Vibration of circular plates with mixed edge conditions. Part III: Localized frequency curve veering phenomena

Main Article Content

Yos Sompornjaroensuk


This paper aims to investigate and examine the phenomenon of mode localization and frequency curve veering for vibratory circular plates with mixed edge conditions. An important characteristic of curve veering is that when two loci of the curves approach each other as system parameters vary, they often exactly cross (intersections) or abruptly diverse away (avoided crossings). The latter case is termed as curve veering. Thus, in the present paper, the carried out results reveal a significant effect on the occurrence of curve veering possibilities due to support length variations that can be detected by plotting the variation of frequency parameter against the angle provided the circumferential plate support by means of finite element method with discretized refinement model.

Article Details



Nair PS, Durvasula S. On quasi-dege-neracies in plate vibration problems. Int J Mech Sci. 1973; 15: 975-86.

Stephen NG. On veering of eigen-value loci. J Vib Acoust. 2009; 131: 054501.

Sompornjaroensuk Y, Chantarawichit P. Vibration of circular plates with mixed edge conditions. Part I: Review of research. UTK RESEARCH JOURNAL. 2020. (Accepted for publication)

Sompornjaroensuk Y. Vibration of cir-cular plates with mixed edge condi-tions. Part II: Numerical determination for higher frequencies. UTK RESEARCH JOURNAL. 2020. (Accepted for publication)

Leissa AW. On a curve veering aber-ration. J Appl Math Phys (ZAMP). 1974; 25: 99-111.

Claassen RW, Thorne CJ. Vibrations of thin rectangular isotropic plates. J Appl Mech. 1961; 28: 304-5.

Claassen RW, Thorne CJ. Vibrations of a rectangular cantilever plate. J Aero Sci. 1962; 29: 1300-5.

Claassen RW. Vibrations of skew can-tilever plates. AIAA Journal. 1963; 1: 1222.

Kuttler JR, Sigillito VG. On curve veering. J Sound Vib. 1981; 75: 585-8.

Perkins NC, Mote CD. Comments on curve veering in eigenvalue problems. J Sound Vib. 1986; 106: 451-63.

Pierre C. Mode localization and eigen-value loci veering phenomena in dis-ordered structures. J Sound Vib. 1988; 126: 485-502.

Pierre C, Plaut RH. Curve veering and mode localization in a buckling pro-blem. J Appl Math Phys (ZAMP). 1989; 40: 758-61.

Chen PT, Ginsberg JH. On the rela-tionship between veering of eigenva-lue loci and parameter sensitivity of eigenfunctions. J Vib Acoust.1992; 114: 141-8.

Chen PT, Ginsberg JH. Modal pro-perties and eigenvalue veering pheno-mena in the axisymmetric vibration of spheroidal shells. J Acoust Soc Am. 1992; 92: 1499-508.

Rim KH, Lee CW. Curve veering in outer-clamped annular plates subjected to nonuniform in-plane force. KSME Journal. 1993; 7: 70-5.

Shin C, Kim W, Chung J. Free in-plane vibration of an axially moving mem-brane. J Sound Vib. 2004; 272: 137-54.

Saito A, Castanier MP, Pierre C. Vibra-tion response of cracked cantilevered plates near natural frequency veering. Proceedings of the 49th AIAA/ASME /ASCE/AHS/ASC Structures, Structu-ral Dynamics, and Materials Confe-rence; 7-10 April 2008; Schaumburg, IL. 2008. AIAA 2008-1872.

Saito A, Castanier MP, Pierre C. Esti-mation and veering analysis of non-linear resonant frequencies of cracked plates. J Sound Vib. 2009; 326: 725-39.

du Bois JL, Adhikari S, Lieven NAJ. On the quantification of eigenvalue curve veering: A veering index. J Appl Mech. 2011; 78: 041007.

Huang T, Lu H, McFarland DM, et al. Natural frequency veering and mode localization caused by straight through-cracks in rectangular plates with elas-tic boundary conditions. Acta Mech. 2018; 229: 4017-31.

Bauer HF, Eidel W. Approximate Na-tural Frequencies of Circular Plates with Mixed Boundary Conditions. Forschungsbericht: Universität der Bundeswehr München; LRT-WE-9-FB-1, 2004.

Bauer HF, Eidel W. Determination of the lower natural frequencies of circu-lar plates with mixed boundary condi-tions. J Sound Vib. 2006; 292: 742-64.

Brouet F, Twiefel J, Wallaschek J. Frequency veering and mode dege-neration of a rectangular disc. Pro-ceedings in Applied Mathematics and Mechanics. 2015; 15: 175-6.

Sari M, Shaat M, Abdelkefi A. Fre-quency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal resi-duals. Compos Struct. 2017; 163: 280-92.

Zhang H, Yuan H, Yang W, Zhao T. Study on localization influences of frequency veering on vibration of mistuned bladed disk. Journal of Mechanical Science and Technology. 2017; 31: 5173-84.

Zinkovskii AP, Tokar IG. Influence of local surface damage on the natural frequencies of the higher modes of flexural vibration of cantilever rods. Strength Mater. 2018; 50: 557-64.

Shaat M. Mode localization pheno-menon of functionally graded nano-beams due to surface integrity. Int J Mech Mater Des. 2019; 15: 245-70.

ANSYS Inc. ANSYS Mechanical APDL Theory Reference, Release 14.5; 2012.

ANSYS Inc. ANSYS Mechanical APDL Element Reference, Release 14.5; 2012.

Leissa AW. Vibration of Plates. Re-printed ed. Washington, DC: Acousti-cal Society of America; 1993.