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  1. 1. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT 2M SOLID MECHANICS VIBRATION LECTURES October 2005 Lecture 1 Introduction Lecture 2 Free motion of undamped SDOF systems Lecture 3 Free motion of damped SDOF systems Lecture 3A Lagrange’s Equation of Motion Lecture 4 Forced motion of SDOF systems Lecture 5 Vibration Isolation Lecture 6 Base excitation of SDOF systems Lecture 7 Introduction to 2-DOF systems Textbooks B. H. Tongue 2002. Principles of Vibration, Oxford University Press D. J. Inman 1994. Engineering vibration, Prentice-Hall International MI - 2M SM Vibration Lecture 1 1
  2. 2. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT OVERVIEW • Vibration Lectures - 10 lectures • Dynamics Lectures - 6 lectures • Further notes and tutorial questions in: 2M SM - Lecture notes on Vibration (Yellow booklet) See the MED Web for all handouts. MI - 2M SM Vibration Lecture 1 2
  3. 3. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT LECTURE 1 - INTRODUCTION Objectives: • To provide a road map for the Vibrations & Dynamics Course • To give an overview of vibration problems in engineering • To review available solution techniques MI - 2M SM Vibration Lecture 1 3
  4. 4. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT ROAD MAP SOLID MECHANICS STATICS DYNAMICS MATERIALS …….. RIGID BODY VIBRATION 1-DOF DYNAMICS ANALYSIS SYSTEMS STEADY FORCES UNSTEADY FORCES N-DOF RIGID BODIES FLEXIBLE BODIES SYSTEMS CONTINUOUS SYSTEMS MI - 2M SM Vibration Lecture 1 4
  5. 5. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT VIBRATION MODES OF A PLATE MI - 2M SM Vibration Lecture 1 5
  6. 6. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT TIME DOMAIN VS FREQUENCY DOMAIN - I • For vibration analysis, we General arbitrary motion need to describe the motion of each point on a structure. • If the motion is arbitrary, we need to describe the TIME motion in the time domain. • If the motion is harmonic, Harmonic motion we can reduce this requirement by working in the frequency domain. TIME Can be expressed as x(t)=Asinωt MI - 2M SM Vibration Lecture 1 6
  7. 7. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT TIME DOMAIN VS FREQUENCY DOMAIN - II AMPLITUDE We observe the motion of a FREQUENCY given point at a given frequency MI - 2M SM Vibration Lecture 1 7
  8. 8. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT EXAMPLE OF FREQUENCY DOMAIN ANALYSIS Vibration shape at natural frequency Vibration shape at any other =>Mode shape frequency =>Operating deflection shape Natural frequency MI - 2M SM Vibration Lecture 1 8
  9. 9. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT WAYS OF REPRESENTING A STRUCTURE • SPATIAL DESCRIPTION • Finite element model • Mass-spring model ω=82 Hz • MODAL DESCRIPTION • Use natural frequencies and mode shapes • RESPONSE DESCRIPTION • Use the actual behaviour of the structure MI - 2M SM Vibration Lecture 1 9
  10. 10. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT VIBRATION MEASUREMENTS Shaker + “sand” method Shaker + Laser method MI - 2M SM Vibration Lecture 1 10
  11. 11. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT CONSEQUENCES OF VIBRATION • Noise • Discomfort • Malfunction • Shutdown • Structural failure MI - 2M SM Vibration Lecture 1 11
  12. 12. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT TOTAL STRUCTURAL FAILURE - I MI - 2M SM Vibration Lecture 1 12
  13. 13. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT TOTAL STRUCTURAL FAILURE - II Engine casing Turbine disk MI - 2M SM Vibration Lecture 1 13
  14. 14. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT NOISE & TRANSMISSION OF VIBRATION SHAKER (FORCE INPUT) CAR ENGINE MOUNTS CHASSIS POINT (RESPONSE OUTPUT) MI - 2M SM Vibration Lecture 1 14
  15. 15. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT FREQUENCY RESPONSE OF A HELICOPTER THESE MODES OF VIBRATION MAY BE EXCITED BY THE FORCES DUE TO ROTATION MI - 2M SM Vibration Lecture 1 15
  16. 16. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT NOISE & VIBRATION TRANSMISSION FROM HEAVY MACHINERY MI - 2M SM Vibration Lecture 1 16
  17. 17. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT RAIL CORRUGATION MI - 2M SM Vibration Lecture 1 17
  18. 18. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT BRIDGE FLUTTER The unsteady aerodynamic forces caused by the wind excited a torsional mode of the bridge, causing total structural failure. MI - 2M SM Vibration Lecture 1 18
  19. 19. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT GAS TURBINE BLADE VIBRATION MI - 2M SM Vibration Lecture 1 19
  20. 20. IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY & MEDICINE MECHANICAL ENGINEERING DEPARTMENT WHAT IS THE OBJECTIVE ? • Find the critical frequencies • Determine the excitation • ……………………. • MINIMISE THE RESPONSE Higher the response, more likely is noise, malfunction, failure due to high cycle fatigue. Σ FORCES RESPONSE = [SYSTEM DESIGN] ∑ DAMPING • Modify the design • Change operating conditions • Increase damping MI - 2M SM Vibration Lecture 1 20

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