
Examine free vibrations in a damped mass–spring system, derive m x¨ + c x˙ + k x = 0, and explain critical damping, damping ratio, and the underdamped solution.
Explore forced vibration of a single degree-of-freedom system under harmonic forcing, derive the free-body equations of motion, and analyze the mass–spring–damper response and natural frequency.
Explore a two-degree-of-freedom torsional system with two discs on a shaft, deriving the free-vibration equations and natural frequencies using a free-body diagram and Newton's laws.
Explore how reciprocating masses cause unbalance in engines and distinguish primary and secondary unbalanced forces. Learn why complete balancing is impossible and how partial balancing uses opposing mass.
Learn how condition monitoring of machinery uses vibrations, temperature, oil, and noise signals to detect early faults, prevent breakdowns, and ensure safe, efficient operations.
Vibration is a continuous cyclic motion of a structure or a component.
Desirable vibrations-the motion of a tuning fork, the reed in a woodwind instrument or harmonica, a mobile phone, or the cone of a loudspeaker.
Undesirable vibration- wasting energy and creating unwanted sound. For example, the vibrational motions of engines, electric motors, or any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, uneven friction, or the meshing of gear teeth. Careful designs usually minimize unwanted vibrations. Generally, engineers try to avoid vibrations, because vibrations have a number of unpleasant effects Cyclic motion implies cyclic forces. Cyclic forces are very damaging to materials. Even modest levels of vibration can cause extreme discomfort Vibrations generally lead to a loss of precision in controlling machinery.This course expose students to the systems with different Degrees of Freedom of vibratory system The minimum number of independent coordinates required to determine completely the position of all parts of a system at any instant of time defines the degree of freedom of the system principles of the fundamental concepts in mechanical vibrations for the systems like - free Undamped for single degree and two degree of freedom systems, free damped and forced damped systems. Students also learn the vibration and noise measurement techniques. At the end of this course students would be in a position to apply the skills related to vibrations necessary in industries.