Phân tích động lực học phi tuyến tấm FGM và vỏ trụ tròn sandwich FGM chứa đầy chất lỏng

BỘ GIÁO DỤC VÀ ĐÀO TẠO BỘ QUỐC PHÒNG VIỆN KHOA HỌC VÀ CÔNG NGHỆ QUÂN SƯ  LÊ XUÂN ĐOAN PHÂN TÍCH ĐỘNG LƯC HỌC PHI TUYẾN TẤM FGM VÀ VỎ TRỤ TRÒN SANDWICH-FGM CHỨA ĐẦY CHẤT LỎNG LUẬN ÁN TIẾN SỸ KỸ THUẬT Hà Nội – 2020 BỘ GIÁO DỤC VÀ ĐÀO TẠO BỘ QUỐC PHÒNG VIỆN KHOA HỌC VÀ CÔNG NGHỆ QUÂN SƯ  LÊ XUÂN ĐOAN PHÂN TÍCH ĐỘNG LƯC HỌC PHI TUYẾN TẤM FGM VÀ VỎ TRỤ TRÒN SANDWICH-FGM CHỨA ĐẦY CHẤT LỎNG Chuyên nghành: Cơ kỹ thuật Mã số: 9.52.01.01 LUẬN ÁN TIẾN SỸ KỸ THUẬT NGƯỜI HƯỚNG DẪN KHOA HỌC: PGS.TS Khúc văn Phú PGS.TS Nguyễn Minh Tuấn Hà Nội – 2020 i LỜI CAM ĐOAN Tôi cam đoan cơng trình nghiên cứu tơi Các kết nghiên cứu trình bày luận án trung thực chưa công bố nước quốc tế, tài liệu tham khảo trích dẫn đầy đủ, xác NGƯỜI CAM ĐOAN Lê Xuân Đoan ii LỜI CẢM ƠN Cơng trình nghiên cứu thực Viện Tên lửa, thuộc Viện Khoa học Công nghệ qn - Bộ Quốc phịng Tơi xin bày tỏ lòng biết ơn chân thành sâu sắc đến PGS TS Khúc Văn Phú PGS.TS Nguyễn Minh Tuấn tận tình hướng dẫn, giúp đỡ, động viên để tơi hồn thành luận án Tác giả xin chân thành cảm ơn Nhà khoa học thuộc ngành học có nhiều ý kiến đóng góp trình hồn thiện luận án Tơi xin trân trọng cảm ơn Đảng ủy, Ban Giám đốc Viện KH&CN quân sự, thủ trưởng Viện Tên lửa-Viện KH&CN quân sự, Phòng Đào tạo -Viện KH&CN quân thủ trưởng Phòng KTPN- Viện Tên lửa tạo điều kiện thuận lợi cho tơi q trình học tập nghiên cứu đơn vị Tôi xin trân trọng cảm ơn thủ trưởng Trường Sỹ quan Kỹ thuật quân sự-Đại học Trần Đại nghĩa, thủ trưởng Phòng Đào tạo-Trường Sỹ quan Kỹ thuật quân quan trường cổ vũ, tạo điều kiện thuận lợi để hồn thành luận án Tơi xin trân trọng cảm ơn GS TSKH Đào Huy Bích cho tơi nhiều ý kiến q báu q trình hồn thành luận án Cuối cùng, tơi xin bày tỏ lịng biết ơn sâu sắc đến gia đình, người thân, bạn bè đồng nghiệp luôn động viên, cổ vũ suốt q trình hồn thành luận án Tác giả luận án iii MỤC LỤC DANH MỤC CÁC KÍ HIỆU, CÁC CHỮ VIẾT TẮT .vi DANH MỤC CÁC BẢNG vii DANH MỤC CÁC HÌNH VẼ ix MỞ ĐẦU CHƯƠNG 1: TỔNG QUAN CÁC NGHIÊN CỨU VỀ ĐỘNG LƯC HỌC KẾT CẤU TẤM VÀ VỎ FGM 1.1 Khái quát chung vật liệu FGM 1.1.1 Khái niệm FGM 1.1.2 Tính chất FGM 1.1.3 Ứng dụng vật liệu FGM kỹ thuật đời sống 10 1.2 Tình hình nghiên cứu kết cấu vỏ FGM 12 1.2.1 Kết phân tích dao động kết cấu vỏ FGM 12 1.2.2 Kết phân tích ổn định kết cấu vỏ FGM 17 1.2.3 Các kết nghiên cứu kết cấu vỏ trụ FGM chứa chất lỏng .22 1.2.4 Các kết nghiên cứu kết cấu vỏ FGM có độ dày thay đổi 23 1.3 Nhận xét kết đề xuất hướng nghiên cứu .26 1.3.1 Nhận xét kết 26 1.3.2 Những vấn đề cần nghiên cứu 27 1.4 Những nội dung mà luận án cần tập trung giải 28 1.5 Kết luận chương 29 CHƯƠNG 2: PHÂN TÍCH ĐỘNG LƯC HỌC PHI TUYẾN TẤM FGM 30 2.1 Đặt vấn đề 30 2.2 Các phương trình .30 2.2.1 Trường chuyển vị 31 iv 2.2.2 Quan hệ chuyển vị biến dạng 31 2.2.3 Quan hệ ứng suất biến dạng: 32 2.2.4 Nội lực 33 2.2.5 Phương trình tương thích biến dạng 34 2.2.6 Hệ phương trình chuyển động 34 2.3 Phân tích đáp ứng động lực phi tuyến Sandwich-FGM có dạng lượn sóng chịu tác dụng tải trọng học 34 2.3.1 Mơ hình Sandwich FGM lượn sóng phương trình 35 2.3.2 Phương pháp giải 39 2.3.3 Một số kết phân tích dao động phi tuyến Sandwich FGM có dạng lượn sóng 42 2.4 Phân tích đáp ứng động lực phi tuyến FGM có độ dày thay đổi 48 2.4.1 Đặt vấn đề 48 2.4.2 Mơ hình có độ dày thay đổi phương trình 49 2.4.3 Phương pháp giải 56 2.4.4 Kết tính tốn 59 2.5 Kết luận chương 69 CHƯƠNG 3: PHÂN TÍCH DAO ĐỘNG PHI TUYẾN VỎ TRỤ TRÒN FGM CÓ GÂN GIA CƯỜNG CHỨA CHẤT LỎNG .71 3.1 Đặt vấn đề 71 3.2 Mơ hình vỏ trụ trịn Sandwich FGM có gân gia cường chứa chất lỏng 72 3.3 Các phương trình .73 3.4 Phương trình chuyển động vỏ trụ trịn FGM-Sandwich có gân gia cường chứa chất lỏng đàn hồi .78 3.5 Phương pháp giải 81 v 3.5.1 Phân tích dao động phi tuyến vỏ trụ trịn Sandwich-FGM có gân gia cường chứa chất lỏng 83 3.5.2 Tần số dao động riêng vỏ trụ chứa chất lỏng 84 3.6 Kết tính toán 85 3.6.1 Kiểm tra độ tin cậy phương pháp tính tốn 85 3.6.2 Phân tích đáp ứng động lực học phi tuyến vỏ trụ tròn Sandwich-FGM chứa đầy chất lỏng 87 3.7 Kết luận chương 95 CHƯƠNG 4: PHÂN TÍCH ỔN ĐỊNH ĐỘNG PHI TUYẾN VỎ TRỤ TRÒN FGM CÓ GÂN GIA CƯỜNG CHỨA CHẤT LỎNG 96 4.1 Đặt vấn đề 96 4.2 Khái quát chung ổn định 96 4.2.1 Định nghĩa phân loại ổn định 96 4.2.2 Các tiêu chuẩn ổn định 98 4.3 Phương trình động lực học vỏ trụ trịn FGM có chứa chất lỏng .102 4.4 Phương pháp giải 103 4.5 Kết tính tốn 105 4.5.1 Kiểm tra độ tin cậy phương pháp tính 105 4.5.2 Kết số 106 4.6 Kết luận chương .115 KẾT LUẬN VÀ KIẾN NGHỊ 116 DANH MỤC CÁC CƠNG TRÌNH KHOA HỌC ĐÃ CÔNG BỐ 118 TÀI LIỆU THAM KHẢO 119 vi DANH MỤC CÁC KÍ HIỆU, CÁC CHỮ VIẾT TẮT E(z) Mô đun đàn hồi FGM, hàm tọa độ z Ec Mô đun đàn hồi gốm vật liệu FGM Mô Em đun đàn hồi kim loại vật liệu FGM h, hm, hc Chiều dày kết cấu, chiều dày lớp kim loại lớp k gốm Chỉ số đặc trưng tỷ phần thể tích (0≤k≤∞) K , K2 Hệ số đàn hồi Winkler pcr, qcr Pasternak Tải trọng tới hạn R, L Bán kính vỏ trụ, chiều dài kết cấu tcr Thời gian tới hạn v Vc Hệ số Poisson Vm Tỷ phần thể tích gốm vật liệu FGM CST DQM E-FGM FGM FSDT Mode PFGM SFGM Tỷ phần thể tích kim loại vật liệu FGM Lý thuyết vỏ cổ điển Phương pháp cầu phương vi phân FGM phân bố theo quy luật hàm mũ Fuctionally Graded Material-Vật liệu tính biến thiên lý thuyết biến dạng trượt bậc Kiểu dáng, dạng FGM phân bố theo quy luật hàm lũy thừa FGM phân bố theo quy luật Sigmoid vii DANH MỤC CÁC BẢNG Trang Bảng 1.1 Tính chất số vật liệu thành phần FGM thường gặp 10 Bảng 2.1 Các tham số lượn sóng [135] 37 Bảng 2.2 Ảnh hưởng (m, n) đến tần số dao động riêng (s-1) 43 Bảng 2.3 Ảnh hưởng tỷ phần thể tích k đến tần số dao động riêng lượn sóng (s-1) .43 Bảng 2.4 So sánh thông số tần số dao động riêng ω* FGM .60 Bảng 2.5 Ảnh hưởng giá trị (m, n) đến tần số dao động riêng (s-1) 61 Bảng 2.6 Ảnh hưởng tỷ phần thể tích đến tần số dao động riêng FGM độ dày thay đổi (s-1) .61 Bảng 2.7 Ảnh hưởng tỉ số a/b đến tần số dao động riêng (s-1) 64 -1 Bảng 2.8 Ảnh hưởng tỉ số h0/h1 đến tần số dao động riêng (s ) 64 Bảng 2.9 Ảnh hưởng tỷ phần thể tích k đến tải trọng tới hạn FGM có độ dày thay đổi (MPa) 66 Bảng 2.10 Tải tới hạn (MPa) tỉ số a/b thay đổi 67 Bảng 2.11 Tải tới hạn (MPa) tỉ số h0/h1 thay đổi 68 Bảng 2.12 Tải tới hạn (MPa) thay đổi giá trị m,n .69 Bảng 3.1 So sánh tần số dao động riêng tự vỏ trụ FGM không chứa chất lỏng (Hz) 86 Bảng 3.2 So sánh tần số dao động riêng tự vỏ trụ chứa chất lỏng (rad/s) 86 Bảng 3.3 Tần số dao động riêng vỏ trụ Sandwich-FGM có gân gia cường 121 Roque, R M N Jorge, C M M Soares, (2013), “Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-thethickness deformations.”, European J of Mechanics A/Solids, Vol 37, pp 24-34 [21] A M A Neves, A J M Ferreira, E Carrera, M Cinefra, C M C Roque, R M N Jorge, C M M Soares, (2013), “Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique.”, Composites: Part B: Engineering, Vol 44, pp 657–674 [22] A R Akbari, S A Ahmadi, (2014), “Buckling Analysis of Functionally Graded Thick Cylindrical Shells with Variable Thickness Using DQM.”, Arabian Journal for Science and Engineering, Vol 39(11), pp 8121-8133 [23] A R Ghasemi, M Meskini, (2019), “Investigations on dynamic analysis and free vibration of FGMs rotating circular cylindrical shells.”, SN Applied Sciences, DOI: 10.1007/s42452-019-0299-5 [24] A S Volmir, (1972), Nonlinear Dynamics of Plates and Shells, Science edition, Moscow [25] B Budiansky, R S Roth, (1962), “Axisymmetric dynamic buckling of clamped shallow spherical shells.”, NASA Technical Note D.510, pp 597-609 [26] B Uymaz, M Aydogdu, (2007), “Three-Dimensional Vibration [27] Analyses of Functionally Graded Plates under Various Boundary Conditions.”, Journal of Reinforced Plastics and Composites, Vol 26(18), pp 1847–1863 C K Susheel, R Kumar V S Chauhan, (2017), “Nonlinear vibration analysis of piezolaminated functionally graded cylindrical shell.”, International Journal of Nonlinear Dynamics and Control, Vol 1(1), pp 27-50 [28] C T Loy, K Y Lam, J N Reddy, (1999), “Vibration of functionally graded cylindrical shells.”, International Journal of Mechanical Sciences, Vol 41, pp 309–324 122 [29] D G Ninh and D H Bich, (2016), “Nonlinear torsional buckling and post-buckling of eccentrically stiffened ceramic-functionally graded material-metal layer cylindrical shell surrounded by elastic foundation subjected to thermo-mechanical load.”, Journal of Sandwich Structures and Materials, Vol 18 (6), pp 712-738 [30] D H Bich, D G Ninh , T I Thinh, (2016), “Non-linear buckling analysis of FGM toroidal shell segments filled inside by an elastic medium under external pressure loads including temperature effects.”, Composites Part B: Engineering, Vol 87, pp 75-91 [31] D H Bich, D V Dung, L K Hoa, (2012), “Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects.”, Composite Structures, Vol 94(9), pp 2952-2960 [32] D H Bich, D V Dung, V H Nam, (2012), “Nonlinear dynamical [33] analysis of eccentrically stiffened functionally graded cylindrical panels.”, Composite Structures, Vol 94, pp 2465-2473 D H Bich, D V Dung, V H Nam, N T, Phuong, (2013), “Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally grade circular cylindrical thin shells under axial compression.”, International Journal of Mechanical Sciences, 74, pp 190-200 [34] D H Bich, G D Ninh and T I Thinh, (2016), “Buckling Analysis of Eccentrically Stiffened Functionally Graded Toroidal Shell Segments under Mechanical Load.”, Journal of Engineering Mechanics, Vol 142(1), pp 28-38 [35] D H Bich, H V Tung, (2011), “Nonlinear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects.”, International Journal of Nonlinear Mechanics, Vol 46(9), pp.1195-1204 [36] D H Bich, N X Nguyen, (2012), “Nonlinear vibration of functionally grade circular cylindrical shells based on improved Donnell equations”, Journal of Sound and Vibration, Vol 331(25), pp.5488-5501 123 [37] D H Bich, N X Nguyen, H V Tung, (2013), “Postbuckling of [38] functionally grade cylindrical shell based on improved Donnell equations.”, Vietnam Journal of Mechanics VAST, Vol 35(1), pp.1-15 D H Bich, V D Long,(2010), “Non-linear dynamic alanalysis of imperfect functionally graded material shallow shells.”, Vietnam Journal of Mechanics, VAST, Vol 32 (1), pp 1–14 [39] D H Bich, V H Nam, N T, Phuong, (2011), “Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells.”, Vietnam Journal of Mechanics, Vol 33 (3), pp 131-147 [40] D O Brush, Almroth (1975), Buckling of Bars, Plates and Shells, New York, Mc Graw-Hill, Inc., [41] D V Dung, N T Nga, P M Vuong, (2017) “Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory.”, Journal of Sandwich Structures & Materials, Vol 21(3), pp 938-972, [42] D V Dung, P M Vuong, (2016) “Nonlinear analysis on dynamic buckling of eccentrically stiffened functionally graded material toroidal shell segment surrounded by elastic foundations in thermal environment and under time-dependent torsional loads.”, Applied Mathematics and Mechanics Ed, Vol 37 pp 835-860 [43] Dai Hong-Liang, Luo Wei-Feng, Dai Ting, (2017), “Exact solution of [44] thermoelectroelastic behavior of a fluid-filled FGPM cylindrical thinshell.”, Composite Structures, Vol 162, pp 411-423 Dai Ting, Dai Hong-Liang, (2016) “Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed.”, Applied Mathematical Modelling, Vol 40(17-18), pp 7689-7707 [45] Dang Thuy Dong, Dao Van Dung, (2017), “A third-order shear deformation theory for nonlinear vibration analysis of stiffened 124 functionally graded material sandwich doubly curved shallow shells with four material model.”, Journal of Sandwich Structures & Materials, Vol 21(4) pp 1316-1356 [46] Dao Huy Bich, Dao Van Dung & Vũ Hoai Nam, (2013), “Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells.”, Composite Structures, Vol 96, pp 384–395 [47] Dao Van Dung, Le Thi Ngoc Anh and Le Kha Hoa, (2018), “Analytical investigation on the free vibration behavior of rotating FGM truncated conical shells reinforced by orthogonal eccentric stiffeners.”, Mechanics of Advanced Materials and Structures Vol 25(1), pp 32-46 [48] Dinh Gia Ninh, Dao Huy Bich, (2016), “Nonlinear thermal vibration of eccentrically stiffened Ceramic-FGM-Metal layer toroidal shell segments surrounded by elastic foundation.”, Thin-Walled Structures, Vol 104, pp 198-210 [49] Dinh Gia Ninh, Dao Huy Bich, Bui Huy Kien, (2015), “Torsional buckling and post-buckling behavior of eccentrically stiffened [50] functionally graded toroidal shell segments surrounded by an elastic medium.”, Acta Mechanica, Vol 226(10), pp 3501-3519 E Bagherizadeh, Y Kiani, M R Eslami, (2011), “Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation.”, Composite Structures, Vol 93, pp 3063–3071 [51] E Selahi, A R Setoodeh, M Tahani, (2014), “Three-dimensional transient analysis of functionally graded truncated conical shells with variable thickness subjected to an asymmetric dynamic pressure.”, International Journal of Pressure Vessels and Piping, Vol 119, pp 29-38 [52] F A Fazzolari, E Carrera, (2014), “Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core.”, Journal of Sound and Vibration, Vol 333, pp 1485–1508 [53] F M A da Silva, R O Pires Montes, P B Goncalves and Z J G N 125 del Prado, (2015), “Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload.”, Journal of Mechanical Engineering Science, 230(1), pp 102-119 [54] F Pellicano, M Amabili, (2003), “Stability and vibration of empty and fluid-filled circular cylindrical shells under static and periodic axial loads” International Journal of Solids and Structures, Vol 40, pp 3229-3251 [55] F Tornabene, N Fantuzzi, M Bacciocchi, E Viola and J N Reddy, (2017), “A Numerical Investigation on the Natural Frequencies of FGM Sandwich Shells with Variable Thickness by the Local Generalized Differential Quadrature Method.”, Applied Sciences, Vol 7(2), pp 131-170 [56] Fuzhen Pang, Haichao Li, Xueren Wang, Xuhong Miao, Shuo Li, (2018), “A semi analytical method for the free vibration of doublycurved shells of revolution.”, Computers and Mathematics with Applications, Vol 75(9), pp 3249-3268 [57] G G Sheng and X Wang, (2008), “Thermal Vibration, Buckling and Dynamic Stability of Functionally Graded Cylindrical Shells Embedded in an Elastic Medium.”, Journal of Reinforced Plastics and Composites, Vol 27(2), pp 117 -134 [58] G G Sheng and X Wang, (2008), “Thermomechanical vibration analysis of a functionally graded shell with flowing fluid.”, European Journal of Mechanics A/Solids, Vol.27, pp 1075–1087 [59] G G Sheng and X Wang, (2010), “Dynamic characteristics of fluidconveying functionally graded cylindricalbshells under mechanical and thermal loads.”, Composite Structures, Vol.93, pp 162–170 [60] H Babaei, Y Kiani, M R Eslami, (2019), “Thermal Buckling and Post- buckling Analysis of Geometrically Imperfect FGM Clamped Tubes on Nonlinear Elastic Foundation.”, Applied Mathematical Modelling, Vol 71, pp 12-30 [61] H H Shen, (2012), “Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium.”, Composite 126 Structures, Vol 94:1144-54 [62] H S Shen, (2013) “Thermal Post-buckling of Shear Deformable FGM Cylindrical Shells Surrounded by an Elastic Medium.”, Journal of Engineering Mechanics, Vol.139, pp 979-991 [63] H S Shen, J Yang, S Kitipornchai, (2010) “Postbuckling of internal [64] pressure loaded FGM cylindrical shells surrounded by an elastic medium.”, European Journal Mechanic- A/Solids, Vol.29, pp 448-460 H V Tung, N D Duc, (2010), “Nonlinear analysis of stability for functionally graded plates under mechanical and thermal load.”, Compos- Struct, Vol.92(5), pp 1184-1191 [65] H V Tung, N D Duc, (2010), “Thermoelastic stability of thick imperfect functionally graded plate.”, Vietnam Journal of Mechanics, VAST, Vol 32(1), pp 47-58 [66] Huaiwei Huang, Qiang Han, (2008), “Buckling of imperfect functionally graded cylindrical shells under axial compression.”, European Journal of Mechanics A/Solids, Vol 27, pp 1026–1036 [67] Huaiwei Huang, Qiang Han, (2010), “Nonlinear buckling of torsionloaded functionally graded cylindrical shells in thermal environment.”, European Journal of Mechanics A/Solids, Vol 29, pp 42–48 [68] Huaiwei Huang, Qiang Han, (2010), “Nonlinear dynamic buckling of [69] functionally graded cylindrical shells subjected to time-dependent axial load.”, Composite Structures, Vol 92, pp 593–598 Huaiwei Huang, Qiang Han, (2010), “Research on nonlinear [70] postbuckling of functionally graded cylindrical shells under radial loads.”, Composite Structures, Vol 92, pp 1352–1357 J Zhang, S Pan, L Chen , (2018), “Dynamic thermal buckling and postbuckling of clamped–clamped imperfect functionally graded annular plates.”, Nonlinear Dynamics Vol 95(1), pp 565–577 [71] J Zhao, K Choe, C Shuai, A Wang, Q Wang, (2018), “Free vibration analysis of functionally graded carbon nanotube reinforced composite 127 truncated conical panels with general boundary conditions” Composites Part B: Engineering Vol 160, pp 225-240 [72] K Daneshjou, M Bakhtiari, A Tarkashvand, (2017) “Wave propagation and transient response of a fluid-filled FGM cylinder with rigid core using the inverse Laplace transform.”, European J of Mechanics / A Solids, Vol 61, pp 420-432 [73] K Gao, W Gao, D Wu, C Song, (2018), “Nonlinear dynamic buckling of the imperfect orthotropic E-FGM circular cylindrical shells subjected to the longitudinal constant velocity.”, International Journal of Mechanical Sciences, Vol 138-139, pp 199–209 [74] K Kowal-Michalska, R J Mania, (2011), “Static and dynamic buckling of FGM plates under compressive loading.”, International Conference on Computational & Experimental Engineering and Sciences, Vol 16, pp 55-56 [75] K V Avramov, (2012), “Nonlinear modes of vibrations for simply supported cylindrical shell with geometrical nonlinearity.”, Acta Mechanica, Vol 223, pp 279-292 [76] Kim Young-Wann, (2015), “Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge.”, Composites Part B: Engineering, Vol 70, pp 263-276 [77] Kwangnam Choe, Jinyuan Tang, Cijun Shui, Ailun Wang, Qingshan Wang, (2018), “Free vibration analysis of coupled functionally graded [78] (FG) doubly-curved revolution shell structures with general boundary conditions.”, Composite Structures, Vol 194, pp 413-432 L Czechowski, K Kowal-Michalska, (2013), “Static and Dynamic [79] Buckling of Rectangular Functionally Graded Plates Subjected to Thermal Loading.”, Strength of Materials, Vol 45(6), pp 666–673 M Akbari, Y Kiani, M R Eslami, (2015), “Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge support.”, Acta Mechanica, 226(3), pp 897–915 [80] M Bayat, M Rahimi, M Saleem, A.H Mohazzab, I Wudtke, H Talebi, 128 “One-dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk.”, Applied Mathematical Modelling, Vol 38(19-20): pp 4625-4639 [81] M Bodaghi, A R Saidi, (2010), “Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory” Applied Mathematical Modelling, 34(11), pp 3659-3673 [82] M Ghannad, G H Rahimi, M Z Nejad, (2013) “Elastic analysis of [83] pressurized thick cylindrical shells with variable thickness made of functionally graded materials.”, Composites Part B: Engineering, Vol 45, pp 388–396 M J Khoshgoftar, M J Mirzaali, G H Rahimi, (2015), “Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with [84] variable thickness using first order shear deformation theory (FSDT) and perturbation method.”, Chinese Journal of Mechanical Engineering.Vol 28(6), pp 1149–1156 M Jabbari, M Z Nejad, M Ghannad,(2015), “Thermo-elastic analysis [85] of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading.”, International Journal of Engineering Science, Vol 96, pp 1–18 M R Barati and A M Zenkour, (2019) “Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions.”, Mechanics of Advanced Materials and Structures Vol 26(18), pp 1580-1588 [86] M Shariyat, (2009), “Vibration and dynamic buckling control of imperfect hybrid FGM plates with temperature-dependent material [87] properties subjected to thermo-electro-mechanical loading conditions.”,Composite Structures, Vol 88(2), pp 240–252 M Shariyat, D Asgari, (2013), “Non-linear thermal buckling and postbuckling analyses of imperfect variable thickness temperature- 129 dependent bidirectional functionally graded cylindrical shells.”, International Journal of Pressure Vessels and Piping, Vol 111-112, pp 310320 [88] M Shariyat, M M Alipou, (2013), “A power series solution for vibration and complex modal stress analyses of variable thickness [89] viscoelastic two-directional FGM circular plates on elastic foundations.”, Applied Mathematical Modelling Vol 37(5), pp 3063–3076 M Z Nejad, M Jabbari, M Ghannad, (2015), “Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading.”, International Journal of Engineering Science, Vol 89(6), pp 86-99 [90] Maciej Taczała, Ryszard Buczkowski, Michal Kleiber, (2015), “Postbuckling analysis of functionally graded plates on an elastic foundation.”, Composite Structures, Vol.132, pp 842-847 [91] Mehdi Jabbaria, Mohammad Zamani Nejada, Mehdi Ghannadb, (2016), “Thermo-elastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness.”, Composites Part B: Engineering, Vol 96, pp.1–17 [92] Mirzavand, M R Eslami and J N Reddy, (2013), “Dynamic thermal postbuckling analysis of shear deformable piezoelectric-FGM cylindrical shells.”, Journal of Thermal Stresses, Vol 36, 189–206 [93] N D Dat, N D Khoa, P D Nguyen and N D Duc, (2019) An‐ analytical solution for nonlinear dynamic response and vibration of FG CNT reinforced nanocomposite elliptical cylindrical shells resting on elastic foundations ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik doi:10.1002/zamm.201800238 [94] N D Duc, H V Tung, (2010) “Nonlinear response of pressure-loaded functionally graded cylindrical panels with temperature effects.”, Composite Structures, Vol 92(7), pp.1664-1672 [95] N D Duc, N D Tuan, P Tran, P H Cong, N D Nguyen, (2016,) 130 “Nonlinear stability of eccentrically stiffened S-FGM elliptical cylindrical shells in thermal environment.”, Thin-Walled Structures Vol 108, pp 280-.290 [96] N D Duc, N D Tuan, T Phuong, N T Dao, N T Dat, (2015), “Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments.”, International Journal of Mechanical Sciences, Vol 101-102, pp 338-348 [97] N D Duc, N D Tuan, T Phuong, T Q Quan, N Van Thanh, (2017), “Nonlinear dynamic response and vibration of imperfect eccentrically stiffened sandwich third-order shear deformable FGM cylindrical panels in thermal environments.”, Journal of Sandwich Structures & Materials, Vol 21 (8), pp 2816-2845 [98] N D Duc, P T Thang, (2014) “Nonlinear response of imperfect eccentrically stiffened ceramic-metal-ceramic FGM thin circular [99] cylindrical shells surrounded on elastic foundations and subjected to axial compression.”, Composite Structures Vol 110, pp 200-206 N D Duc, P T Thang, (2015), “Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations.”, [100] Aerospace Science and Technology, 2015, 40, pp 115-127 N D Duc, P T Thang, N T Dao, H V Tac, (2015), “Nonlinear [101] buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment.”, Composite Structures, Vol 121, pp 134-141 N D Duc, T Q Quan, (2013), “Nonlinear postbuckling of imperfect doubly curved thin shallow FGM shells resting on elastic foundations and subjected to mechanical loads.”, Journal Mechanics of Composite Materials, 49, pp.453-506 [102] N D Duc, T Q Quan, V D Luat, (2015), “Nonlinear dynamic analysis 131 and vibration of shear deformable piezoelectric FGM double curved shallow shells under damping-thermo-electro-mechanical loads.”, Composite Structures, Vol 125, pp 29-40 [103] N D Duc,T Q Quan, (2017), “Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation.”, Journal of Vibration and Control, Vol 21(7), pp 1340-1362 [104] N D Khoa, H T Thiem, N D Duc, (2017), “Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal–ceramic–metal layers in thermal environment using Reddy’s third-order shear deformation shell theory.”, Mechanics of Advanced Materials and Structures, Vol 26(3) pp 248-259 [105] N Jooybar, P Malekzadeh, A Fiouz, M Vaghefi, (2016), “Thermal effect on free vibration of functionally graded truncated conical shell panels.”, Thin-Walled Structures, Vol 103, pp 45-61 [106] N V Thanh, V D Quang, N D Khoa, K Seung-Eock and N D Duc , (2018), “Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature-dependent material properties and surrounded on elastic foundations Journal of Sandwich Structures & Materials doi:10.1177/1099636217752243 [107] Nuttawit Wattanasakulpong, Arisara Chaikittiratana, (2015), “An analytical investigation on free vibration of FGM doubly curved shallow shells with stiffeners under thermal environment.”, Aerospace Science and Technology, Vol 40, pp 181-190 [108] Nguyen Dinh Duc, Pham Dinh Nguyen, Nguyen Dinh Khoa, (2017), “Nonlinear dynamic analysis and vibration of eccentrically stiffened SFGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments.”, Thin-Walled Structures, Vol 117, pp 178-189 [109] Nguyen Dinh Duc, Vu Dinh Quang, Vu Thi Thuy Anh, (2017), “The nonlinear dynamic and vibration of the S-FGM shallow spherical shells 132 resting on an elastic foundations including temperature effects.”, International Journal of Mechanical Sciences, Vol 123, pp 54-63 [110] P Jiao, Z Chen, Y Li, H Ma, J Wu (2019), “Dynamic buckling analyses of functionally graded carbon nanotubes reinforced composite [111] (FG-CNTRC) cylindrical shell under axial power-law time-varying displacement load.”, Composite Structures, Vol 220, pp 784–797 P M Vuong, D V Dung, (2017), “Nonlinear Analysis on Buckling and Postbuckling of Stiffened FGM Imperfect Cylindrical Shells Filled Inside by Elastic Foundations in Thermal Environment Using TSDT.”, Latin American Journal of Solids and Structures, 14, pp 950-977 [112] P Malekzadeh, (2009), “Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations.”, Composite Structure, Vol 89, pp 367–373 [113] Park Kyung-Jo, Kim Young-Wann, (2016), “Vibration characteristics of fluid-conveying FGM cylindrical shells resting on Pasternak elastic foundation with an oblique edge.”, Thin-Walled Structures, Vol 106, pp 407–419 [114] Pham Toan Thang, Nguyen Dinh Duc, Nguyen Thoi Trung, (2016), “Effects of variable thickness and imperfection on nonlinear buckling of sigmoid-functionally graded cylindrical panels.”, Composite Structures, 155, pp 99-106 [115] Pham Toan Thang, Nguyen Thoi Trung, (2016), “A new approach for [116] nonlinear dynamic buckling of S-FGM toroidal shell segments with axial and circumferential stiffeners.”, Aerospace Science and Technology, Vol 53, pp 1–9 Pham-Toan Thang, Nguyen Thoi Trung, Jaehong Lee, (2016), “Closedform expression for nonlinear analysis of imperfect sigmoid-FGM plates with variable thickness resting on elastic medium.”, Composite Structures, 143, pp 143-150 [117] Q Li, V P Iu , K P Kou, (2009), “Three-dimensional vibration analysis of functionally graded material plates in thermal environment.”, Journal 133 of Sound and Vibration, Vol 324, pp 733–750 [118] R Bahadori , M M Najafizadeh, (2015), “Free Vibration Analysis of two-dimensional Functionally Graded Axisymmetric Cylindrical Shell on Winkler- Pasternak elastic Foundation by First-order Shear [119] Deformation Theory and using Navier-Differential Quadrature solution methods.”, Applied Mathematical Modelling, Vol 40, pp 115-127 S H H Hashemi, H R D Taher, H Akhavan, (2010), “Vibration [120] analysis of radially FGM sectorial plates of variable thickness on elastic foundations.”, Composite Structures, Vol 92, pp 1734–1743 S R Li , X H Fu, R C, Batra, (2010), “Free vibration of three-layer circular cylindrical shells with functionally graded middle layer.”, Mechanics Research Communications, Vol 37(6), pp 577–580 [121] T Q Quan and N D Duc, (2016), “Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double- [122] curved shallow shells resting on elastic foundations in thermal environments.”, Journal of Thermal Stresses, Vol 39(4), pp 437-459 V R Kar, S K Panda, (2014), “Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method.”, Journal of Vibration and Control, Vol 22(7), pp 1-15 [123] V H Nam, N T Phuong, C V Doan, & N T Trung, (2019), “Nonlinear thermo-mechanical stability analysis of eccentrically spiral stiffened Sandwich functionally graded cylindrical shells subjected to external pressure.”,International Journal of Applied Mechanics Vol 11(5), 1950045 (24 pages) [124] V H Nam, N T Phuong, N T Trung (2019), “Nonlinear buckling and [125] postbuckling of sandwich FGM cylindrical shells reinforced by spiral stiffeners under torsion loads in thermal environment.”, Acta Mechanica, Vol 230(9), pp 3183–3204 V Tajeddini, A Ohadi, M Sadighi, (2012), “Three-dimensional free vibration of variable thickness thick circular and annular isotropic and 134 functionally graded plates on Pasternak foundation.”, International Journal of Mechanical Sciences, Vol 53, pp 300–308 [126] Vu Hoai Nam, Nguyen Thi Phuong, Dao Huy Bich, Dao Van Dung, (2014), “Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation.”, Vietnam Journal of Mechanics, Vol 36 (1), pp 27-47 [127] Vu Quoc Hien, Tran Ich Thinh, Nguyen Manh Cuong, (2016), “Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid” Vietnam Journal of Mechanics, Vol 38 (4), pp 249-265 [128] W Q Chen , X Wang, H J Ding, (1999), “Free vibration of a fluid- [129] filled hollow sphere of a functionally graded material with spherical isotropy.”, The Journal of the Acoustical Society of America, Vol 106(5), pp 2588–2594 W Q Chen, Z G Bian, H J Ding, (2004), “Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells.”, International Journal of Mechanical Sciences, 46, pp 159–171 [130] W Zhang, Y X Hao, J Yang, (2012) “Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges.”, Composite Structures, Vol 94, pp 1075–1086 [131] X Liang, X Zha, Y Yu, Z Cao, X Jiang & J Leng, (2019), “Semianalytical vibration analysis of FGM cylindrical shells surrounded by elastic foundations in a thermal environment.”, Composite Structures, Vol 223, 110997, DOI:10.1016/j.compstruct.2019.110997 [132] X Zhao, K M Liew, (2011), “Free vibration analysis of functionally graded conical shell panels by a meshless method.”, Composite Structures, Vol 93, pp 649–664 [133] X Zhao, K M Liew, (2011), “Free vibration analysis of functionally [134] graded conical shell panels by a meshless method, Composite Structures, Vol 93, pp 649–664 Xiang Xie, Hui Zheng, Guoyong Jin, (2015), “Free vibration of four- 135 parameter functionally graded spherical and parabolic shells of revolution with arbitrary boundary conditions.”, Composites Part B: Enggineering, Vol 77, pp 59-73 [135] Y Xia, M I Friswell, E I S Flores, (2012), “Equivalent models of corrugated panels.”, International Journal of Solids and Structures, Vol 49, pp 1453–1462 [136] Yan Qing Wanga,, Yu He Wana , Jean W Zu (2019), “Nonlinear dynamic characteristics of functionally graded sandwich thinnanoshells conveying fluid incorporating surface stress influence.”, Thin-Walled Structures, Vol 135, pp 537-547, [137] Yepeng Xu, Ding Zhou, (2009), “Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness.”, Composite Structures, Vol 91, pp 56-65 [138] Z Qin, X Pang, B Safaei & F Chu, (2019), “Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions” Composite Structures Vol 220, pp 847-860, [139] Zafar Iqbal, N Muhammad N Sultana, S H Arshad, A G Shah, (2009), “Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach.”, Applied Mathematics and Mechanics Ed, Vol 30(11), pp 1393–1404 ... đổi thành ? ?Phân tích động lực học phi tuyến FGM vỏ trụ tròn sandwich -FGM chứa đầy chất lỏng? ?? Mục tiêu nghiên cứu luận án Luận án tập trung giải toán động lực học phi tuyến số kết cấu FGM có hình... tích đáp ứng động lực học phi tuyến vỏ trụ tròn Sandwich -FGM chứa đầy chất lỏng 87 3.7 Kết luận chương 95 CHƯƠNG 4: PHÂN TÍCH ỔN ĐỊNH ĐỘNG PHI TUYẾN VỎ TRỤ TRÒN FGM CÓ GÂN... thuyết vỏ Donnell phi tuyến để phân tích dao động phi tuyến vỏ trụ tựa đơn FGM chứa đầy chất lỏng chịu tải trọng học Kim cộng [113] sử dụng phương pháp giải tích để nghiên cứu dao động tự vỏ trụ FGM