Mechanical Vibrations
 
 
Subject Code: EME4076
Aim of Subject: To introduce the basic concepts and train the students to analyse vibration problems in mechanical engineering
Learning Outcome of Subject: At the completion of the subject, students should be able to :
  • Use the basic concepts of vibration
  • Apply free and force vibration analysis for single degree of freedom systems
  • Derive and apply vibration response of a single degree of freedom system under general forcing condition.
  • Apply and determine equation of motion for a free undamped vibration systems, forced vibration for undamped and viscously damped system for a two degree of freedom system.
  • Apply Newton’s equation and Lagrange’s equations to multi-degree of freedom systems
  • Investigate vibration of continuous systems
  • Test and analyze lab experiment results on frequency response of rotating machinery under various conditions
Programme Outcomes:
  • Ability to acquire and apply fundamental principles of science and engineering(50%)
  • Capability to communicate effectively(10%)
  • Acquisition of technical competence in specialised areas of engineering discipline(10%)
  • Ability to identify, formulate and model problems and find engineering solutions based on a systems approach(20%)
  • Ability to be a multi-skilled engineer with good technical knowledge, management, leadership and entrepreneurship skills(10%)
Assessment Scheme:
  • Lab Experiments - work in groups, lab report writing, oral assessment at the end of lab (10%)
  • Tutorial / Assignment - group assignment,focus group discussion at tutorial,to enhance understanding of basic concepts in lecture(15%)
  • Test Quiz - written exam (15%)
  • Final Exam - written exam (60%)
Teaching and Learning Activities: This subject will be delivered using the following means:
  • Lecture Hours = 42 hours
  • Supervised Tutorial Hours = 6
  • Laboratory Experiments = 6
    • Total Contact Hours = 54
Credit Hours: 3
Pre-Requisite: EME1076 Applied Dynamics
References:
  • S.S. Rao, “Mechanical Vibrations”, SI ed. Prentice Hall, 2005 (Textbook)
  • G. Kelly, “Fundamentals of Mechanical Vibrations”, 2nd Edition, MrGraw-Hill, 2000.
  • L. Meirovitch, “ Fundamentals of Vibrations”, McGraw Hill, 2001.
  • D.J. Inman, “Engineering Vibration”, 3rd ed. Prentice Hall, 2008.
  • Hanselman and Littlefield, “Mastering Matlab 7” Prentice Hall 2005.

Subject Contents

  • Fundamentals of Vibration

    • Derivation of equations of motion. Principle of work-energy. Elementary parts of vibrating mechanical systems. Derivation of equivalent mass, stiffness and damping of mechanical systems
     
  • Free and Forced Vibration of Single Degree of Freedom Systems

    • Undamped and viscously damped vibration, logarithmic decrement, Coulomb damping, Hysteretic damping, Base excitation, force transmissibility and isolation, rotating unbalance.
     
  • Vibration Under General Forcing Conditions

    • Convolution Integral, response under a periodic force of irregular form, response under a non-periodic force.
     
  • Introduction to Two Degree of Freedom Systems

    • Newton’s equations, Lagrange’s equations, matrix formulation, influence coefficients, normal-mode solution, eigenvalues and eigenvectors, orthogonality, orthonormalisation. Proportional damping. General viscous damping. Free-forced vibration of undamped and damped systems in matrix form.
     
  • Introduction to Multi-Degree of Freedom Systems

    • Newton's equations, Lagrange's equations, matrix formulation, influence coefficients, normal-mode solution, eigenvalues and eigenvectors, orthogonality, orthonormalisation, , Proportional damping, General viscous damping. Free-Forced vibration of undamped and damped systems in matrix form.
     
  • Vibration of Continuous Systems

    • Vibration of strings, bars, and beams. Rayleigh's Method, Rayleigh-Ritz Method.
     

Laboratory

1. Machine Imbalance
2. Machine Bearing Damage and Foundation Stiffness Looseness