luận án tiến sĩ 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 Vm Hệ số Poisson Tỷ phần thể tích gốm vật liệu FGM Tỷ phần thể tích kim loại vật liệu CST FGM Lý thuyết vỏ cổ điển DQM Phương pháp cầu phương vi phân E-FGM FGM phân bố theo quy luật hàm mũ FGM Fuctionally Graded Material-Vật liệu tính biến FSDT thiên lý thuyết biến dạng trượt bậc Kiểu dáng, Mode PFGM SFGM 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 chứa chất lỏng (s-1) .88 121 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.”, 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shells filled with fluid using wave propagation approach.”, Applied Mathematics and Mechanics Ed, Vol 30(11), pp 1393–1404 ... tài luận án đề xuất 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. .. 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. .. 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