Ngày nhận bài: 02-10-2014
Ngày duyệt đăng: 25-11-2014
DOI:
Lượt xem
Download
Cách trích dẫn:
PHÂN TÍCH DAO ĐỘNG RIÊNG TẤM BẰNG VẬT LIỆU CÓ CƠ TÍNH BIẾN THIÊN (FGM) THEO LÝ THUYẾT BIẾN DẠNG CẮT BẬC CAO (HSDT)
,
Dương Thành Huân
3
,
Lê Minh Lư
3
Tóm tắt
Vật liệu có cơ tính biến thiên(Functionally Graded Materials -FGM)là loại vật liệu không đồng nhất, đẳng hướngcó tính chất cơ học thay đổi trơn, liên tục theo chiều dày của tấm. Bài báo sử dụng lý thuyết biến dạng cắt bậc cao (Higher Order Shear Deformation Theory - HSDT) để phân tích dao động riêng của tấm bằng vật liệu có cơ tính biến thiên. Mô đun đàn hồi kéo (nén) của vật liệu giả thiết biến thiên theo qui luật hàm mũ, hệ số Poisson là hằng số theo tọa độ chiều dày. Hệ phương trình cân bằng động của tấm được xác định theo nguyên lý Hamilton. Ảnh hưởng của chỉ số tỉ lệ thể tích, tỉ số các kích thước tấm đến tần số dao động riêng được khảo sát. Kết quả số được so sánh với các công bố trên các tạp chí quốc tế đã xuất bản nhằm kiểm chứng mô hình tính mà bài báo đã xây dựng.
Tài liệu tham khảo
Dao Huy Bich, Dao Van Dung, Vu Hoai Nam, Nguyen Thi Phuong (2013). Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression. International Journal of Mechanical Sciences, 74: 190-200.
Dao Huy Bich, Dao Van Dung, Vu Hoai Nam (2012). Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Composite Structures, 94: 2465-2473
Chen CS, Hsu CY, Tzou GJ (2009). Vibration and stability of functionally graded plates based on a higher-order deformation theory. J Reinf Plast Compos, 28(10): 1215-34.
Nguyen Dinh Duc, Hoang Van Tung (2011). Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. Composite Structures, 93: 2874-2881.
Nguyen Dinh Duc, Pham Hong Cong (2014). Nonlinear postbuckling of an eccentrically stiffened thin FGM plate resting on elastic foundations in thermal environments. Thin-Walled Structures, 75: 103-112.
Nguyen Dinh Duc, Pham Hong Cong (2013). Nonlinear postbuckling of symmetric S-FGM plates resting on elastic foundations using higher order shear deformation plate theory in thermal environments. Composite Structures, 100: 566-574.
DaoVan Dung, Le Kha Hoa, Nguyen Thi Nga, Le Thi Ngoc Anh (2013). Instability of eccentrically stiffened functionally graded truncated conical shells under mechanical loads. Composite Structures, 106: 104-113.
Fares ME, Elmarghany MK, Atta D (2009). An efficient and simple refined theory for bending and vibration of functionally graded plates. Compos Struct, 91(3): 296-305.
Ferreira AJM, Carrera E, Cinefra M, Roque CMC, Polit O (2011). Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations. Compos Part B: Eng, 42(5): 1276-84.
Jha. D.K, Tarun Kant, Singh .R.K (2012). Higher order shear and normal deformation theory for natural frequency of functionally graded rectangular plates. Nuclear Engineering and Design 250: 8-13.
Huu-Tai Thai, Seung-Eock Kim (2013). A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Composite Structures, 96: 165-173.
Hosseini-Hashemi. Sh, H. Rokni Damavandi Taher, H. Akhavan, M. Omidi (2010). Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Applied Mathematical Modelling, 34: 1276-1291.
Huu-Tai Thai, Dong-Ho Choi (2013). A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Composite Structures, 101: 332-340.
Kant.T, Swaminathan.K (2001). Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite Structures, 53: 73-85.
Mantari JL, Oktem AS, Guedes Soares C. (2012a). A new higher order shear deformation theory for sandwich and composite laminated plates. Compos Part B: Eng, 43(3): 1489-99.
Mantari JL, Oktem AS, Guedes Soares C (2012b). A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int J Solids Struct, 49(1): 43-53.
Mantari JL, Oktem AS, Guedes Soares C (2012c). Bending response of functionally graded plates by using a new higher order shear deformation theory. Compos Struct, 94(2): 714-23.
Mantari JL, Guedes Soares C (2012d). Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates. Compos Struct, 94(8): 2561-75.
Matsunaga H (2008). Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Compos Struct, 82(4): 499-512.
Neves AMA, Ferreira AJM, Carrera E, Roque CMC, Cinefra M, Jorge RMN, et al (2012a). A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Part B: Eng, 43(2): 711-25.
Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Roque CMC, Jorge RMN, et al (2012b). A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos Struct, 94(5): 1814-25.
Neves AMA, Ferreira AJM, Carrera E, Cinefra M, Roque CMC, Jorge RMN, et al. (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. Compos Part B: Eng, 44(1): 657-74.
Pradyumna S, Bandyopadhyay JN (2008). Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation. J Sound Vib, 318(1-2): 176-92.
Reddy JN (2000). Analysis of functionally graded plates. Int J Numer Methods Eng, 47(1-3): 663-84.
Reddy JN (1984). A simple higher-order theory for laminated composite plates. J Appl, Mech, 51: 745-52.
Reddy JN (2011). A general nonlinear third-order theory of functionally graded plates. Int J Aerosp Lightweight Struct, 1(1):1-21.
Talha M, Singh BN (2010). Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model, 34(12): 3991-4011.
Xiang S, Kang GW (2013). A nth-order shear deformation theory for the bending analysis on the functionally graded plates. Eur J Mech - A/Solids, 37: 336-43.
Xiang S, Jin YX, Bi ZY, Jiang SX, Yang MS (2011). A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Compos Struct, 93(11):2826-32.
Zenkour AM (2006). Generalized shear deformation theory for bending analysis of functionally graded plates. Appl Math Model, 30(1): 67-84.