Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness
Email:
phamminhphuc@utc.edu.vn
Từ khóa:
rectangle plate, varying thickness, crack, vibration, finite element method, HSDT, phase field theory
Tóm tắt
The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditionsTài liệu tham khảo
[1]. T. Sakiyama, M. Huang, Free vibration analysis of retangular plates with variable thickness, Journal of Sound and Vibration, 216 (1998) 268–286. https://doi.org/10.1006/jsvi.1998.1732
[2]. P. Malekzadeh, G. Karami, Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates, Engineering Structures, 27 (2005) 1563-1574. https://doi.org/10.1016/j.engstruct.2005.03.017
[3]. I. Shufrin , M. Eisenberger, Vibration of shear deformable plates with variable thickness – first-order and higher-order analyses, J Sound Vib, 290 (2006) 465-489. https://doi.org/10.1016/j.jsv.2005.04.003
[4]. U.S. Gupta, R. Lal, Seema Sharma, Vibration of non-homogeneous circular Mindlin plates with variable thickness, Journal of Sound and Vibration, 302 (2007) 1–17. https://doi.org/10.1016/j.jsv.2006.07.005
[5]. E. Efraim, M. Eisenberger, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration, 299 (2007) 720-738. https://doi.org/10.1016/j.jsv.2006.06.068
[6]. V. Tajeddini, A. Ohadi, M. Sadighi, Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation, International Journal of Mechanical Sciences, 53 (2011) 300-308. https://doi.org/10.1016/j.ijmecsci.2011.01.011
[7]. M. Bacciocchi, M. Eisenberger, N. Fantuzzi, F. Tornabene, E. Viola, Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method, Composite Structures, 156 (2016) 218-237. https://doi.org/10.1016/j.compstruct.2015.12.004
[8]. C.S. Huang, A.W. Leissa, C.W. Chan, Vibrations of rectangular plates with internal cracks or slits, International Journal of Mechanical Sciences, 53 (2011) 436-445. https://doi.org/10.1016/j.ijmecsci.2011.03.006
[9]. P.M. Pham, D.V.Thom, D.H. Duc, N.D. Duc, The stability of cracked rectangular plate with variable thickness using phase field method, Thin-Walled Structures, 129 (2018) 157-165. https://doi.org/10.1016/j.tws.2018.03.028
[10]. H.D. Duc, V.D. Thom, P.M. Pham, N.D. Duc, Validation simulation for free vibration and buckling of cracked Mindlin plates using phase-field method, Mech Adv Mater Struct, 26 (2018) 1018-1027. https://doi.org/10.1080/15376494.2018.1430262
[11]. P.M. Pham, 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, 175 (2019) 107086. https://doi.org/10.1016/j.compositesb.2019.107086
[12]. P. M. Pham, Anynasys free vibration of the functionally graded material cracked plates with varying thickness using the phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-131. (in Vietnamese) https://doi.org/10.25073/tcsj.70.2.35
[13]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[2]. P. Malekzadeh, G. Karami, Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates, Engineering Structures, 27 (2005) 1563-1574. https://doi.org/10.1016/j.engstruct.2005.03.017
[3]. I. Shufrin , M. Eisenberger, Vibration of shear deformable plates with variable thickness – first-order and higher-order analyses, J Sound Vib, 290 (2006) 465-489. https://doi.org/10.1016/j.jsv.2005.04.003
[4]. U.S. Gupta, R. Lal, Seema Sharma, Vibration of non-homogeneous circular Mindlin plates with variable thickness, Journal of Sound and Vibration, 302 (2007) 1–17. https://doi.org/10.1016/j.jsv.2006.07.005
[5]. E. Efraim, M. Eisenberger, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration, 299 (2007) 720-738. https://doi.org/10.1016/j.jsv.2006.06.068
[6]. V. Tajeddini, A. Ohadi, M. Sadighi, Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation, International Journal of Mechanical Sciences, 53 (2011) 300-308. https://doi.org/10.1016/j.ijmecsci.2011.01.011
[7]. M. Bacciocchi, M. Eisenberger, N. Fantuzzi, F. Tornabene, E. Viola, Vibration analysis of variable thickness plates and shells by the generalized differential quadrature method, Composite Structures, 156 (2016) 218-237. https://doi.org/10.1016/j.compstruct.2015.12.004
[8]. C.S. Huang, A.W. Leissa, C.W. Chan, Vibrations of rectangular plates with internal cracks or slits, International Journal of Mechanical Sciences, 53 (2011) 436-445. https://doi.org/10.1016/j.ijmecsci.2011.03.006
[9]. P.M. Pham, D.V.Thom, D.H. Duc, N.D. Duc, The stability of cracked rectangular plate with variable thickness using phase field method, Thin-Walled Structures, 129 (2018) 157-165. https://doi.org/10.1016/j.tws.2018.03.028
[10]. H.D. Duc, V.D. Thom, P.M. Pham, N.D. Duc, Validation simulation for free vibration and buckling of cracked Mindlin plates using phase-field method, Mech Adv Mater Struct, 26 (2018) 1018-1027. https://doi.org/10.1080/15376494.2018.1430262
[11]. P.M. Pham, 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, 175 (2019) 107086. https://doi.org/10.1016/j.compositesb.2019.107086
[12]. P. M. Pham, Anynasys free vibration of the functionally graded material cracked plates with varying thickness using the phase-field theory, Transport and Communications Science Journal, 70 (2019) 122-131. (in Vietnamese) https://doi.org/10.25073/tcsj.70.2.35
[13]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
Tải xuống
Chưa có dữ liệu thống kê
Nhận bài
21/07/2020
Nhận bài sửa
14/09/2020
Chấp nhận đăng
28/09/2020
Xuất bản
30/09/2020
Chuyên mục
Công trình khoa học
Kiểu trích dẫn
Pham Minh, P. (8800). Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness. Tạp Chí Khoa Học Giao Thông Vận Tải, 71(7), 853-867. https://doi.org/10.47869/tcsj.71.7.10
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