Indian Institute of Technology Kharagpur

Ocean Engineering and Naval Architecture

Autumn 2014 NA31007 3-1-0, 4 credits

Vibration of Floating Structures Instructor : Dr. N. Datta

Contact Hours : Mon (10:30-11:25), Tue (7:30-9:25), Thu (11:30-12-25)

Office hours: Monday 11:30-12:25pm, Thursday 10:30-11:25am

Grading Homeworks 20% Midterm 25% Term paper 10% Endterm 45%

Skills Required Microsoft Office (WORD, EXCEL, POWERPOINT), Matlab, ANSYS.

Prerequisite Mechanics, Mechanics of Solids. Ship Strength.

Mathematics: Solutions to linear differential equations. Matrix algebra. Complex analysis. Fourier

analysis. Partial differential equations. Probability and Statistics.

Books

1) Theory of Vibration with applications, 5th edition, W.T.Thomson. (TEXTBOOK) 2) Vibration Problems in Engineering, by S.Timoshenko. (TEXTBOOK) 3) Structural Dynamics : Vibrations and Systems, by Madhujit Makhopadhyay, Ane Books India. (Chapter 8) 4) Tutorial : Mechanical Vibrations, by S. Graham Kelly, Tata-McGraw Hill. 5) Tutorial : Textbook of Mechanical Vibrations, Rao V.Dukkapati and J. Srinivas, Prentice-Hall, India. 6) Reference : Principles of Naval Architecture, Volume 2.

Syllabus

Module I Practical aspects of Vibration. Fatigue. Stress-Strain Diagram. Vibration induced in floating elastic structure like ship due to wave, propeller (PIV) and machinery. Empirical formulae for the evaluation of frequencies in ship hull vibration. Ship

Vibration Excitation Forces. Sloshing induced vibration, Baffle vibration. Hull resonance diagram. Selection of engine and propeller

based on vibration considerations. Classification society rule book guidelines in global and local ship vibrations. Vibration

instrumentation : strain gauge, load cell, accelerometer, oscilloscope, torsiongraph, transducer. Mechanical impedance.

Module II The basic concept of structural vibration. Free and forced vibration of single degree of freedom system. Rotary Imbalance (static and dynamic). Whirling of rotating shafts. Torsional pendulum. Coulomb Damping. Bilinear spring. Viscous

damping. Vehicle shock absorbers and silencers. Hysteresis damping. Vibration isolation. Transient Vibrations.

Module III Free and forced vibration of multi-degree of freedom system. Eigen value analysis. Vibration absorber. Vibration of continuous systems. Mode summation method. Classical methods. Energy Based methods. Dynamic Direct stiffness matrix

(DDSM) method. Rayleigh Ritz method. Vibration of machine and diesel engine shafts; Design of engine mounts. Machine

alignment and balancing. Torsional vibration of rotating and reciprocating engines.

Module IV Introduction to hydroelasticity. Radiation pressure. Added mass and its effect in ship hull vibration. Wet vibrations. Offshore structure vibrations. Vortex induced vibrations (VIV).

Module V Random Vibrations. Non-linear Vibrations. Complexities in beam vibration : Timoshenko beam, intermediate fixities, non-uniform beams, stiffened structures, multi-span beams, composite beams. Plate vibration (Rectangular and Circular

plates). Finite Element Analysis. Stiffened plate vibration. 2D and 3D Frame and truss vibration.

# Date Hrs Course Schedule : Topics HW given HW due

1 17/7 1 Module-I Practical aspects of Vibration. Ship Vibration Excitation Forces.

2 21/7 1 Empirical formulae, Hull resonance diagram.

3 22/7 2 Rule book guidelines, Vibration instrumentation

4 24/7 1 Module II Basic concepts. Free vibration of 1 DOF system 1

5 28/7 1 Forced vibration of single DOF system.

6 31/7 1 -do-

7 4/8 1 -do-

8 5/8 2 Tutorial (Chapter 1,2,3)

9 7/8 1 Transient Vibration

10 11/8 1 -do-

11 12/8 2 Tutorial (Chapter 4) 1

12 14/8 1 Module III Free vibration of multi-DOF system

13 19/8 2 Tutorial (Chapter 5) 2

14 21/8 1 Forced vibration of multi-DOF system

15 25/8 1 -do-

16 26/8 2 Vibration of continuous systems.

17 28/8 1 Mode summation method.

18 1/9 1 Tutorial (Chapter 8, 9)

19 2/9 2 Energy methods 2

20 4/9 1 Vibration of machine and diesel engine shafts

21 8/9 1 -do-

22 9/9 2 Tutorial (Chapter 6)

23 11/9 1 Term paper distribution

MID-SEMESTER EXAMINATION

24 25/9 2 Module IV Introduction to Hydroelasticity

25 7/10 2 -do-

26 9/10 1 Offshore structure vibration 3

27 13/10 1 Module V Random Vibrations

28 14/10 2 -do-

29 16/10 1 Tutorial (Chapter 12)

30 20/10 1 Non-linear Vibrations

31 21/10 2 -do-

32 23/10 1 Tutorial (Chapter 9)

33 27/10 1 Complexities in beam vibration

34 28/10 2 -do- 3

35 30/10 1 Plate Vibration

36 3/11 1 Finite Element Analysis

37 10/11 1 -do- 4

38 11/11 2 Computational Tutorial : ANSYS 4

39 13/11 1 Term paper presentations (2 teams)

40 17/11 1 Term paper presentations (2 teams)

41 18/11 2 Term paper presentations (Remaining teams)

END-SEMESTER EXAMINATION

Tutorials There will be 13 tutorial hours in the semester. All tutorials will be scored in the class. Calculator is a must. Any

student without it cannot attend the tutorial. Bring your laptop for computational tutorials. The student has to solve the tutorials in

class. Programs must generate outputs for score.

Homeworks (20% marks) Each homework will be of 10 marks. There will be 4 homeworks in the semester. It has to be

compulsorily done individually. It can be discussed with the instructor in the office hours. All homeworks are due in the office hours.

All programming homeworks need to be run in front of the instructor to generate outputs. All written homeworks will be scrutinized

and cross-questioned on the spot. The student will be graded immediately. There is penalty of 2 marks (out of 10) for late submission.

Term Paper Presentation (10% marks)

There will be self-made 12 teams of 5 members each. Make your teams and inform the instructor by 9/9/2014. Create and excel file

with roll, Number, Name, CGPA. Team numbers will be provided by the instructor. One presentation per team and one 10-page report

per team, are due in the 3rd

week of November 2014. A 10-page Report per team is due by : November 18, 2014, 6 pm.

Duration of PPT : 12 min + 3 min discussion. Venue : Seminar Room, Dept. of Ocean Engg and Naval Arch.

November 13, 2014 : 11:30 am 12:30 pm, November 17, 2014 : 10:30 am - 12:00 noon, November 18, 2014 : 7:30 am 9:30 am

Term paper Topics (Topic will be given on 11/9/2014)

1) Dynamics of marine risers due to vortex-induced vibration. 2) Compliant tower flexural-axial vibration due to earthquake loading. 3) Rudder dry free vibration, including rigid body modes. 4) Propeller blade singing due to vortex-shedding. 5) Drillship rudder dynamics, including drift : non-linear vibration and chaos. 6) Propeller blade vibration under non-uniform wake-loading (FLUENT and ANSYS) 7) Propeller shaft thrust block design. 8) Propeller induced vibration of stern overhang. (FLUENT and ANSYS) 9) Multi-span elastically supported floating airport. 10) Hexagonal helideck dynamic response spectrum under helicopter impact and step-function loading.

SL # Homework Title

HW 1 Single DOF system : Free and Forced Vibration. Transient Vibration.

HW 2 Multi-DOF system : Free and Forced Vibration. Vibration of a Floating beam.

HW 3 Hydroelasticity. Random Vibration. Non-linear vibration.(MATLAB)

HW 4 Finite Element Analysis of plate vibration. (ANSYS)