Effects of porosity on free vibration and nonlinear dynamic response of multi layered functionally graded materials subjected to blast loads

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO THI THU HA EFFECTS OF POROSITY ON FREE VIBRATION AND NONLINEAR DYNAMIC RESPONSE OF MULTI-LAYERED FUNCTIONALLY GRADED MATERIALS SUBJECTED TO BLAST LOAD MASTER’S THESIS VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO THI THU HA EFFECTS OF POROSITY ON FREE VIBRATION AND NONLINEAR DYNAMIC RESPONSE OF MULTI-LAYERED FUNCTIONALLY GRADED MATERIALS SUBJECTED TO BLAST LOAD MAJOR: INFRASTRUCTURE ENGINEERING CODE: 8900201.04QTD RESEARCH SUPERVISOR: Dr TRAN QUOC QUAN Ha Noi, 2020 ACKNOWLEDGEMENT First of all, I would like to express my sincere appreciation to my supervisor , Dr Tran Quoc Quan who has guided and created favorable conditions and regularly encouraged me to complete this thesis Thank you for all your thorough and supportive instructions, your courtesy and your enthusiasm Without your dedicated guidance, I absolutely have not conducted this research well Secondly, I would like to express my great thankfulness to Master’s Infrastructure Engineering Program for their wonderful supports, especially Prof.Sci Nguyen Dinh Duc, Prof Kato, Prof Nagayama, Dr Phan Le Binh, Dr Nguyen Tien Dung and Mr Bui Hoang Tan Their encouragement and assistance has facilitated me a lot during years studying in the VietNam – Japan University I also want to give my special thanks to all lecturers and staffs at The University of Tokyo for their warmly welcome and supports me in the internship time at Japan Thirdly, I would like to thank all the members at the Advanced Materials and Structural Laboratory, University of Technology- VNU, especially for Mr Vu Dinh Quang, Mr Vu Minh Anh, Mr Pham Dinh Nguyen spending their precious time to point out for me which theories and methodology should I use and give me advices to improve my thesis Finally, there are my family and my friends, who always stay by my side, motivate and encourage me from the beginning until the end of my studying I TABLE OF CONTENTS ACKNOWLEDGEMENT LIST OF TABLES LIST OF FIGURES NOMENCLATURES AND ABBREVIATIONS ABSTRACT CHAPTER 1: 1.1 Overview 1.1.1 Composite material – Functionally Graded Materials 1.1.2 FG 1.1.3 Bla 1.2 Research objectives 1.3 The layout of the thesis CHAPTER 2: 2.1 Structures 2.2 Porosity 2.3 Blast load CHAPTER 3: 3.1 Configurations of analyzed models 3.2 Methodology 3.3 Theoretical formulation 3.4 Solution procedure 3.5 Vibration analysis 3.5.1 Dy 3.5.2 Na CHAPTER 4: 4.1 Validation of the present results 4.2 Natural frequency 4.3 Dynamic response CHAPTER 5: APPENDIX II LIST OF TABLES Table 1.1 Properties of component materials of FGM material [3] Table 4.1 Comparison the natural frequencies s1  of homogenous plates with a / b  1, a / h  20, k1  0, k2 0 Table 4.2 Comparison of natural fundamental frequency parameters  of simply square FGM plates with other theories ( h / b  0.1 ) .29 Table 4.3 The effects of porosity ratio on natural frequency of FGM sandwich plates 31 Table 4.4 Influences of temperature increment, elastic foundations and the volume fraction index on natural frequencies of the FGM sandwich plate with porosity I 32 III LIST OF FIGURES Fig 1.1 The distribution types of FGM sandwich material Fig 3.1 FGM sandwich plate resting on elastic foundation 12 Fig 3.2 FGM-ceramic- FGM model 13 Fig 3.3 Porosity – I: evenly distributed, Porosity – II: unevenly distributed .14 Fig 3.4 Blast pressure function 17 Fig 4.1 Influences of power law index N on the nonlinear dynamic response of the FGM sandwich plates with porosity I 33 Fig 4.2 Influences of power law index N on nonlinear dynamic response of the FGM sandwich plates with porosity II 33 Fig 4.3 Influences of porous ratio on nonlinear dynamic response of the FGM sandwich plates with porosity I 34 Fig 4.4 Influences of type of porosity on nonlinear dynamic response 35 Fig 4.5 Influences of a / b ratio on nonlinear dynamic response of the FGM sandwich plates with porosity I 36 Fig 4.6 Influences of a / h ratio on nonlinear dynamic response of the FGM sandwich plates with porosity I 37 Fig 4.7 Influences of Pasternak foundation on nonlinear dynamic response of the FGM sandwich plates with porosity I 37 Fig 4.8 Influences of Winkler foundation on nonlinear dynamic response of the FGM sandwich plates with porosity I 38 Fig 4.9 Effect of parameter characterizing the duration of the blast pulse Ts on nonlinear response of the FGM sandwich plate with porosity I under blast load 39 IV NOMENCLATURES AND ABBREVIATIONS h h Functionally Graded Material The length of plate The width of plate The thickness of plate The thickness of the core layer h The thickness of FGM face-sheet FGM a b The Winker foundation k k GPa m, n The Pasternak foundation GigaPascal =109 Pascal Numbers of half waves in x , y direction V ABSTRACT The effects of porosity ratio on free vibration and nonlinear dynamic response of FGM sandwich plates with two FGM face-sheets and a homogeneous core as ceramic resting on elastic foundations subjected to blast load are investigated in this thesis by implementing the third-order shear deformation theory Two types of porosity are proposed, namely evenly distributed porosity and unevenly distributed porosity Assumption that the material properties of multilayered FGM plate to be changed in the thickness direction accord with a simplepower law distribution with regard to the volume proportion of the components This study obtains numerical results by using the Galerkin method and fourth-order Runge-Kutta method illustrating the significant effects of porous fractions, geometrical parameters, the elastic foundation, blast loads on the nonlinear dynamic response of FGM sandwich plates Key words: Porosity, Functionally graded sandwich plate, Blast loading, The third-order shear deformation theory VI CHAPTER 1: 1.1 INTRODUCTION Overview 1.1.1 Composite material – Functionally Graded Materials Composite material is a material composed of two or more different types of component materials in order to achieve superior properties such as light weight, high stiffness and strength, ability of heat resistance and chemical corrosion resistance, good soundproofing, thus it plays a crucial role in advanced industries in the world that are extensively applied across wide range of fields such as: aviation, aerospace, mechanics, construction, automotive [1] [2] However, this material has a defect as a sudden change of material properties at the junction between the layers is likely to generate large contact stresses at this surface One of the solutions to overcome this disadvantage of layered composite material is to use Functionally Graded Material (FGM) which is a material made up of two main component materials as ceramic and metal, in which the volume ratio of each component varies smoothly and continuously from one side to the other according to the thickness of the structure so the functional materials avoid the common disadvantages in composite types such as the detachment between layers material, fibers breakage and high stress in the surface, which can cause material destruction and reduce the efficiency of the structure, especially in heatresistant structures Due to the high modulus of elasticity E , the thermal conduction coefficient K and the very low coefficient of thermal expansion  , the ceramic composition makes the material highly variable with high hardness and very good heat resistance While the metal components make the modified materials more flexible, more durable and overcome the cracks that may occur due to the brittleness of ceramic materials when subjected to high temperature (Table 1.1) Table 1.1 Properties of component materials of FGM material [3] Material Aluminum ( Al ) Ti  Al  4V Ceramic: Zirconia ( ZrO2 ) Aluminum oxide 1.1.2 FGM classification Depending on the power law of the volume ratio of component materials, we can classify different types of FGM Each of these FGM materials is characterized by different mechanical and physical properties by a function that determines the material properties (effective properties), and the value of the function varies with thickness Mathematical functions of material properties used to classify materials [4] Specifically, there are three main types of FGM A power-law distribution P-FGM: is a type of material having a volume fractions of ceramic and metal components which is assumed to vary according to thickness of structure and conforming to the power-law function [5, 6]: Vm ( z )     where Vm ,Vc N : the volume fractions of metal and ceramic, respectively 2h : t he volum e distrib ution (0  N ) CHAPTER 5: CONCLUSIONS Based on higher order shear deformation, thesis investigates the effects of porosity on nonlinear dynamic response and free vibration of the multi-layered FGM plate subjected to blast load Thesis obtains main results as follows: - The differential motion equations analyze nonlinear dynamic response of porous FGM sandwich plates on elastic foundations subjected to blast load and natural frequency - Generally, the existence of porosity reduces the stiffness of FGM sandwich plate Consequently, the deflection amplitude increases and the natural frequency decreases as the porosity fraction rises However, the natural frequency is not affected by the porosity I fraction of porous FGM sandwich plate Besides, the dynamic deflection of porosity I sandwich plate is larger than this ones of porosity II as considering the same porosity value The elastic foundations have positive impacts on dynamic behavior of the sandwich plate, and the Pasternak foundation have more beneficial effect than the Winkler one - Temperature increment significantly effects on the nonlinear vibration of the porous sandwich plate Temperature increment is considered as external impact which is disadvantage to natural frequency and deflection amplitude of the sandwich plate - The effects of geometrical parameters ( parameter characterizing the duration of the blast pulse Ts on the nonlinear dynamic responses of the FGM sandwich plates with porosity are remarkable 40 APPENDIX Appendix A  h cm  I m  I N1     h5 m  I4 N1 cm  h   N 80   I m h  N 448 (N  2)(N  3)(N  4)  (N  2)(N  3)(N  4)(N  6)(N  7) Appendix B  H 12  x  c      41   H  H 1 13 y   H  c  1    P x , f   H  w   H H 31 w  11  c H 32 x      H 33  y    1    2(1  )  E  3c E ,  w  y, 42 Appendix C h   11 c12  n  2   h 12 m  c     a c    h 13 n  c     c   E n  b 43 n  b    15 h  21 h   1m   E  3c E   c E  3c E  , 2(1  ) a  11 3231  h 16  22  4 2(1  ) h  23 h ,     31 n  E  3c E  c E  3c E  , 2(1  ) b  11 3231  E c E c E    E1 2  m    n  h 17 45 REFERENCES [1] Nguyễn Hoa Thịnh, Nguyễn Đình Đức, Vật liệu Composite-Cơ học Cơng Nghệ, Hà Nội: Nhà xuất khoa học kĩ thuật, 2002 [2] Trần Ích Thịnh, Vật liệu Compozit- Cơ hoc tính tốn kết cấu, Hà Nội: Nhà xuất Giáo dục, 1994 [3] M.Koizumi, "FGM activities in Japan," Composites B, vol 28, pp 1-4, 1997 [4] B Q Bình, "Vật liệu chức tiềm ứng dụng VIệt Nam," Tạp chí khoa học cơng nghệ hàng hải 18, 2009, pp 58-63 [5] K M., "The concept of FGM Ceramic transactions," Functionally Graded Materials, vol 34, pp 3-10, 1993 [6] S HS., "Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties," International Journal of Mechanical Sciences, vol 4, pp 466-478, 2007 [7] J.N Reddy, C.D Chin, "Therm-mechanical analysis of functionally graded cylinders and plates," J Thermal Stress, vol 21, pp 593-626, 1998 [8] Chen, H , Wang, A , Hao, Y., Zang, W., "Free vibration of FGM sandwich doubly- curved shallow shell based on a new shear deformation theory with stretching effects," Composite Structures , vol 179, pp 50-60, 2017 [9] Chen Liang, Yan Qing Wang, "A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation," Composite Structures, vol 247, September 2020 [10] S.J.Singh, S.P.Harsha, "Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach," Thin-Walled Structures, vol 150, p 106668, 2020 [11] S Kitipornchai, J Yang, K M Liew, "Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections," International Journal of Solids and Structures, vol 41, no 9-10, pp 22352257, 2004 [12] H VanTung, "Thermal and thermomechanical postbuckling of FGM sandwich plates resting on elastic foundations with tangential edge constraints and temperature dependent propertie," Composite Structures, vol 131, pp 1028-1039, 2015 46 [13] A.Alibeigloo, "Three dimensional coupled thermoelasticity solution of sandwich plate with FGM core under thermal shock," Composite Structures, vol 177, pp 96-103, 2017 [14] Xian-Kun Xia, Hui-Shen Shen, "Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment," Journal of Sound and Vibration, vol 314, no 1-2, pp 254-274, 2008 [15] Behzad Mohammadzadeh, Hyuk ChunNoh, "Analytical method to investigate nonlinear dynamic responses of sandwich plates with FGM faces resting on elastic foundation considering blast loads," Composite Structures, vol 174, pp 142-157, 2017 [16] MohammedSobhy, "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment," International Journal of Mechanical Sciences, vol 110, pp 6277, 2016 [17] Chien H.Thai, S.Kulasegaram, Loc V.Tran, H.Nguyen-Xuan, "Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach," Computers & Structures, vol 141, pp 94-112, 2014 [18] TaoFu, Zhaobo Chen, Hongying Yu, Zhonglong Wang, Xiaoxiang Liu, "An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material," Composites Part B: Engineering, vol 151, pp 161-172, 2018 [19] A M.Zenkour, "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities," Composite Structures, vol 201, pp 38-48, 2018 [20] S.J.Singh, S.P.Harsha, "Thermo-mechanical analysis of porous sandwich S-FGM plate for different boundary conditions using Galerkin Vlasov's method: A semi-analytical approach," Thin-Walled Structures, vol 150, p 106668, 2020 [21] A.Mojahedin, M.Jabbarib, A.R.Khorshidvand, M.R.Eslamic, "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory," ThinWalled Structures, vol 99, pp 83-90, 2016 [22] AhmetPolat, OzkanSarikaya, ErdalCelik, "Effects of porosity on thermal loadings of functionally graded Y2O3–ZrO2/NiCoCrAlY coatings," Materials & Design, vol 23, no 7, pp 641-644, 2002 47 [23] D.Chen, J.Yang, S.Kitipornchai, "Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method," Archives of Civil and Mechanical Engineering, vol 19, no 1, pp 157-170, 2019 [24] Yan QingWang, Jean W.Zu, "Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment," Aerospace Science and Technology, vol 69, pp 550-562, 2017 [25] YuewuWang, DafangWu, "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory," Aerospace Science and Technology, vol 66, pp 83-91, 2017 [26] P.Phung-Van, M.Abdel Wahab, "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis," Composites Part B: Engineering, vol 164, pp 215-225, 2019 [27] Pham HongCong, Nguyen DinhDuc, "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT, " Aerospace Science and Technology, vol 77, pp 419-428, 2018 [28] Minh-ChienTrinh, Dinh-DucNguyen, Seung-EockKim, "Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature," Aerospace Science and Technology, vol 87, pp 119-132, 2019 [29] Tuan Duc Ngo, Priyan Mendis, "Behavior of Ultrahigh-Strength Prestressed Concrete Panels Subjected to Blast Loading," Journal of Structural Engineering , vol 133, no 11, pp 1582-1590, 2007 [30] Tin V.Do, Thong M.Pham, HongHao, "Stress Wave Propagation and Structural Response of Precast Concrete Segmental Columns under Simulated Blast Loads," International Journal of Impact Engineering, vol 143, p 103595, 2020 [31] DemetBalkan, ệzgỹrDemir, AytaỗArkolu, "Dynamic analysis of a stiffened composite plate under blast load: A new model and experimental validation, " International Journal of Impact Engineering, vol 103591, p 143, 2020 [32] NanZhao, ShujianYao, DuoZhang, FangyunLu, ChengmingSun, "Experimental and numerical studies on the dynamic response of stiffened plates under confined blast loads," Thin-Walled Structures, vol 154, p 106839, 2020 [33] C.Geretto, S.Chung Kim Yuen, G.N.Nurick, "An experimental study of the effects of degrees of confinement on the response of square mild steel plates subjected to blast loading," International Journal of Impact Engineering, vol 79, pp 32-44, 2015 48 [34] CenkAksoylar, Akın Ömercikoğlu, Zahit Mecitoğlu, Mehmet H.Omurtag, "Nonlinear transient analysis of FGM and FML plates under blast loads by experimental and mixed FE methods," Composite Structures, vol 94, no 2, pp 731-744, 2012 [35] Mustafa Übeyli, Erhan Balci, BertanSarikan, M Kemal Öztaş,NecipCamuşcu, R Orhan Yildirim, Ömer Keleş, "The ballistic performance of SiC–AA7075 functionally graded composite produced by powder metallurgy," Materials & Design (1980-2015), vol 56, pp 31-36, 2014 [36] M.Bodaghi, A.R.Damanpack, M.M.Aghdam, M.Shakeri, "Nonlinear active control of FG beams in thermal environments subjected to blast loads with integrated FGP sensor/actuator layers," Composite Structures, vol 94, no 12, pp 3612-3623, 2012 [37] Nelson Lam, Priyan Mendis, Tuan Ngo, "Response Spectrum Solutions for Blast Loading," Electronic Journal of Structural Engineering, vol 4, pp 28-44, 2004 [38] J Reddy, Mechanics of laminated composite plates and shells: theory and analysis, Boca Raton: CRC Press, 2004 [39] Xian-KunXia, Hui-Shen Shen, "Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment," Journal of Sound and Vibration, vol 314, no 1-2, pp 254-274, 2008 49 ... is to investigate the effects of porosity on vibration and nonlinear dynamic response of multi- layered FGM subjected to blast load  Studies the effects of porosity to FGM sandwich plates and. .. NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY DO THI THU HA EFFECTS OF POROSITY ON FREE VIBRATION AND NONLINEAR DYNAMIC RESPONSE OF MULTI- LAYERED FUNCTIONALLY GRADED MATERIALS SUBJECTED TO. .. Influences of a / b ratio on nonlinear dynamic response of the FGM sandwich plates with porosity I 36 Fig 4.6 Influences of a / h ratio on nonlinear dynamic response of the FGM sandwich