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Course Detail

Course Name Theory of Vibrations
Course Code 19MEE338
Program B. Tech. in Mechanical Engineering
Year Taught 2019


Unit 1

Vibration of sdf systems- Free vibration of sdf systems – undamped and damped free vibration-underdamped, overdamped and critically damped systems-estimation of damping by logarithmic decrement. Forced vibration of sdf systems- Harmonically excited sdf systems-rotating unbalance-support harmonic excitation- vibration isolation-sdf system as a vibration measuring instrument- Half power point method for the estimation of damping- Response to periodic excitation – method of Fourier series. Types of damping – viscous, Coulomb, structural and material damping models- Equivalent viscous damping. Response of sdf system to arbitrary excitation (Transient Vibration)- Convolution integral – method of Fourier transforms.

Unit 2

Vibration of two dof systems-Undamped free vibration of the two dof systems -matrix eigenvalue problem – natural frequencies and natural modes – elastic and inertial coupling – coordinate selection to remove coupling- beat phenomenon – response to harmonic excitation- vibration absorbers – orthogonality of natural modes. Vibration of multi dofsystems-Equations of motion – formulation and solution of matrix eigenvalue problem – computational methods for the solution of matrix eigenvalue problem – decoupling of equations of motion by modal analysis.

Unit 3

Vibration of continuous systems
Transverse vibration of a string – axial vibration of a rod – torsional vibration of a shaft – bending vibration of a beam – formulation and solution of differential eigenvalue problem.

Objectives and Outcomes

Course Objectives

  • Familiarize students with the mathematical modeling and analysis of mechanical vibration systems
  • Make students understand the importance of vibration analysis in the design of dynamical systems

Course Outcomes

  • CO1: Classify different types of vibrations and develop mathematical models of vibratory systems.
  • CO2: Analyze free and forced vibrations of single degree of freedom systems.
  • CO3: Estimate the natural frequencies and mode shapes of multi degree of freedom systems.
  • CO4: Analyze free vibrations of continuous systems

CO – PO Mapping

CO1 3 3 1 1 1 3
CO2 3 3 1 1 1 1 3
CO3 3 3 1 1 1 1 3
CO4 3 3 1 1 1 1 3

Textbook / Reference


  • Theory of vibrations, W T Thomson, M D Dahleh and C Padmanabhan, Pearson Education,2018.
  • Fundamentals of vibrations, Leonard Meirovitch, McGraw Hill International edition,2010


  • Elements of vibration analysis, Leonard Meirovitch, Tata McGraw Hill, 2010.
  • Mechanical vibrations, S.S Rao.Pearson Education, 2018.
  • Engineering Vibrations, D.J Inman, Pearson International Education, 2011.

Evaluation Pattern

Assessment Internal External
Periodical 1 15
Periodical 2 15
*Continuous Assessment (CA) 20
End Semester 50
*CA – Can be Quizzes, Assignment, Projects, and Reports.

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