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Home / Syllabus / B.E. (Automobile Engineering) / Third Year AE / Semester 6 / Mechanical Vibrations

B.E. (Automobile Engineering) Mechanical Vibrations Syllabus - Mumbai University 2026

The University has moved this degree onto NEP 2020 one year at a time. The first and second years are NEP 2020 syllabi; the third and fourth years are still examined on the REV-2019 'C' Scheme, which is what the University sets for them this year.

Mechanical-Vibrations.pdf
Semester 6 · Third Year AE · 3 credits · 100 marks

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Syllabus for Mechanical Vibrations

Semester 6 · Third Year AE · 3 credits · 100 marks

Module 1: Course Code Course Name

  • AEC602 Mechanical Vibrations 1. To study the basic concepts of vibration analysis. 2. To estimate the natural frequency/frequencies of vibration systems in free vibration, using both exact and numerical methods. 3. To estimate the response of 1 degree of freedom under forced vibration. 4. To acquaint with the basic principles of vibration measuring instruments. 5. To study the balancing of rotating and reciprocating mass systems. Learner will be able to... 1. Develop mathematical models to represent dynamic system. 2. Estimate natural frequency of mechanical system using various methods. 3. Analyze vibratory response of mechanical system under forced vibration. 4. To estimate the natural frequencies and mode shapes of multi-degree of freedom system, using both exact and numerical methods. 5. Balance an existing unbalanced system partially/completely. Details
  • 1.1 Basic Concepts of Vibrations: Vibration and oscillation, causes and effects of vibrations, vibration parameters spring, mass and damper, minimum number of parameters required for vibration to occur, vibration terminology, classification of vibrations, steps involved in vibration analysis.
  • 1.2 Free Undamped Single Degree of Freedom Vibration Systems: Methods to formulate differential equation—Newton’s method or D’Alembert’s principle, and Energy methods—Based on conservation of total energy, Rayleigh’s energy method, Lagrange’s energy method, equivalent system method. Springs in series and parallel combination, inclined spring, effect of spring’s own mass to University of Mumbai , Rev 2019 44

Module 2: calculate natural frequency of system. Application of these methods in longitudinal, transverse and torsional single degree of freedom vibration systems, or a combination of these.

  • 2.1 Free Damped Single Degree of Freedom Vibration Systems: Need of damping in vibration systems, introduction to damper models—viscous, Coulomb (dry friction), slip/interfacial, solid/structural/hysteresis damping (Note: only basic introduction to slip and solid dampings, no calculations expected). Viscous damping—Derivation of differential equation of motion, derivation of solution (response) equations, damping ratio or damping factor, critical damping coefficient, underdamped, critically damped and over damped systems. Logarithmic decrement, Work done by viscous damper, inclined damper, dampers in series and parallel combinations. Coulomb/dry-friction damping—derivation of differential equation, number of cycles covered by the mass to stop once disturbed (disturbance in the form of initial displacement only), comparison of viscous and Coulomb dampings.
  • 3.1 Free Undamped Multi Degree of Freedom Vibration Systems: Exact methods for derivation of differential equations of motion for multi degree of freedom systems—Newton method and Lagrangian energy method, matrix analysis to estimate eigenvalues and eigenvectors & hence natural frequencies and mode shapes for multi-mass undamped vibration systems (limited to 2 degree of freedom only), Holzer’s method for longitudinal and torsional unbranched vibration systems, Dunkerley’s and Rayleigh’s methods for estimating fundamental frequency of tranverse vibration of simply supported and cantilever beams (up to a maximum of 4 point loads only), influence coefficients and Maxwell’s reciprocal theorem.
  • 4.1 Forced Single Degree of Freedom Vibration Systems: Analysis of linear and torsional systems subjected to harmonic excitation in terms of force and motion (viscous damping only), force isolation and transmissibility, isolators and mounts.
  • 4.2 Vibration Measuring Instruments: Principle of seismic instruments, vibrometer, accelerometer, velometer—with and without measurement errors. Principle of frequency-measuring instruments, Fullarton’s tachometer and Frahm’s reed tachometer.
  • 5.1 Balancing of Rotating Masses: University of Mumbai , Rev 2019 45

Module 6: Static and dynamic balancing of multi-rotor system.

  • 5.2 Balancing of Reciprocating Masses: Approximate analytical method for finding acceleration of reciprocating piston (mass of connecting rod and crank neglected), primary and secondary unbalanced forces, inline engine, direct and reverse crank method.

Reproduced from the University of Mumbai syllabus for B.E. (Automobile Engineering) under REV-2019 'C' Scheme, in force from the academic year 2021-22. Wording is as printed in that syllabus. Module numbering is as printed there too.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF 7.39 (R-A) B.E. (Automobile Engineering) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.46 (N) B.E. (Automobile Engineering) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.10 B.E. (Automobile Engineering) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
PDF 6.46 (R) B.E. (Automobile Engineering) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
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