Mechanical Vibrations (MV)

• Vibration, its main causes, advantages and disadvantages
• Engineering applications of vibration and noise
• Vector method of representing harmonic motion
• Characteristics of vibration, harmonic analysis and beats phenomenon, work done by harmonic forces on harmonic motion
• Periodic and non‑harmonic functions – Fourier series analysis and evaluation of Fourier coefficients
• Elements of vibratory system; lumped and distributed parameter systems
• Undamped free vibrations – derivation of differential equation of motion using energy method, Newton’s second law, and Rayleigh’s method
• Solution of differential equation of motion – natural frequency of vibration
• Systems involving angular oscillations such as the compound pendulum

• Viscous damping: damping coefficient and damping ratio
• Under‑damped, over‑damped and critically damped systems
• Logarithmic decrement
• Frequency of damped free vibration
• Coulomb (dry‑friction) damping and comparison with viscous damping (frequency, decay rate)
• Solid and structural damping
• Slip or interfacial damping

• One‑degree‑of‑freedom forced harmonic vibration
• Vector representation of forces
• Excitation due to rotating and reciprocating unbalance
• Vibration isolation, force and motion transmissibility
• Absolute and relative motion of mass (seismic instruments)
• Whirling motion and critical speed – definitions, significance and calculation for a vertical light flexible shaft with single rotor (with and without damping)
• Critical speed of a shaft carrying multiple discs (without damping) and secondary critical speed

• Un‑damped free vibration of 2‑DOF systems and principal modes of vibration
• Torsion vibrations
• Forced un‑damped vibrations with harmonic excitation
• Coordinate coupling
• Dynamic vibration absorber
• Torsion vibration absorber
• Pendulum‑type dynamic vibration absorber

• Frequency‑dependent human response to sound and the decibel scale
• Relationship among sound pressure level (SPL), sound power level and sound intensity level
• Addition, subtraction, averaging of sound levels; sound spectra and octave‑band analysis
• Loudness, weighting networks, equivalent sound level, auditory effects of noise
• Hazardous noise, exposure from machines/equipment, hearing conservation, damage‑risk criteria and daily noise dose
• Noise sources, isolation and control – road and industrial sources, construction equipment, industrial noise control strategies at source, along the path and at the receiver
• Control measures: sound enclosures, acoustic barriers, ear defenders, earplugs, semi‑insert protectors

The syllabus lists no separate topics for this unit.