Nonlinear static and dynamic analysis of mulltilayer nanocomposite structures in solar cell

VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY VU MINH ANH NONLINEAR STATIC AND DYNAMIC ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN SOLAR CELL MASTER’S THESIS Ha Noi, 2019 VIETNAM NATIONAL UNIVERSITY, HANOI VIETNAM JAPAN UNIVERSITY VU MINH ANH NONLINEAR STATIC AND DYNAMIC ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN SOLAR CELL MAJOR: INFRASTRUCTURE ENGINEERING RESEARCH SUPERVISORS: Prof Dr Sci NGUYEN DINH DUC Ha Noi, 2019 ACKNOWLEDGEMENT Firstly, I want to send deep gratitude to my instructor, Professor Nguyen Dinh Duc, who has extended his arms to receive and inspire me to carry out his thesis over the years Despite many difficulties and failures in implementing this thesis, this thesis is still completed with his dedicated guidance as well as help with time, ideas and indepth knowledge I will remember his sharing, helping, guiding me with enthusiasm I would like to thank all the teachers who came from Infrastructure Engineering Program: Professor Kato, Professor Dao Nhu Mai, Professor Nagai, Doctor Phan Le Binh and Doctor Nguyen Tien Dung The professors and doctors have always given me great advice, orientations, pointing out the irrational points in the thesis to get me the best, most useful thesis Besides, I was always assisted by the program assistant Bui Hoang Tan In particular, in the process of studying and implementing the thesis, I always get support from Vietnam Japan University, I feel happy and happy for that Indispensably, I want to say thank you to Doctor Tran Quoc Quan, Doctor Nguyen Thi Thuy Anh for not only giving valuable reviews but also making new developments in world studies to help my thesis have more attractions through discussions at the laboratory meetings I would like to thank all VJU students, classmate for the happy time, for sharing and helping, Finally, I sincerely thank my family, close friends who are always by my side motivate and help me complete this thesis I TABLE OF CONTENTS ACKNOWLEDGEMENT I LIST OF FIGURES IV LIST OF TABLES VI NOMENCLATURES AND ABBREVIATIONS VII ABSTRACT VIII CHAPTER 1: INTRODUCTION 1.1 Background 1.2 Research objectives 1.3 The layout of the thesis CHAPTER 2: LITERATURE REVIEW 2.1 Literature review in Outside Vietnam 2.2 Literature review in Vietnam 13 CHAPTER 3: METHODOLOGY 15 3.1 Modelling of SC 15 3.2 Methodology 16 3.3 Basic Equation 17 3.4 Boundary Conditions 22 3.5 Nonlinear Dynamic Analysis 23 3.6 Nonlinear Static Stability 25 CHAPTER 4: RESULTS AND DISCUSSION 27 4.1 Introduction 27 II 4.2 Natural frequency 27 4.3 Dynamic response 28 4.4 Frequency – amplitude relation 32 4.5 Nonlinear Static 33 4.6 Critical buckling load 35 CHAPTER 5: CONCLUSIONS AND FURTHER WORKS 37 5.1 Conclusions 37 5.2 Future works 37 APPENDIX 39 PUBLICATIONS 40 REFERENCES 40 III LIST OF FIGURES Figure 1.1 Modelling of surface transitions organic solar cell Figure 1.2 Modelling of a solar cell using perovskite as a light-sensitive substance and structure of the energy zone of the solar cell Figure 3.1 Geometry and coordinate system of nanocomposite multilayer SC 16 Figure 4.1 Influence of ratio a / b on the SC’s nonlinear dynamic response ( P = 0, P x y = ) 29 Figure 4.2 Influence of ratio a/h on the SC’s nonlinear dynamic response ( P = 0, P x y = ) 29 Figure 4.3 Effect of the exciting force amplitude Q on the dynamic response of SC ( P = 0, P x y = ) 30 Figure 4.4 Influence of the pre-loaded axial compression Px on SC’ dynamic response 30 Figure 4.5 Effect of the pre-loaded axial compression Py on the dynamic response of SC 31 Figure 4.6 Effect of initial imperfection W0 on the dynamic response of the SC 31 Figure 4.7 Influence of external force F on SC’ frequency – amplitude curves 32 Figure 4.8 The influence of initial geometrical imperfection on the SC’ stability with uniaxial compressive load 33 Figure 4.9 The influence of a/b ratio the SC’ load – deflection amplitude curve 34 IV Figure 4.10 The effect of elastic foundations on the SC’ the load – deflection amplitude curve 34 V LIST OF TABLES Table Initial thickness and properties materials of layers of SC 27 Table Effects of the thickness of layers and modes on natural frequencies of the nanocomposite multilayer organic solar cell 28 Table Effects of the elastic foundations and ratio a/b on the critical buckling load of the SC 35 VI NOMENCLATURES AND ABBREVIATIONS SC a b h Oxyz E ,n Solar Cell The length of SC The width of SC The thickness of SC The space coordinates system The elastic modulus and Poisson ratio u , v , w0 k1 The displacements in the x, y and z directions k2 The Pasternak foundation W0 = µ h The initial imperfection IM FM Immovable Freely movable GygaPascal = 109 Pascal Numbers of half waves in x, y direction GPa m, n The Winker foundation VII ABSTRACT This thesis focuses on the study of the mechanical behavior of Solar Cell (SC) As we know, SC is a sustainable solution for energy supply and greenhouse gas reduction Therefore, SC is currently hot topic that attracted a lot of interest from scientists worldwide Currently, there are many research about SC such as Replace component materials in OS or how to improve SC performance … However, there is very little research on mechanical properties, mechanical behavior of SC Therefore, this thesis will focus on investigation of mechanical behavior of SC SC are made by layers under mechanical load Besides, SC are supported by elastic foundations: winker foundation and Pasternak foundation In details, nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell will be investigated By using classical plate theory, Glarkin method along with Runge - Kutta method, the effect of geometrical parameter, elastic foundation, load, and imperfection on the nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell will be described in detail Besides, some numerical results as critical buckling load and natural frequency also will be shown Key words: Dynamic Analysis, Nonlinear Static, Organic Solar Structures, The Classical Theory, Mechanical Load VIII Figure 4.6 indicate that the SC’ dynamic response is impacted by initial imperfection W0 Clearly, the amplitudes of SC’ nonlinear vibration will change much when the amplitude of initial imperfection rise 4.4 Frequency – amplitude relation Figure 4.7 shows the influence of external force F on the frequency – amplitude relations of SC’ frequency – amplitude curves As can be seen, when the excitation force decreases, the curves of forced vibration are closer to the curve of free vibration 0.1 F=0N F = x 107 N Amplitude A) 0.08 F = x 107 N 0.06 0.04 (m,n)=(1,1), P x = 0, P y = 0, W0 = 0,q=300sin(3500t) 0.02 0 10 20 30 40 50 Frequency ratio 60 70 80 Figure 4.7 Influence of external force F on SC’ frequency – amplitude curves 32 4.5 Nonlinear Static 0.25 =0 = 0.1 = 0.2 = 0.3 0.2 Fx (GPa) 0.15 0.1 0.05 a=b; m=n=1; k1 = 0.1 GPa/m; k2 = 0.02 GPa.m 0 0.2 0.4 0.6 0.8 1.2 1.4 1.6 1.8 W/h Figure 4.8 The influence of initial geometrical imperfection on the SC’ stability with uniaxial compressive load The effect of imperfection about geometrical on the SC’ load – deflection amplitude curve is described in figure 4.8 It can be noted that there is always point where SC's load carrying capacity will be changed under the influence of initial gemetrical imperfection Specifically, the SC’s static stability will be negatively affected by imperfection parameter along with condition is small defection’value The SC's load carrying capacity will reduce when the rising the initial imperfection However, when passing the point that is mentioned above, the SC's load carrying capacity will rise with the increasing of initial imperfection 33 Figure 4.9 The influence of a/b ratio the SC’ load – deflection amplitude curve The effect of a / b ratio on the SC’ load – deflection amplitude curve is demonstrated in figure 4.9 From figure 4.9, there is point like in the discussion of the figure 4.8 Besides, the static stability will reduce when incresing ratio a / b On contrary, the load rise of ratio a/b inrease static stability of SC 0.6 =0 = 0.1 0.5 (1): k1 = 0.1 GPa/m; k2 = 0.02 GPa.m F x(GPa) 0.4 (2): k1 = 0.2 GPa/m; k2 = 0.04 GPa.m (3) (3): k1 = 0.4 GPa/m; k2 = 0.05 GPa.m 0.3 (2) 0.2 (1) 0.1 a=b; m=n=1 0 0.5 1.5 2.5 W/h Figure 4.10 The effect of elastic foundations on the SC’ the load – deflection amplitude curve 34 Figure 4.10 shows the influnce of elastic foundation on the SC’ load – deflection ampiltude curved It can be seen that the rise of the modulus k1 , k2 will improve the SC’ load carring capacity while initial imperfection still the same It demonstrates that elastic foundations have significant influence on the SC’s static stability 4.6 Critical buckling load Table 4.3 Effects of the elastic foundations and ratio a/b on the SC’ critical buckling load (unit: GPa) k1 ; k2 a/b (GPa / m; GPa.m) 1.5 2.5 0.1; 0.02 0.29368 0.71574 1.4681 2.6607 0.1; 0.04 0.29371 0.71580 1.4682 2.6610 0.2; 0.02 0.29373 0.71585 1.4684 2.6614 0.2; 0.04 0.29376 0.71593 1.4685 2.6615 0.3; 0.02 0.29383 0.71611 1.4696 2.6623 0.3; 0.04 0.29387 0.71617 1.4704 2.6633 Table 4.3 shows the influence of elastic foundations and a / b ratio on the SC’ critical buckling load Table 4.3 indicated that when elastic foundations and ratio a / b increase, the critical buckling load of SC will raise Specifically, if the value of ratio a/b is fixed along with the value of elastic foundations increase, the crirical buckling load will increase In case, the critical buckling load reachs the highest value at a / b = 2.5 In contrast, if the value of elastic foundations is fixed along with the value of ratio a / b increase, the crirical buckling load will increase In case, the critical buckling load reachs the highest value at k1 = 0.3 GPa / m; k2 = 0.04 GPa.m The critical buckling load is 35 determined that will very helpful If there are the same values elastic foundation and a / b ratio, applying force to SC less than the critical buckling load’ value will help SC operate in a safe environment 36 CHAPTER 5: CONCLUSIONS AND FURTHER WORKS 5.1 Conclusions This thesis investigates the nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell In order to evaluate the role of geometrical parameter, initial imperfection, elastic foundation and load on the nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell; classical theory, Galerkin method as well as Runge – Kutta method are used This thesis has some remarkable conclusions as: The geometrical parameter, elastic foundation has positive influence on the nonlinear static and dynamic analysis of solar cell The increasing of excitation force amplitude Q and Px rise nonlinear dynamic amplitude of solar cell The amplitudes of SC’ nonlinear vibration will change much when the amplitude of initial imperfection rise Natural frequency of OS will significant changes according to geometrical parameter and mode m, n Changing the value of elastic foundations and geometrical parameter will lead to changing of critical buckling load This thesis has some remarkable results These results are the scientific basis to improve currently durability of solar panels Based on the obtained results, designers, scientists and manufacturers will select geometric parameters to ensure load capacity of solar panels Besides, it ensures the electrical performance of solar panels 5.2 Future works This thesis has obtained some remarkable results But, those results don’t compare with other research’s results yet to include the reliability of those results It can be explained that those results are the first result in this research direction Besides that, this thesis focuses on using analytical method, to have more interesting results this thesis can implement some simulation about dynamic … 37 In this thesis, the results are obtained with a number of assumption such as: placed on elastic foundations, uniformly distributed force on the surface and stress at the contact surface between layers is ignored This is unlikely to happen in practice Therefore, in order to develop this research in the future, the above-mentioned assumption should be considered in conjunction with the problem In addition, the impact of environmental factors should also be considered 38 APPENDIX n Ek hk vk Ek hk ; A = ;A22 = A11 ; å 12 2 k =1 - vk k =1 - vk n A11 = å n Ek hk ; k =1 (1 + vk ) A16 = A26 = 0; A66 = å n Ek hk zk vk Ek hk zk ; B = ;B22 = B11 ; å 12 2 k =1 - vk k =1 - vk n B11 = å n Ek hk zk ; k =1 (1 + vk ) B16 = B26 = 0; B66 = å n Ek ỉ hk3 vk Ek hk zk h z + ; D = ;D22 = D11 ; ữ 12 ỗ k k 12 ø k =1 - vk è k =1 - vk n D11 = å æ hk3 Ek ỗ hk zk + ữ ; 12 ø k =1 (1 + vk ) è n D16 = D26 = 0; D66 = å D = - A122 + A22 A11 , C*31 = B , C*32 = - 66 A66 A66 A22 * A A B - A22 B11 * A12 B22 - A22 B12 * , C12 = - 12 , C13 = 12 12 , C14 = D D D D A A B -A B A B -A B * C22 = 11 , C*23 = 12 11 11 12 , C*24 = 12 12 11 22 D D D C11* = H1 = S14a m4 + S15 b n4 + S16a m2 b n2 - éë k1 + k2 (a m2 + b ) ùû æ2 S b a S12 b n a m ö H = - ỗ 11 *n m + ữ A11* ứ è A22 ỉ b n4 a m4 H3 = - ỗ + * * ữ ố 16 A22 16 A11 ø 39 ab ỉS S ỉ -8a b T1 = ỗ 11* + 12* ữ ç ÷, è A22 A11 ø è 3ab ø é é A* b + A23* a m4 - ( A32* - A13* - A24* )a m2 b n2 ù ù 4 2 ë 14 n ûú, T2 = ê( S11a + S12 b + S13a b ) * * * * * 2 é A11b n + A22a m + ( A12 + A12 + A31 )a m b n ù ú êë ë û û T3 = - b4 A22* , * * * * * 2 æ 32 ö A14 b + A23a - ( A32 - A13 - A24 ) a b T4 = b a , ỗ - ữ ab ố 9 ø A11* b + A22* a + ( A12* + A12* + A31* ) a b T5 = ( S14a + S15 b + S16a b ) (W + W0 ) , T6 = ab PUBLICATIONS Duc, ND; Seung – Eock, K; Quan, TQ; Minh Anh, V (2018) Noninear dynamic response and vibration of nanocomposite multilayer organic solar cell Composite Structures, 184, 1137- 1144 REFERENCES Akbari, A., Bagri, A., & Natarajan, S (1 October 2018) Dynamic response of viscoelastic functionally graded hollow cylinder subjected 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UNIVERSITY VU MINH ANH NONLINEAR STATIC AND DYNAMIC ANALYSIS OF MULTILAYER NANOCOMPOSITES STRUCTURES IN SOLAR CELL MAJOR: INFRASTRUCTURE ENGINEERING RESEARCH SUPERVISORS: Prof Dr Sci NGUYEN DINH DUC... foundation and Pasternak foundation In details, nonlinear static and dynamic analysis of multilayer nanocomposite structure in solar cell will be investigated By using classical plate theory, Glarkin