibrations, Plenum Press, New York, U.S.A. (1969).Google Scholar
2.Holland, R., “Contour Extensional Resonant Properties of Rectangular Piezoelectric Plates,” IEEE Transactions on Sonics and Ultrasonics, 15, pp. 97">–105 (1968).CrossRefGoogle Scholar
3.Eer Nisse, E. P., “Variational Method for Electroe-lastic Vibration Analysis,” IEEE Transactions on Sonics and Ultrasonics, 14, pp. 153–160 (1967).Google Scholar
4.Shaw, E. A. G., “On the Resonant Vibrations of Thick Barium Titanate Disks,” Journal of the Acoustical Society of America, 28, pp. 38–50 (1956).CrossRefGoogle Scholar
5.Kunkel, H. A., Locke, S. and Pikeroen, B., “Finite-element Analysis of Vibrational Modes in Piezoelectric Ceramics Disks,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 37, pp. 316–328 (1990).Google Scholar
6.Guo, N., Cawley, P. and Hitchings, D., “The Finite Element Analysis of the Vibration Characteristics of Piezoelectric Discs,” Journal of Sound and Vibration, 159, pp. 115–138 (1992).Google Scholar
7.Ivina, N. F., “Numerical Analysis of the Normal Modes of Circular Piezoelectric Plates of Finite Dimensions,” Soviet Physics Acoustics, 35, pp. 385–388 (1990).Google Scholar
8.Huang, C. H., “Resonant Vibration Investigations for Piezoceramic Disks and Annuli by Using the Equivalent Constant Method,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 52, pp. 1217–1228 (2005).CrossRefGoogle ScholarPubMed
9.Huang, C. H. and Chen, Y. Y., “Transverse Vibration Analysis for Piezoceramic Rectangular Plates using Ritz's Method with Equivalent Constants,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 53, pp. 265–273 (2006).Google Scholar
10.Leissa, A. W., McGee, O. G. and Huang, C. S., “Vibrations of Circular Plates Having V-Notches or Sharp Radial Cracks,” Journal of Sound and Vibration, 161, pp. 227–239 (1993).CrossRefGoogle Scholar
11.McGee, O. G., Leissa, A. W., Huang, C. S. and Kim, J. W., “Vibrations of Circular plates with Clamped V-Notches or Rigidly Constrained Radial Cracks,” Journal of Sound and Vibration, 181, pp. 185–201 (1995).CrossRefGoogle Scholar
12.McGee, O. G, Leissa, A. W., Kim, J. W. and Kim, Y. S., “Vibration of Plates with Constrained V-Notches or Cracks,” Journal of Engineering Mechanics, 129, pp. 812–822 (2003).Google Scholar
13.Williams, M. L., “Surface Stress Singularities resulting form Various Boundary Conditions in Angular Plates under Bending,” Proceeding of the First U.S. National Congress of Applied Mechanics, U.S.A., pp. 325–329 (1952).Google Scholar
14.ABAQUS User's Manual, ver. 6.3, Pawtucket RI: Hibbit, Karlsson, and Sorensen, Inc., U.S.A. (2002).Google Scholar