Ảnh hưởng của tải trọng nổ tới dao động cưỡng bức của tấm làm bằng vật liệu có cơ tính biến đổi với chiều dày không đồng nhất
Email:
hungb3z131@gmail.com
Từ khóa:
Tải trọng nổ; sóng xung kích; vật liệu cơ tính biên thiên; động lực học; phần tử hữu hạn
Tóm tắt
Hiện tượng dao động của kết cấu chịu tác dụng của tải trọng nổ, đặc biệt là các tấm có chiều dày không đồng nhất làm từ vật liệu có cơ tính biến thiên (FGM), đang thu hút nhiều sự quan tâm trong lĩnh vực cơ học kỹ thuật hiện đại. Trong nghiên cứu này, phương pháp phần tử hữu hạn kết hợp với phương pháp tích phân trực tiếp Newmark trên cơ sở lý thuyết biến dạng cắt bậc nhất được phát triển để phân tích dao động cưỡng bức của tấm FGM có chiều dày thay đổi chịu tác dụng của sóng xung kích do nổ gây ra. Sự thay đổi chiều dày của tấm được xét theo hai phương với quy luật phi tuyến, trong khi đặc tính vật liệu biến thiên theo chiều dày tấm. Tính chính xác của mô hình và phương pháp được xác minh thông qua so sánh với kết quả trong các nghiên cứu đã công bố. Sau đó, bài báo thực hiện khảo sát ảnh hưởng của các tham số như biên độ tải trọng, tốc độ lan truyền sóng, hệ số biến thiên vật liệu, và hệ số thay đổi chiều dày đến đáp ứng động của tấm. Kết quả nghiên cứu cung cấp các cơ sở quan trọng trong thiết kế và phân tích an toàn kết cấu FGM chịu tải nổTài liệu tham khảo
[1]. M. Patel, S. Patel, Dynamic behavior analysis of steel, aluminum, and composite plates under extreme air blast loadings, Mechanics of Advanced Materials and Structures, 2024 (2024) 1–17. https://doi.org/10.1080/15376494.2024.2427933
[2]. D. Van Doan, P. Van Minh, T. Van Ke, N.T.C. Nhung, D. Van Thom, An Overview of Functionally Graded Materials: From Civil Applications to Defense and Aerospace Industries, Journal of Vibration Engineering & Technologies, 13 (2025) 68. https://doi.org/10.1007/s42417-024-01691-8
[3]. A. Karakoti, S. Pandey, V.R. Kar, Nonlinear transient analysis of porous P-FGM and S-FGM sandwich plates and shell panels under blast loading and thermal environment, Thin-Walled Structures, 173 (2022) 108985. https://doi.org/10.1016/j.tws.2022.108985
[4]. X.H. Dang, V.L. Nguyen, M.T. Tran, B.D. Tran, V.L. Nguyen, Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading, Proceedings of the Institution of Mechanical Engineers, 238 (2024) 6831–6846. https://doi.org/10.1177/09544062231226050.
[5]. B. Mohammadzadeh, H.C. Noh, Analytical method to investigate nonlinear dynamic responses of sandwich plates with FGM faces resting on elastic foundation considering blast loads, Composite Structures, 174 (2017) 142–157. https://doi.org/10.1016/j.compstruct.2017.03.087.
[6]. P. Shi, V.N.V. Hoang, J. Yang, H. Shou, Q. Li, F. Turan, Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches, Thin-Walled Structures, 206 (2025) 112667. https://doi.org/10.1016/j.tws.2024.112667
[7]. S. Chandrasekaran, S. Pachaiappan, Numerical analysis and preliminary design of topside of an offshore platform using FGM and X52 steel under special loads, Innovative Infrastructure Solutions, 5 (2020) 86. https://doi.org/10.1007/s41062-020-00337-4
[8]. A. Reza; P. Puya, D. Ali, G. Majid, Dynamic Response of FGM Plates Under Blast Load, International Journal of Advanced Design & Manufacturing Technology, 16 (2023) 37. https://doi.org/10.30486/ADMT.2021.1920150.1239
[9]. T. Dao Minh, T. Do Van, M. Phung Van, H. Pham Huy, Bending and buckling responses of organic nanoplates considering the size effect, Transport and Communications Science Journal, 75 (2024) 2015–2029. https://doi.org/10.47869/tcsj.75.7.1
[10]. T. Van Toan, T.T.H. Huyen, D. Van Doan, Vibration and buckling analysis of nanoplates resting on variable elastic foundations, Transport and Communications Science Journal, 75 (2024) 2238–2251. https://doi.org/10.47869/tcsj.75.9.1
[11]. M.S.H. Al-Furjan, M.X. Xu, A. Farrokhian, G.S. Jafari, X. Shen, R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves in Random and Complex Media, 35 (2025) 1147–1171. https://doi.org/10.1080/17455030.2022.2030499.
[12]. P. Pham Minh, 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, 71 (2020) 853–867. https://doi.org/10.25073/tcsj.71.7.10.
[13]. D.H. Duc, D. Van Thom, P.M. Phuc, Buckling Analysis of Variable Thickness Cracked Nanoplatesconsiderting the Flexoelectric Effect, Transport and Communications Science Journal, 73 (2022) 470–485. https://doi.org/10.47869/tcsj.73.5.3
[14]. T. Vu Van, T. Do Van, Determine the influence factor of geometrical parameters on the dynamic characteristics of the micro crab-shaped beam, Transport and Communications Science Journal, 76 (2025) 530–540. https://doi.org/10.47869/tcsj.76.4.7.
[15]. M.A. Al-Shugaa, A.E.S. Musa, H.J. Al-Gahtani, Ritz Method-Based Formulation for Analysis of FGM Thin Plates Undergoing Large Deflection with Mixed Boundary Conditions, Arabian Journal for Science and Engineering, 49 (2024) 14225–14239. https://doi.org/10.1007/s13369-024-08871-4.
[16]. H.H. Le, V.K. Tran, N.T. Hoang, T.H. Phuong Thanh, Nonlinear free oscillation of tri-directional functionally graded porous skew-plates with variable thickness in high-thermal environment, Case Studies in Thermal Engineering, 70 (2025) 106101. https://doi.org/10.1016/j.csite.2025.106101.
[17]. N. Van Chinh, L.X. Phong, P. Van Vinh, T. Van Ke, P. Van Minh, Nonlinear vibration characteristics of multi-directionally graded porous material beams resting partly on elastic foundations, The Journal of Strain Analysis for Engineering Design, 60 (2025) 505-525. https://doi.org/10.1177/03093247251326446.
[18]. N.T.K. Lam, P. Mendis, T. Ngo, Response Spectrum Solutions for Blast Loading, Electronic Journal of Structural Engineering, 4 (2004) 28–44. https://doi.org/10.56748/ejse.439.
[19]. V. K. Trai, P. Malekzadeh, V.K. Tran, Q.H. Pham, T.M. Ket, A novel triangular element model for vibration analysis of FG-TPMS plate integrated with magneto-electric layers subjected to double explosive load, Ships and Offshore Structures, 2025 (2025) 1–25. https://doi.org/10.1080/17445302.2025.2457460.
[20]. N.T. Hong, Analysis of composite honeycomb sandwich panels under blast loads, Ships and Offshore Structures, 2024 (2024) 12-34. https://doi.org/10.1080/17445302.2024.2395186.
[21]. Q.H. Pham, P.C. Nguyen, V.K. Tran, Effects of hygro-thermal environment on dynamic responses of variable thickness functionally graded porous microplates, Steel and Composite Structures, 50 (2024) 563–581. https://doi.org/10.12989/scs.2024.50.5.563.
[22]. Q.H. Pham, T.A. Nguyen, N.T. Do, V.K. Tran, M.N. Nguyen, Static and vibration analyses of functionally graded porous shell structures by using an averaged edge/node-based smoothed MITC3 element, Computers & Mathematics with Applications, 153 (2024) 56–70. https://doi.org/10.1016/j.camwa.2023.10.037.
[23]. Q.H. Pham, V. Ke Tran, T. Thanh Tran, V. Chinh Nguyen, A.M. Zenkour, Nonlocal higher-order finite element modeling for vibration analysis of viscoelastic orthotropic nanoplates resting on variable viscoelastic foundation, Composite Structures, 318 (2023) 117067. https://doi.org/10.1016/j.compstruct.2023.117067.
[24]. V.K. Tran, Q.H. Pham, T. Nguyen-Thoi, A finite element formulation using four-unknown incorporating nonlocal theory for bending and free vibration analysis of functionally graded nanoplates resting on elastic medium foundations, Engineering with Computers, 38 (2022) 1465–1490. https://doi.org/10.1007/s00366-020-01107-7.
[25]. T.T. Tran, V.K. Tran, P.B. Le, V.M. Phung, V.T. Do, H.N. Nguyen, Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method, Advances in Civil Engineering, 2020 (2020) 12-30. https://doi.org/10.1155/2020/1471037.
[26]. P. Van Minh, T. Van Ke, A Comprehensive Study on Mechanical Responses of Non-uniform Thickness Piezoelectric Nanoplates Taking into Account the Flexoelectric Effect, Arabian Journal for Science and Engineering, 48 (2023) 11457–11482. https://doi.org/10.1007/s13369-022-07362-8.
[27]. T.T.T. Thi, V.K. Tran, Q.H. Pham, Static and Dynamic Analyses of Multi-Directional Functionally Graded Porous Nanoplates with Variable Nonlocal Parameter Using MITC3 + Element, Journal of Vibration Engineering & Technologies, 12 (2024) 5147–5171. https://doi.org/10.1007/s42417-023-01189-9.
[28]. I. ANSYS, Theory Reference 24.1, Southpointe 275 Technology Driver Canonsburg, 2024.
[29]. P.H. Tu, T. Van Ke, V.K. Trai, L. Hoai, An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading, Defence Technology, 41 (2024) 159–180. https://doi.org/10.1016/j.dt.2024.06.005.
[30]. M. Song, S. Kitipornchai, J. Yang, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composite Structure, 159 (2017) 579–588. https://doi.org/10.1016/j.compstruct.2016.09.070.
[31]. T. Van Do, D.K. Nguyen, N.D. Duc, D.H. Doan, T.Q. Bui, Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Structures, 119 (2017) 687–699. https://doi.org/10.1016/j.tws.2017.07.022.
[32]. H.N. Nguyen, T.N. Canh, T.T. Thanh, T.V. Ke, V.D. Phan, D.V. Thom, Finite element modelling of a composite shell with shear connectors, Symmetry, 11 (2019), 527. https://doi.org/10.3390/sym11040527
[33]. N.C. Tho, N.T. Ta, D.V. Thom, New numerical results from simulations of beams and space frame systems with a tuned mass damper, Materials, 12 (2019), 1329. https://doi.org/ 10.3390/ma12081329
[34] T. V. Ke, P. V. Minh, N.T. Dung, L.M. Thai, D. V. Thom, Flexoelectric effect on bending and free vibration behaviors of piezoelectric sandwich FGP nanoplates via nonlocal strain gradient theconory, Journal of Vibration Engineering & Technologies, 12 (2024), 6567-6596. https://doi.org/10.1007/s42417-023-01270-3
[2]. D. Van Doan, P. Van Minh, T. Van Ke, N.T.C. Nhung, D. Van Thom, An Overview of Functionally Graded Materials: From Civil Applications to Defense and Aerospace Industries, Journal of Vibration Engineering & Technologies, 13 (2025) 68. https://doi.org/10.1007/s42417-024-01691-8
[3]. A. Karakoti, S. Pandey, V.R. Kar, Nonlinear transient analysis of porous P-FGM and S-FGM sandwich plates and shell panels under blast loading and thermal environment, Thin-Walled Structures, 173 (2022) 108985. https://doi.org/10.1016/j.tws.2022.108985
[4]. X.H. Dang, V.L. Nguyen, M.T. Tran, B.D. Tran, V.L. Nguyen, Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading, Proceedings of the Institution of Mechanical Engineers, 238 (2024) 6831–6846. https://doi.org/10.1177/09544062231226050.
[5]. B. Mohammadzadeh, H.C. Noh, Analytical method to investigate nonlinear dynamic responses of sandwich plates with FGM faces resting on elastic foundation considering blast loads, Composite Structures, 174 (2017) 142–157. https://doi.org/10.1016/j.compstruct.2017.03.087.
[6]. P. Shi, V.N.V. Hoang, J. Yang, H. Shou, Q. Li, F. Turan, Free vibration and nonlinear transient analysis of blast-loaded FGM sandwich plates with stepped face sheets: Analytical and artificial neural network approaches, Thin-Walled Structures, 206 (2025) 112667. https://doi.org/10.1016/j.tws.2024.112667
[7]. S. Chandrasekaran, S. Pachaiappan, Numerical analysis and preliminary design of topside of an offshore platform using FGM and X52 steel under special loads, Innovative Infrastructure Solutions, 5 (2020) 86. https://doi.org/10.1007/s41062-020-00337-4
[8]. A. Reza; P. Puya, D. Ali, G. Majid, Dynamic Response of FGM Plates Under Blast Load, International Journal of Advanced Design & Manufacturing Technology, 16 (2023) 37. https://doi.org/10.30486/ADMT.2021.1920150.1239
[9]. T. Dao Minh, T. Do Van, M. Phung Van, H. Pham Huy, Bending and buckling responses of organic nanoplates considering the size effect, Transport and Communications Science Journal, 75 (2024) 2015–2029. https://doi.org/10.47869/tcsj.75.7.1
[10]. T. Van Toan, T.T.H. Huyen, D. Van Doan, Vibration and buckling analysis of nanoplates resting on variable elastic foundations, Transport and Communications Science Journal, 75 (2024) 2238–2251. https://doi.org/10.47869/tcsj.75.9.1
[11]. M.S.H. Al-Furjan, M.X. Xu, A. Farrokhian, G.S. Jafari, X. Shen, R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves in Random and Complex Media, 35 (2025) 1147–1171. https://doi.org/10.1080/17455030.2022.2030499.
[12]. P. Pham Minh, 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, 71 (2020) 853–867. https://doi.org/10.25073/tcsj.71.7.10.
[13]. D.H. Duc, D. Van Thom, P.M. Phuc, Buckling Analysis of Variable Thickness Cracked Nanoplatesconsiderting the Flexoelectric Effect, Transport and Communications Science Journal, 73 (2022) 470–485. https://doi.org/10.47869/tcsj.73.5.3
[14]. T. Vu Van, T. Do Van, Determine the influence factor of geometrical parameters on the dynamic characteristics of the micro crab-shaped beam, Transport and Communications Science Journal, 76 (2025) 530–540. https://doi.org/10.47869/tcsj.76.4.7.
[15]. M.A. Al-Shugaa, A.E.S. Musa, H.J. Al-Gahtani, Ritz Method-Based Formulation for Analysis of FGM Thin Plates Undergoing Large Deflection with Mixed Boundary Conditions, Arabian Journal for Science and Engineering, 49 (2024) 14225–14239. https://doi.org/10.1007/s13369-024-08871-4.
[16]. H.H. Le, V.K. Tran, N.T. Hoang, T.H. Phuong Thanh, Nonlinear free oscillation of tri-directional functionally graded porous skew-plates with variable thickness in high-thermal environment, Case Studies in Thermal Engineering, 70 (2025) 106101. https://doi.org/10.1016/j.csite.2025.106101.
[17]. N. Van Chinh, L.X. Phong, P. Van Vinh, T. Van Ke, P. Van Minh, Nonlinear vibration characteristics of multi-directionally graded porous material beams resting partly on elastic foundations, The Journal of Strain Analysis for Engineering Design, 60 (2025) 505-525. https://doi.org/10.1177/03093247251326446.
[18]. N.T.K. Lam, P. Mendis, T. Ngo, Response Spectrum Solutions for Blast Loading, Electronic Journal of Structural Engineering, 4 (2004) 28–44. https://doi.org/10.56748/ejse.439.
[19]. V. K. Trai, P. Malekzadeh, V.K. Tran, Q.H. Pham, T.M. Ket, A novel triangular element model for vibration analysis of FG-TPMS plate integrated with magneto-electric layers subjected to double explosive load, Ships and Offshore Structures, 2025 (2025) 1–25. https://doi.org/10.1080/17445302.2025.2457460.
[20]. N.T. Hong, Analysis of composite honeycomb sandwich panels under blast loads, Ships and Offshore Structures, 2024 (2024) 12-34. https://doi.org/10.1080/17445302.2024.2395186.
[21]. Q.H. Pham, P.C. Nguyen, V.K. Tran, Effects of hygro-thermal environment on dynamic responses of variable thickness functionally graded porous microplates, Steel and Composite Structures, 50 (2024) 563–581. https://doi.org/10.12989/scs.2024.50.5.563.
[22]. Q.H. Pham, T.A. Nguyen, N.T. Do, V.K. Tran, M.N. Nguyen, Static and vibration analyses of functionally graded porous shell structures by using an averaged edge/node-based smoothed MITC3 element, Computers & Mathematics with Applications, 153 (2024) 56–70. https://doi.org/10.1016/j.camwa.2023.10.037.
[23]. Q.H. Pham, V. Ke Tran, T. Thanh Tran, V. Chinh Nguyen, A.M. Zenkour, Nonlocal higher-order finite element modeling for vibration analysis of viscoelastic orthotropic nanoplates resting on variable viscoelastic foundation, Composite Structures, 318 (2023) 117067. https://doi.org/10.1016/j.compstruct.2023.117067.
[24]. V.K. Tran, Q.H. Pham, T. Nguyen-Thoi, A finite element formulation using four-unknown incorporating nonlocal theory for bending and free vibration analysis of functionally graded nanoplates resting on elastic medium foundations, Engineering with Computers, 38 (2022) 1465–1490. https://doi.org/10.1007/s00366-020-01107-7.
[25]. T.T. Tran, V.K. Tran, P.B. Le, V.M. Phung, V.T. Do, H.N. Nguyen, Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method, Advances in Civil Engineering, 2020 (2020) 12-30. https://doi.org/10.1155/2020/1471037.
[26]. P. Van Minh, T. Van Ke, A Comprehensive Study on Mechanical Responses of Non-uniform Thickness Piezoelectric Nanoplates Taking into Account the Flexoelectric Effect, Arabian Journal for Science and Engineering, 48 (2023) 11457–11482. https://doi.org/10.1007/s13369-022-07362-8.
[27]. T.T.T. Thi, V.K. Tran, Q.H. Pham, Static and Dynamic Analyses of Multi-Directional Functionally Graded Porous Nanoplates with Variable Nonlocal Parameter Using MITC3 + Element, Journal of Vibration Engineering & Technologies, 12 (2024) 5147–5171. https://doi.org/10.1007/s42417-023-01189-9.
[28]. I. ANSYS, Theory Reference 24.1, Southpointe 275 Technology Driver Canonsburg, 2024.
[29]. P.H. Tu, T. Van Ke, V.K. Trai, L. Hoai, An isogeometric analysis approach for dynamic response of doubly-curved magneto electro elastic composite shallow shell subjected to blast loading, Defence Technology, 41 (2024) 159–180. https://doi.org/10.1016/j.dt.2024.06.005.
[30]. M. Song, S. Kitipornchai, J. Yang, Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Composite Structure, 159 (2017) 579–588. https://doi.org/10.1016/j.compstruct.2016.09.070.
[31]. T. Van Do, D.K. Nguyen, N.D. Duc, D.H. Doan, T.Q. Bui, Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Structures, 119 (2017) 687–699. https://doi.org/10.1016/j.tws.2017.07.022.
[32]. H.N. Nguyen, T.N. Canh, T.T. Thanh, T.V. Ke, V.D. Phan, D.V. Thom, Finite element modelling of a composite shell with shear connectors, Symmetry, 11 (2019), 527. https://doi.org/10.3390/sym11040527
[33]. N.C. Tho, N.T. Ta, D.V. Thom, New numerical results from simulations of beams and space frame systems with a tuned mass damper, Materials, 12 (2019), 1329. https://doi.org/ 10.3390/ma12081329
[34] T. V. Ke, P. V. Minh, N.T. Dung, L.M. Thai, D. V. Thom, Flexoelectric effect on bending and free vibration behaviors of piezoelectric sandwich FGP nanoplates via nonlocal strain gradient theconory, Journal of Vibration Engineering & Technologies, 12 (2024), 6567-6596. https://doi.org/10.1007/s42417-023-01270-3
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Nhận bài
11/08/2025
Nhận bài sửa
25/09/2025
Chấp nhận đăng
06/10/2025
Xuất bản
15/10/2025
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Kiểu trích dẫn
Nguyễn Vũ, H. (1760461200). Ảnh hưởng của tải trọng nổ tới dao động cưỡng bức của tấm làm bằng vật liệu có cơ tính biến đổi với chiều dày không đồng nhất. Tạp Chí Khoa Học Giao Thông Vận Tải, 76(8), 1049-1063. https://doi.org/10.47869/tcsj.76.8.2
