Introduction to engineering dynamics for structural engineering student

Introduction to engineering dynamics for structural engineering student

1. L. N. Ojha Ph.D. Welcome Students DEPARTMENT Structural Engineering Chair M. Sc. (Structural Engineering) Structural Dynamics ( CEng 6505)

2. This lecture is aimed to introduce the curriculum and the basic concepts of the Structural Dynamics As an outcome, you will understand : Course outline and learning Methodology Scope of Structural Dynamics Vibration and related Terms Modelling and related Terms Aim and Contents DOS

3. Curriculum Structural Dynamics deals with the vibrations of structures, their engineering aspects, and covers the topics like; Mechanical Vibrations and their Types, Vibration Modelling, and Equations of Motion Applications- discrete and continuos structures; Solution Methods etc. Course and Objective Modelling of the dynamic behaviour of civil engineering structures DOS

4. Grading S. No. Evaluation Marks 1 Assignments , Tests and Term Paper 40 2 3 Hour Written Examination-1 30 3 3 Hour Written Examination-2 30 Score ≥90 ≥80 ≥75 ≥70 ≥ 65 ≥ 60 ≥ 50 ≥ 45 ≥ 43 ≥ 40 ≥ 35 F< 35 Grade A+ A A- B+ B B- C+ C C- D+ D F Point 4.0 3.5 3.0 2.5 2.0 1.5 1.0 Rating GOOD SATISFACTORY AVERAGE POOR FAIL Make-up exam : No makeup for Mid, Absent Zero, Final Exam Only Through Proper Channel DOS Chopra - Dynamics of Structures-Text Hart- Structural Dynamics for Structural Engineers- Ref. Book

5. 16 Week Course Completion Plan DOS Day Time Details Oct 28 (Week -0) 9:00 – 9:45 Course outlines and Teaching Learning Methodology 9:45-11:45 Lecture 1: Introduction to Structural Dynamics (PPT) 11:45-12:00 Distribution of Assignment No. 1 Nov 04 (Week -1) 9:00- 9:45 Submission Assignment 1 and Test 1 9:45-11:45 Lecture 2: SDoF- Free Response (PPT +Tutorial) 11:45-12:00 Distribution of Assignment No. 2 Nov 11 (Week -2) 9:00- 9:45 Submission Assignment 2 and Test 2 9:45-11:45 Lecture 3: SDoF- Harmonic Response (PPT+ Tutorial) 11:45-12:00 Distribution of Assignment No. 3 Nov 18 (Week -3) 9:00- 9:45 Submission Assignment 3 and Test 3 9:45-11:45 Lecture 4: SDoF- Transient Response (PPT+ Tutorial) 11:45-12:00 Distribution of Assignment No. 4 Nov 25 (Week -4) 9:00- 9:45 Submission Assignment 4 and Test 4 9:45-11:45 Lecture 5: SDoF- Numerical Techniques (PPT+ Tutorial) 11:45-12:00 Distribution of Assignment No. 5 Dec 02 (Week -5) 9:00- 9:45 Submission Assignment 5 and Test 5 9:45-11:45 Lecture 6: Generalized SDoF (PPT+ Tutorial) 11:45-12:00 Distribution of Assignment No. 6 Dec 07 (Week -6) 9:00- 9:45 Submission Assignment 6 and Test 6 9:45-11:45 Lecture 7: Tutorial 11:45-12:00 Guidelines for 3 Hour Examination-1 Dec 16 9:00-12:00 3 Hour Examination-1 (Week -7)

6. 16 Week Course Completion Plan DOS Dec 23 (Week -8) 9:00- 9:45 Feedback on 3 Hour Examination-1 (Showing the checked answer books) 9:45-11:45 Lecture 8: MDoF - Eigen Values 11:45-12:00 Distribution of Assignment No. 7 Dec 30 (Week -9) 9:00- 9:45 Submission Assignment 7 and Test 7 9:45-11:45 Lecture 9: MDoF - Damping Models 11:45-12:00 Distribution of Assignment No. 8 Jan 06 (Week -10) 9:00- 9:45 Submission Assignment 8 and Test 8 9:45-11:45 Lecture 10: MDoF - Mode-superposition 11:45-12:00 Distribution of Assignment No. 9 Jan 13 (Week -11) 9:00- 9:45 Submission Assignment 9 and Test 9 9:45-11:45 Lecture 11: IDoF - Eigen values and Mode-superposition 11:45-12:00 Distribution of Assignment No. 10 Jan 20 (Week -12) 9:00- 9:45 Submission Assignment 10 and Test 10 9:45-11:45 Lecture 12: IDoF - Rayleigh Ritz Method 11:45-12:00 Distribution of Assignment No. 11 Jan 27 (Week -13) 9:00- 9:45 Submission Assignment 11 and Test 11 9:45-11:45 Lecture 13: Design and Control Aspects 11:45-12:00 Distribution of Assignment No. 12 Feb 03 (Week -14) 9:00- 9:45 Submission Assignment 12 and Test 12 9:45-11:45 Lecture 14: Tutorial 11:45-12:00 Guidelines for Term paper Feb 10 9:00-12:00 3 Hour Examination-2 (Week -15) Feb 17 (Week -16) 9:00- 10:00 Submission of Term-paper, and Feedback on 3 Hour Examination-2 10:00-12:00 Submission of Grades

7. Structural Dynamics Structural Dynamics: Structural analysis under dynamic loading Engineering mechanics dealing with the behavior of structures subjected to dynamic loading (excitation). Dynamic means time varying Dynamic loads include, wind, waves, traffic, earthquakes, blasts, and people etc.. Any structure can be subject to dynamic loading. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis . Definitions DOS No Force Force No Motion Who Cares Statics Motion Kinematics Dynamics

8. Static load No change with time. A dynamic load changes with time. Dynamic analysis for simple structures can be carried out manually For complex structures finite element analysis can be used to calculate the mode shapes and frequencies. Dynamic Analysis Structural Dynamics DOS

9. Structural Dynamics Structures DOS

10. CEng 6505 Vibration Analysis The outputs of a vibrating system, in general, depend upon the initial conditions, and external excitations. The vibration analysis of a physical system may be summarised by the four steps: 1. Mathematical Modelling of a Physical System 2. Formulation of Governing Equations 3. Mathematical Solution of the Governing Equations 4. Physical interpretation of the results

11. Structural Dynamics Type of Dynamic Analysis The choice of method depends upon Type of loading (how the loading is defined). If the time variation of loading is fully known, the analysis of the response of a structural system is known as a deterministic analysis. On the other hand, if the time variation is not completely known but can be defined in a statistical sense, then the analysis of response is known as a random analysis . DOS

12. Dynamic Loading Clough Structural Dynamics DOS

13. EQE Loads

14. Dynamic Loading CEng 6505 Deterministic / Non- deterministic (Random) Periodic Loading it repeats itself with a fixed period T, p(t) = p(t + T) holds for every t. Harmonic Loading it is modulated by a harmonic function, characterized by a frequency and a phase Non Periodic Loading here we see two sub-cases, the loading can be described in terms of analytical functions, e.g., p(t) = po exp(t), the loading is (a) experimentally measured and (b) is known only in a discrete set of instants; in this case, we say that we have a time-history.

15. Vibration is mechanical oscillation about a reference position . (Engineering) Vibration Definition Any motion that repeats itself after an interval of time (Scientific) Deals with the relationship between forces and oscillatory motion of mechanical systems (Engineering) Property Oscillation Vibration Motion To and Fro Any Direction Changes Movement Physical /Elastic DOS

16. Vibration is a result of dynamic force. Different parts of the structure will vibrate with various frequencies and amplitudes. Vibration causes fatigue and is often responsible for failure of structure. Vibration in structures Vibration DOS

17. Vibration in structures Vibration Causes and Effects Beard Excitation Dynamics Characteristics Response Theory Experiment DOS

18. Vibration Vibration in structures DOS

19. Earthquake-Induced Vibrations of Buildings Sources of Vibration in structures Vibration DOS

20. Vibration The first Tacoma Narrows suspension bridge collapsed due to wind-induced vibrations on Nov. 7, 1940. Sources of Vibration in structures Wind-Induced Vibrations of Structures DOS

21. Vibration Classification Free or Forced Harmonic, Transient Periodic, Non-periodic Damped and Un-damped SdoF , MDoF , IDoF Linear or Non-linear Deterministic or Random DOS

22. Vibration Definition DOS

23. Vibration Definition DOS

24. Vibration Definition DOS

25. Modeling Definition Real World The Model Analysis Information for decision making Physical ( Building) , Analogous (Drawing) Symbolic(Equation / Spreadsheet / Simulation) Deterministic/Probabilistic A model is a system that represents one or more facets of some other system. Modelling is the part of solution of an engineering problem that aims for producing its mathematical description (for a better understanding) DOS

26. Idealisation - Analytical Model Newtonian Dynamics ( 3 Laws), Lagrangian , and Hamiltonian Dynamics Identify the problem Begin with a simple model. Identify important variables and constants Develop the equation(s) Variables (Input and Output) and Constants (Paramètres ) Equivalent Dynamic(Mass- Spring-Damper) Model Modeling DOS

27. 1 3 2 Inertia, mass m (stores kinetic energy) Elasticity, Stiffness K (stores potential energy) Realistic Addition Damping c (Energy Dissipation) Dynamic System ( a system that contains Mass and Elasticity) Modeling Model Ingredients DOS

28. Structures and spring-mass models Modeling Analytical Model DOS

29. Modeling The most demanding step in any dynamical analysis is the creation of a analytical model of the structure, which consists of: A list of the simplifying assumptions made in reducing the real structure to the analytical model A drawing that depict the analytical model A list of the design parameters (i.e., sizes, materials, etc.) Analytical models fall into two basic categories: continuous and discrete parameter models. Analytical Model- An Idealised Structure DOS

30. Mathematical Model-A Mathematical Description Modeling To analyse motion of a system it is necessary to develop a mathematical description that approximates its dynamic behaviour. This mathematical description is referred to as the mathematical model. Mathematical model can be obtained by applying the laws of mechanics to the adopted analytical model of a structure. DOS

31. Generalized Coordinates and DoF Modeling A set of coordinates or parameters, which uniquely describes the geometric position and/or orientation of a structure is called the generalized coordinates of the structure. The minimum number of independent generalized coordinates required to describe the state (geometry) of a structure is known as the degrees of freedom of that structures. DOS

32. Generalized Coordinates and DoF Modeling Dynamic degrees of freedom are a set of independent displacements / rotations that completely define the displaced position of the mass with respect to its initial position. A vertical cantilever with the mass concentrated at its tip can be idealised as a single degree of freedom (SDoF) system. The DoF is represented by the lateral displacement u of the mass. A multi-storey frame with the masses concentrated the storey levels can be idealised as a multi degree of freedom (MDoF) system. The degrees of freedom are the lateral displacements of the storey masses. The system has 4 dynamic degrees of freedom – displacements u1 – u4. DOS

33. Generalized Coordinates and DoF Modeling Structures modeled as MDoF Analytical Model for MDoF DOS

34. Modeling (Chopra) Structures DOS

35. Modeling Structures Building Frame (Rao SS) Equivalent Dynamic(Mass- Spring) Model DOS

36. Metrikine Structures Modeling DOS

37. Modeling Model corresponding to given schematic of a building frame Model masses correspond to slab masses Model stiffnesses correspond to column stiffnesses Structures DOS

38. Modeling Structures DOS

39. The Space Needle (Rao SS) Modeling of tall Structures Structures Modeling DOS

40. CEng 6505 Classification SDoF MDoF IDoF Undamped Damped Linear Nonlinear Free Forced Harmonic Periodic Random Transient Impulse Blast Wind Earthquake Transverse Longitudinal Torsional

41. Discrete Versus Continuous Structures Structural Dynamics-I p v CONTINUM MODEL SDoF MDoF IDoF

42. Thank you