The Effect of Cracks on the Free Vibration of a Plate with Parabolic Thickness
Received: 7 April 2023 | Revised: 29 April 2023 and 13 May 2023 | Accepted: 17 May 2023 | Online: 6 June 2023
Corresponding author: Xuan Tung Nguyen
This paper uses first-order shear deformation theory and the finite element method to analyze the vibrations of rectangular plates with one or more cracks. The study investigated the influence of cracks (length, angle of inclination), the number of cracks, and the ratio of plate thickness to the natural vibration frequency of the plate, using phase field simulation. Plate thickness varies nonlinearly with the parabolic function. The results of the proposed method were compared with reputable studies to verify its reliability. In addition, some pictures of the characteristic vibration patterns of the plate with varying thickness are presented when cracks appear.
Keywords:cracked plate, free vibration, variable thickness phase field, variable thickness
K. Akiyama and M. Kuroda, "Fundamental Frequencies of Rectangular Plates with Linearly Varying Thickness," Journal of Sound and Vibration, vol. 205, no. 3, pp. 380–384, Aug. 1997.
Y. Xiang and C. M. Wang, "Exact Buckling and Vibration Solutions for Stepped Rectangular Plates," Journal of Sound and Vibration, vol. 250, no. 3, pp. 503–517, Feb. 2002.
I. Shufrin and M. Eisenberger, "Vibration of shear deformable plates with variable thickness — first-order and higher-order analyses," Journal of Sound and Vibration, vol. 290, no. 1, pp. 465–489, Feb. 2006.
M. Saeidifar, S. N. Sadeghi, and M. R. Saviz, "Analytical solution for the buckling of rectangular plates under uni-axial compression with variable thickness and elasticity modulus in the y-direction," Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 224, no. 1, pp. 33–41, Jan. 2010.
H. T. Thai and S.-E. Kim, "Levy-type solution for free vibration analysis of orthotropic plates based on two variable refined plate theory," Applied Mathematical Modelling, vol. 36, no. 8, pp. 3870–3882, Aug. 2012.
G. Fu, Y. Tuo, B. Sun, C. Shi, and J. Su, "Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution," Engineering Computations, vol. 39, no. 7, pp. 2689–2704, Jan. 2022.
T. D. Hien, N. D. Hung, N. T. Hiep, G. V. Tan, and N. V. Thuan, "Finite Element Analysis of a Continuous Sandwich Beam resting on Elastic Support and Subjected to Two Degree of Freedom Sprung Vehicles," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10310–10315, Apr. 2023.
H. T. Duy, N. D. Diem, G. V. Tan, V. V. Hiep, and N. V. Thuan, "Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9985–9990, Feb. 2023.
D. T. Thuy, L. N. Ngoc, D. N. Tien, and H. V. Thanh, "An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9926–9931, Feb. 2023.
P. P. Minh and N. D. Duc, "The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory," Composites Part B: Engineering, vol. 175, Art. no. 107086, Oct. 2019.
P. P. Minh and N. D. Duc, "The effect of cracks and thermal environment on free vibration of FGM plates," Thin-Walled Structures, vol. 159, Feb. 2021, Art. no. 107291.
P. P. Minh, D. T. Manh, and N. D. Duc, "Free vibration of cracked FGM plates with variable thickness resting on elastic foundations," Thin-Walled Structures, vol. 161, Apr. 2021, Art. no. 107425.
N. D. Duc and P. P. Minh, "Free vibration analysis of cracked FG CNTRC plates using phase field theory," Aerospace Science and Technology, vol. 112, May 2021, Art. no. 106654.
P. P. Minh, "Analysis free vibration of the functionally grade material cracked plates with varying thickness using the Phase-field theory," Transport and Communications Science Journal, vol. 70, no. 2, pp. 122–131, 2019.
P. M. Phuc, "Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness," Transport and Communications Science Journal, vol. 71, no. 7, pp. 853–867, 2020.
V. A. Le, M. P. Pham, and T. A. Bui, "Stability of Cracked Plates with Nonlinearly Variable Thickness Resting on Elastic Foundations," Journal of Materials and Engineering Structures, vol. 9, no. 4, pp. 641–651, Dec. 2022.
C. S. Huang, P. J. Yang, and M. J. Chang, "Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks," Composite Structures, vol. 94, no. 9, pp. 2764–2776, Sep. 2012.
How to Cite
MetricsAbstract Views: 342
PDF Downloads: 223
Copyright (c) 2023 Vinh An Le, Xuan Tung Nguyen
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.