Nhận dạng thanh mềm công xôn

ĐẠI HỌC QUỐC GIA TP HCM TRƯỜNG ĐẠI HỌC BÁCH KHOA NGUYỄN VĂN THUẬT NHẬN DẠNG THANH MỀM CÔNG XÔN IDENTIFICATION OF A FLEXIBLE CANTILEVER BEAM Chuyên ngành: Kỹ thuật điện tử Mã số: 8.52.01.14 LUẬN VĂN THẠC SĨ TP HỒ CHÍ MINH, tháng năm 2020 CƠNG TRÌNH ĐƯỢC HỒN THÀNH TẠI TRƯỜNG ĐẠI HỌC BÁCH KHOA - ĐHQG - HCM Cán hướng dẫn khoa học: PGS.TS Nguyễn Quốc Chí Cán chấm nhận xét 1: PDG.TS Nguyễn Thanh Phương Cán chấm nhận xét 2: TS Lê Ngọc Bích Luận văn thạc sĩ bảo vệ Trường Đại học Bách Khoa, ĐHQG Tp HCM ngày 03 tháng 09 năm 2020 Thành phần Hội đồng đánh giá luận văn thạc sĩ gồm: (Ghi rõ họ, tên, học hàm, học vị Hội đồng chấm bảo vệ luận văn thạc sĩ) Chủ tịch: PGS.TS Nguyễn Tấn Tiến Thư ký: TS Trần Việt Hồng Phản biện 1: PGS.TS Nguyễn Thanh Phương Phản biền 2: TS Lê Ngọc Bích Ủy viên: TS Ngơ Hà Quang Thịnh Xác nhận Chủ tịch Hội đồng đánh giá LV Trưởng Khoa quản lý chuyên ngành sau luận văn sửa chữa (nếu có) CHỦ TỊCH HỘI ĐỒNG TRƯỞNG KHOA ĐẠI HỌC QUỐC GIA TP.HCM TRƯỜNG ĐẠI HỌC BÁCH KHOA CỘNG HÒA XÃ HỘI CHỦ NGHĨA VIỆT NAM Độc lập - Tự - Hạnh phúc NHIỆM VỤ LUẬN VĂN THẠC SĨ Họ tên học viên: NGUYỄN VĂN THUẬT MSHV: 1870071 Ngày, tháng, năm sinh: 05/02/1995 Nơi sinh: Lâm Đồng Chuyên ngành: Kỹ thuật Cơ Điện Tử Mã số : 1870071 I TÊN ĐỀ TÀI : NHẬN DẠNG THANH MỀM CÔNG XÔN IDENTIFICATION OF A FLEXIBLE CANTILEVER BEAM II NHIỆM VỤ VÀ NỘI DUNG : - Xây dựng mơ hình động lực học sử dụng phương pháp Galerkin cho hệ thống dầm công xôn có bệ gá đặt chuyển động theo phương ngang - Xây dựng phương pháp nhận dạng hệ thống dầm công xơn - Thực mơ hình số thực nghiệm tìm thơng số hệ thống dầm cơng xơn mơ hình thí nghiệm III NGÀY GIAO NHIỆM VỤ : 19/08/2019 IV NGÀY HOÀN THÀNH NHIỆM VỤ : 07/06/2020 V CÁN BỘ HƯỚNG DẪN : PGS TS NGUYỄN QUỐC CHÍ Tp HCM, ngày 20 tháng 08 năm 2019 CÁN BỘ HƯỚNG DẪN (Họ tên chữ ký) CHỦ NHIỆM BỘ MÔN ĐÀO TẠO (Họ tên chữ ký) TRƯỞNG KHOA (Họ tên chữ ký) ACKNOWLEDGMENT I would like to sincerely and wholeheartedly thank Assoc Prof Nguyen Quoc Chi for his guidance and kindness throughout this work His patience as an advisor, boundless energy while teaching, and giving passion for research are to be commended and worth emulating I am indebted to him for cajoling me into doing experiments and thus opening a whole new exciting world for me His inspiration gives me the ability, mindset, and perseverance to be where I am now I thank Thinkalpha Co., Ltd members for making time in their busy schedules to comments at various stages of my Master's program and help me out on setting up the experimental system A special thanks to Siqi Pan and Assoc Prof James S Welsh at the University of Newcastle - Australia for their valuable suggestions and help with experiments Their cooperation has sprung a great impact on our research work Most importantly, I would like to thank my parents for their unconditional support, love, and affection Their encouragement and neverending kindness made everything easier to achieve ABSTRACT The theoretical and experimental solutions for vibrations of a flexible cantilever beam are studied, which could be found widely in mechanical structures This thesis considers the modeling, simulation, and experiment to identify the parameters of a flexible cantilever beam subjected to a moving hub First, we investigate in modeling a flexible cantilever beam that can be used to obtain its behaviors through numerical simulation The second objective is to develop a method to identify the parameter of the system To this end, we construct an experimental system Experimental techniques, such as forced vibration and pulse propagation, have been used to measure the behaviors and damping of materials Through simple experiments at various frequencies, the response of a cantilever beam subjected to a moving hub This response was successfully modeled with a theoretical solution that includes the presence of damping TÓM TẮT LUẬN VĂN Các phương pháp lý thuyết thực nghiệm cho dao động dầm cơng xơn mềm nghiên cứu, loại dầm tìm thấy rộng rãi kết cấu khí Luận văn xây dựng mơ hình hóa, mô thực nghiệm để xác định thông số dầm công xôn mềm gắn bệ chuyển động Đầu tiên, chúng tơi nghiên cứu mơ hình hóa dầm cơng xơn mềm để thu đáp ứng dầm thông qua mô số Mục tiêu thứ hai phát triển phương pháp xác định tham số hệ thống Để đạt mục tiêu này, xây dựng hệ thống thử nghiệm Các kỹ thuật thực nghiệm, chẳng hạn rung cưỡng lan truyền xung, sử dụng để đo đáp ứng giảm chấn dầm Thơng qua thí nghiệm đơn giản tần số khác nhau, đáp ứng dầm công xôn chịu tác động bệ chuyển động Đáp ứng mơ hình hóa thành cơng với giải pháp từ lý thuyết bao gồm diện giảm chấn LỜI CAM ĐOAN Tôi xin cam kết tất nội dung luận văn không chép cơng trình nghiên cứu cá nhân hay tổ chức Tôi xin thực nghiêm túc việc trích dẫn cơng trình báo, tham luận công bố sử dụng luận văn HỌC VIÊN NGUYỄN VĂN THUẬT TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1.1 Motivation 1.2 Objectives and Scope of The Dissertation CHAPTER 2: FLEXIBLE BEAM MODELING 2.1 Equations of Motion of The Moving Cantilever Beam 2.2 Derivation of Equation of Motion 2.2.1 The variation with respect to variable  2.2.2 The variation with respect to variable 𝑤 2.3 The Galerkin Decomposition 10 2.3.1 Modal shape function 10 2.3.2 Ordinary differential equations 13 CHAPTER 3: IDENTIFICATION METHOD 17 3.1 Introduction to Experimental Modal Analysis 17 3.2 Estimation of Frequency-Response Functions 19 3.3 Modal Parameter Estimation 24 3.4 Measurement Techniques 26 3.4.1 Basic Measurement System 26 3.4.2 Excitation Methods And Measurement 28 3.4.3 Single-Frequency Excitation 28 3.4.4 Broadband Excitation 29 3.4.5 Calibration 30 CHAPTER 4: NUMERICAL SIMULATION AND EXPERIMENTAL RESULTS 32 4.1 Numerical Simulation Result 32 4.2 Experimental Results 34 CHAPTER 5: CONCLUSIONS 51 REFERRENCE 52 APPENDIX: The CONTSID Toolbox: A Software Support for Data-based Continuous-time Modelling 54 LIST OF FIGURES Figure 1.1 Cantilever beam structures Figure 2.1 Configuration of vibration cantilever beam Figure 3.1 Interrelation among dynamic models 19 Figure 3.2 Measurement system with noise sources 21 Figure 4.1 Time response of the chirp excitation and output signal 33 Figure 4.2 Simulation frequencies response of the system 33 Figure 4.3 Comparison of the response obtained by the experiment and the numerical simulation 34 Figure 4.4 Schematic diagram of the experimental set-up 35 Figure 4.5 The studied beam with a dark background 36 Figure 4.6 Measured points in the beam 37 Figure 4.7 Calibration procedure set-up 38 Figure 4.8 Curve fitting line converting the pixels value (from camera) to mm value (from laser sensor) 38 Figure 4.9 Measured chirp input and output signal in time domain 42 Figure 4.10 The two resonance frequencies with the chirp input signal 43 Figure 4.11 Experimental measured input and output signals 46 Figure 4.12 Signal spectrum analyzing 46 Figure 4.13 Bode diagram of estimated model at 10mm 47 Figure 4.14 Bode diagram of estimated model at 225mm 47 Figure 4.15 Model predicted output y10 using dataset E1 vs validation output V2 49 Figure 4.16 Model predicted output y225 using dataset E1 vs validation output V2 49 Figure 4.17 Comparison of estimated models’ responses vs the validation step signal 50 LIST OF TABLES Table 4.1 System Parameters 32 Table 4.2 Model order selection results using dataset E2 for output at 10mm 41 Table 4.3 Model order selection results using dataset E2 for output at 225mm 42 Table 4.4 Excitation signal and its function 43 Table 4.5 Estimated model parameters and validation results at 10mm 44 Table 4.6 Estimated model parameters and validation results at 225mm 45 Table 4.7 Modal parameters for the identified models 48 Table 4.8 The fitness percentage (FP) of identified models with step signal 50 CHAPTER 1: INTRODUCTION 1.1 Motivation Cantilever beams can represent many structures in mechanical, civil, and electronics engineering (for example, MEMS structure) For details, the cantilever beams also can be found in high-speed applications such as fast manipulators, micro CNC milling machines, coordinate measuring machines (CMM), atomic force microscopies (AFM) It is shown that the cantilever beam structures yield is a viable solution for the case of lightweight and compact size However, it is well known that the lightweight structures may result in vibrations when the cantilever beam moves, especially in the case of highspeed motion Therefore, the vibrations of the cantilever beam need to be analyzed during motions of the cantilever beam In this case, the beam is considered flexible (a) Atomic Force Microscope (b) Coordinate-measuring machine (d) Gantry system (c) Micro CNC milling machines Figure 1.1 Cantilever beam structures Figure 4.10 The two resonance frequencies with the chirp input signal Table 4.4 Excitation signal and its function Excitation signal Characteristic Analysis purpose Experiment name Chirp signal frequency varies from to 30 Hz Obtain resonance frequencies Exp1, Exp2, Exp3 Estimate the transfer function Multi sine wave signal Contain some interested periodic frequencies Validate the estimated model Step signal - Validate the estimated model 43 E1 (1, 2, 3, 4, 5, 6, 7, 9, 11, 15 Hz) E2 (1, 3, 5, 10, 20 Hz) E3 (1, 3, 6, 13, 30 Hz) V1 (1, 2, 4, 6, 10 Hz) V2 (1, 2, 4, 8, 16 Hz) V3 (1, 2, 3, 4, 5, 7, 10, 14, 21, 30 Hz) Step1, Step2, Step3 The identified transfer functions based on the three estimation datasets (E1, E2 and E3) for the 10-mm and 225-mm measurements are shown in Tables 4.6 and 4.7 respectively The estimated transfer function parameters as well as the poles, zeros, and gain of the transfer functions are shown The model fit, in terms of 𝑅𝑇2 based on estimation data, and the validation fit in terms of 𝑅𝑇2 of each estimated model against the three validation datasets (V1, V2, and V3) are also displayed in the tables Since the 𝑅𝑇2 values for both the estimation and validation data are close to for all the estimated models, it indicates that the identified models have almost explained all the variations in the data Estimation Table 4.5 Estimated model parameters and validation results at 10mm gain % 𝑅𝑇2 𝑉1 -170.2028 -31.9017 30.3191 −58.140 99.65 E2 0.70140 20217 1390.7 9.8966 × 106 −65.398 −11741 36941 8.8495 × 106 0.9937 -0.0270 ± 22.4050i -0.3238 ± 140.4095i -178.4449 -28.0847 27.0006 -65.398 99.35 E3 0.59452 20215 1225.2 9.9003 × 106 −68.772 −11611 22522 9.0957 × 106 0.9870 -0.0241 ± 22.4102i -0.2733 ± 140.4036i -166.0004 -29.6747 26.8479 −68.772 99.49 % 𝑅𝑇2 𝑉2 99.73 99.31 99.44 % 𝑅𝑇2 𝑉3 99.78 98.69 97.38 𝑎1 𝑎2 𝑎3 𝑎4 𝑏0 𝑏1 𝑏2 𝑏3 𝑅𝑇2 poles Validation zeros E1 0.43708 20216 1343.9 9.9026 × 106 -58.140 -9987.8 40576 9.5715 × 106 0.9986 -0.0293 ± 22.4123i -0.1894 ± 140.4067i 44 Estimation Table 4.6 Estimated model parameters and validation results at 225mm gain % 𝑅𝑇2 𝑉1 -184.9241 0.0684 ± 32.2534i 52.222 99.32 E2 0.69547 20221 1334.8 9.8987 × 106 56.446 10478 54080 1.0311 × 107 99.33 -0.0256 ± 22.4048i -0.3222 ± 140.4254i -185.7586 0.0681 ± 31.3585i 56.446 98.82 E3 52.222 20218 1163 9.9016 × 106 53.02 10225 48569 1.0249 × 107 99.31 -0.0228 ± 22.4099i -0.2627 ± 140.4141i -193.275 0.2176 ± 31.6241i 53.020 99.18 % 𝑅𝑇2 𝑉2 99.57 99.02 99.35 % 𝑅𝑇2 𝑉3 97.47 98.70 97.04 𝑎1 𝑎2 𝑎3 𝑎4 𝑏0 𝑏1 𝑏2 𝑏3 𝑅𝑇2 poles Validation zeros E1 0:4322 20225 1347.8 1347:8 × 106 52.222 9650 53005 1.0046 × 107 99.80 -0.0294 ± 22.4122i -0.1867 + 140.4356i 45 Figure 4.11 Experimental measured input and output signals Figure 4.12 Signal spectrum analyzing 46 Figure 4.13 Bode diagram of the estimated model at 10mm Figure 4.14 Bode diagram of the estimated model at 225mm 47 It can be observed from Table 4.3 that the first two resonance frequencies of the identified models are 3.567 and 22.22 Hz, which are nearly the same as the results obtained from both positions Meanwhile, the two identified models have nearly the same damping ratios for the first two modes within a data set Bode diagrams of the two identified models can be shown in Fig 4.13 and Fig 4.14 A comparison between the actual structure and the identified transfer function when subjected to the step validation signal is shown in Fig 4.17 It can be seen that the output signals are very close, thus confirming that the system identification has performed properly The fitness percentage (FP) between the real output and estimated output relies on the coefficient of determination (𝑅𝑇2 % fit), which is shown in Table 4.8 Table 4.7 Modal parameters for the identified models Model E1 E2 E3 Natural Frequencies Damping ratio 𝑓1 𝑓2 𝜉1 𝜉2 y10 y225 y10 y225 y10 y225 y10 y225 3.5769 3.5769 22.4213 22.4288 0.0078 0.0078 0.0106 0.0101 3.5754 3.5754 22.4248 22.4256 0.0082 0.0077 0.0075 0.0076 3.5746 3.5745 22.4224 22.4211 0.0076 0.0070 0.0106 0.0101 48 Figure 4.15 Model predicted output y10 using dataset E1 vs validation output V2 Figure 4.16 Model predicted output y225 using dataset E1 vs validation output V2 49 Figure 4.17 Comparison of estimated models’ responses vs the validation step signal Table 4.8 The fitness percentage (FP) of identified models with step signal 𝑅𝑇2 fit (%) Data set E1 E2 E3 Model y10 validation with Step signal 96.56 92.25 96.76 Model y225 validation with Step signal 96.57 92.13 96.50 It is clearly observed from the validation data that the identified models considered in this study perform well 50 CHAPTER 5: CONCLUSIONS In this dissertation, we investigated the vibrations of a flexible cantilever beam subjected to a moving hub In particular, we studied both experimentally and theoretically the behaviors of the modeling cantilever beam and the real system By Euler-Bernoulli beam theory, the mode shape frequencies are theoretically calculated for the cantilever beam subjected to a moving hub The flexible cantilever beam modeling was investigated to obtain the natural frequencies and their mode shapes An experimental parametric identification technique to estimate the linear damping coefficients and to obtain the natural frequencies was also deployed We carried out an experimental study of the response of a metallic flexible cantilever beam A system including a motion system and vision system was developed to support the experiment We observed various dynamic phenomena, like two vibration modes, the modulation frequency; which depends on various parameters like the amplitude and frequency of excitation, damping factors, etc The fact that flexible cantilever beam under different excitation could display nonlinear distortions phenomena, which depend on the amplitude of the excitation, the interested frequencies of the excitation, and also the surrounding environment (humidity, thermal noise…), the initial geometric shape of the beam But since these usual distortions have been observed in real engineering structures and mechanical systems, there is a need to study such phenomena in more detail 51 REFERRENCE [1] Yigit, A., Scott, R A., and Ulsoy, G A Flexural motion of a radially rotating beam attached to a rigid body Journal of Sound and Vibration, vol 121, no 2, pp 201210, 1988 [2] Yang, J B., Jiang, L J., and Chen, D CH Dynamic modelling and control of a rotating Euler-Bernoulli beam Journal of Sound and Vibration, vol 274, no 3-5, pp 863-875, 2004 [3] Kane, T R and Ryan, R R Dynamics of a cantilever beam attached to a moving base Journal of Guidance, Control, and Dynamics, vol 10, no 2, pp 139-151, 1987 [4] He, W and Ge, S S Vibration control of a flexible beam with output constraint IEEE Transactions on Industrial Electronics, vol 62, no 8, pp 5023-5030, 2015 [5] Matsuno, F., Ohno, T., and Orlov, V Y Proportional derivative and strain (PDS) boundary feedback control of a flexible space structure with a closed-loop chain mechanism Automatica, vol 38, no 7, pp 1201-1211, 2002 [6] Yang, J B., Jiang, L J., and Chen, D CH Dynamic modelling and control of a rotating Euler-Bernoulli beam Journal of Sound and Vibration, vol 274, no 3-5, pp 863-875, 2004 [7] Dadfarnia, M., Jalili, N., Xian, B., and Dawson, M D Lyapunov-based vibration control of translational Euler-Bernoulli beams using the stabilizing effect of beam damping mechanism Journal of Vibration and Control, vol 10, no 7, pp 933-961, 2004 [8] Paranjape, A A., Guan, J., and Krstic, M PDE boundary control for flexible articulated wings on a robotics aircraft IEEE Transactions on Robotics, vol 29, no 3, pp 625-640, 2013 [9] Shin, H.-C and Choi, S.-Bok Position control of a two-link flexible manipulator featuring piezoelectric actuators and sensors Mechantronics, vol 11, no 6, pp 707729, 2001 52 [10] Weaver W, Timoshenko S P and Young D H 1990 Vibrations Problems in Engineering 5th edn (New York: Wiley) [11] Kerschen, G., Worden, K., Vakakis, A F., & Golinval, J C (2006) Past, present and future of nonlinear system identification in structural dynamics Mechanical systems and signal processing, 20(3), 505-592 [12] Fahy F and Gardonio P 2007 Sound and Structural Vibrations: Radiation, Transmission and Response 2nd edn (New York: Academic) [13] Pham, P T., & Nguyen, Q C (2017) Dynamic model of a three-dimensional flexible cantilever beam attached a moving hub 2017 11th Asian Control Conference (ASCC) doi:10.1109/ascc.2017.8287611 [14] Roy R Craig, Andrew J Kurdila - Fundamentals of Structural Dynamics-Wiley (2006) [15] Silva, J M M (2001) Modal Analysis, Experimental | Measurement Techniques Encyclopedia of Vibration, 813 820 doi:10.1006/rwvb.2001.0027 [16] Romaszko, M., Sapiński, B., & Sioma, A (2015) Forced vibrations analysis of a cantilever beam using the vision method Journal of theoretical and applied mechanics, 53 [17] Lou, J., Liao, J., Wei, Y., Yang, Y., & Li, G (2017) Experimental Identification and Vibration Control of A Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control Applied Sciences, 7(3), 309 53 APPENDIX: The CONTSID Toolbox: A Software Support for Data-based Continuous-time Modelling The CONtinuous-Time System IDentification (CONTSID) toolbox provides Matlab functions for estimating continuous-time black-box models of dynamical systems from measured data without having to fully characterize the mathematics governing the system behavior The toolbox includes tools for standard identification of linear continuous-time models such as simple process, transfer functions and state-space models The toolbox also provides algorithms for more advanced identification such as errors-in-variable (EIV) and closed-loop model estimation or to capture nonlinear system dynamics This paper presents an overview of the main features of the latest release of the CONTSID toolbox and outlines some recent developments for on-line parameter and time-delay system estimation The CONTSID toolbox to be run with Matlab was the first toolbox entirely dedicated to continuous-time (CT) model identification from sampled data It was first released in 1999 (Garnier and Mensler, 1999) at a time where discrete-time model identification was the classical approach Fortunately, things have recently changed and continuous-time model identification has now taken over discrete-time model identification as exemplified by the more pronounced role of continuous-time model in the System identification toolbox (Ljung and Singh, 2012) One of the clear reasons is coming from the fact that control scientists and engineers have a better understanding and every-day practice of continuous time models, while they are less familiar with input/output polynomial black-box models such as discrete-time ARX, ARMAX or Box-Jenkins models The CONTSID toolbox includes tools for basic identification of linear black-box continuous-time models such as: - Identification of simple (low-order) process models; 54 - Identification of transfer function models; - Identification of input/output black-box polynomial models such as autoregressive (CARX), output-error (COE) and Box-Jenkins (CBJ) models; - Identification of state-space models with free or canonical parametrizations; - Identification from time-domain response data; - Identification from frequency-domain response data The CONTSID toolbox also includes tools for more advanced identification such as: - Identification from irregularly sampled data; - Identification of errors-in-variables (EIV) models; - Closed-loop model identification; - Identification of nonlinear block-oriented (Hammerstein and HammersteinWiener) models; - Identification of linear parameter varying (LPV) input/output models; - On-line identification for tracking time-varying system dynamics In practice, the common system identification workflow is iterative as shown in Figure 6.1 (Ljung, 1999) It includes several tasks Starting from measured input/output data, a set of candidate models is estimated by using suitable identification algorithms The identified model which produces the best results according to the chosen validation criterion is finally selected The system identification work flow is general and pragmatic It is independent of the chosen discrete-time or continuous-time model parametrization used, although the latter can present many advantages 55 Figure 6.1 The system identification procedure The latest version 7.3 of the CONTSID toolbox offers a variety of parametric model estimation methods for common linear and nonlinear model structures Tables 6.1 and 3.2 summarize the main CONTSID toolbox commands for standard linear model identification and for more advanced identification respectively Table 6.1 Model type Transfer function models Process models Input/output polynomial models Estimation commands tfsrivc procsrivc lssvf (CARX models) ivsvf (CARX models) coe (COE models) srivc (COE models) rivc (CBJ models) sidgpmf ssivgpmf State-space models 56 CURRICULUM VITAE Full name: Gender: Date of birth: Nationality: Marital status: VAN THUAT NGUYEN Male February 5, 1995 Vietnamese Single Emails: vanthuatme@gmail.com Cell phone: (+84) 909662562 Address: 537/7 Nguyen Oanh St, 17 Ward, Go Vap Dist, HCMC Education: Degree Postgraduate B.Eng Field Mechatronics Engineering Mechatronics Engineering Institution Ho Chi Minh City Univ of Tech Ho Chi Minh City Univ of Tech Date Sep 2018 – present Sep 2013 – Apr 2018 Work Experience: Jun 2019 – Present 2016 – 2019 Aug – Dec 2017 July – Aug 2017 May – July 2017 R&D Engineer, SVN Environmental Consulting Company Limited, Vietnam Reasearch Assistant, Control and Automation Laboratory, School of Mechanical Engineering, Ho Chi Minh City University of Technology, Vietnam Intern, Intel Products Vietnam, Vietnam Intern, Can Sport Vietnam, Vietnam Intern, Saigon High Tech Park Training Center, 57 ... TÀI : NHẬN DẠNG THANH MỀM CÔNG XÔN IDENTIFICATION OF A FLEXIBLE CANTILEVER BEAM II NHIỆM VỤ VÀ NỘI DUNG : - Xây dựng mơ hình động lực học sử dụng phương pháp Galerkin cho hệ thống dầm công xơn... nghiệm cho dao động dầm cơng xơn mềm nghiên cứu, loại dầm tìm thấy rộng rãi kết cấu khí Luận văn xây dựng mơ hình hóa, mô thực nghiệm để xác định thông số dầm công xôn mềm gắn bệ chuyển động Đầu tiên,... KHOA - ĐHQG - HCM Cán hướng dẫn khoa học: PGS.TS Nguyễn Quốc Chí Cán chấm nhận xét 1: PDG.TS Nguyễn Thanh Phương Cán chấm nhận xét 2: TS Lê Ngọc Bích Luận văn thạc sĩ bảo vệ Trường Đại học Bách