1. LECTURE 1 – FUNDAMENTAL OF VIBRATION
BDC 4013 – NOISE AND VIBRATION
ROSLI ASMAWI
Faculty of Mechanical & Manufacturing Engineering
Universiti Tun Hussein Onn Malaysia
LECTURE 1 – FUNDAMENTAL OF VIBRATION

2. OUTLINE What is vibration? Why it is important? Basic Concepts……..
Classification of Vibration….
Definition and Terminology …..
Vibration Analysis Procedure…..
Spring, Mass and Damping Elements…..
Harmonic and Periodic Motions…….

3. DEFINITION Vibration :
Any motion that repeats itself after an interval of time is called vibration or oscillation.
The swinging of a pendulum and the motion of a plucked string are typical examples of vibration. The study of vibration deals with the study of oscillatory motions of bodies and the forces associated with them.
From Encyclopedia Britannica:
Periodic back-and-forth motion of the particles of an elastic
body or medium, commonly resulting when almost any physical
system is displaced from its equilibrium condition and allowed
to respond to the forces that tend to restore equilibrium.

4. WHY STUDY VIBRATION?
Vibrations can lead to excessive deflections and failure on the machines and structures
To reduce vibration through proper design of machines and their mountings
To utilize profitably in several consumer and industrial applications (quartz oscillator for computers)
To improve the efficiency of certain machining, casting, forging & welding processes
To simulate earthquakes for geological research and conduct studies in design of nuclear reactors

5. Importance of Study Vibration
Most human activities involve vibration in one form or other
Most prime movers have vibrational problems due to inherent unbalance in the engine
If natural frequencies are coincided with the frequency external excitations, a dangerous resonance will lead to excessive deflections and failures.
Vibration can be utilized profitably in industrial applications (vibratory equipments)

6. Industrial applications
Vibrating conveyor
Compactor

7. Failure due to resonance (The failure of the Bridge at Tacoma Narrows in May 1940)

8. BASIC CONCEPTS Vibratory System consists of: 1) spring or elasticity
2) mass or inertia
3) damper
Involves transfer of potential energy to kinetic energy and vice versa

9. DEGREE OF FREEDOM (D.O.F)
Minimum number of independent coordinates required to determine completely the positions of all parts of a system at any instant of time
Examples of single degree-of-freedom systems:

10. Examples of two degree-of-freedom systems:
Examples of three degree-of-freedom systems:

11. CLASSIFICATION OF VIBRATION
1. Free Vibration:
A system is left to vibrate on its own after an initial disturbance and no
external force acts on the system. E.g. simple pendulum
2. Forced Vibration:
A system that is subjected to a repeating external force. e.g. oscillation
arises from diesel engines
- Resonance occurs when the frequency of the external force coincides with one of the natural frequencies of the system
3. Undamped Vibration:
When no energy is lost or dissipated in friction or other resistance during
oscillations
4. Damped Vibration:
When any energy is lost or dissipated in friction or other resistance during

12. 5. Linear Vibration:
When all basic components of a vibratory system, i.e. the spring, the
mass and the damper behave linearly
6. Nonlinear Vibration:
If any of the components behave nonlinearly
7. Deterministic Vibration:
If the value or magnitude of the excitation (force or motion) acting on a
vibratory system is known at any given time
8. Nondeterministic or random Vibration:
When the value of the excitation at a given time cannot be predicted
Examples of deterministic and random excitation:

13. DEFINITIONS AND TERMINOLOGY…..
Cycle
The movement of a vibrating body from its undisturbed or equilibrium position to its extreme position in one direction, then to the equilibrium position, then to its extreme position in other direction and back to equilibrium position.
Amplitude
The maximum displacement of a vibrating body from its equilibrium position.
Period of Oscillation
The time taken to complete one cycle of motion, denoted by τ.
Frequency of oscillation
The number of cycles per unit time, denoted by f.

14. Phase angle , Ф.
Consider two vibratory motion:
These two harmonic motion are called synchronous because they have the same frequency or angular velocity, ω.
Natural frequency
Natural frequency is the frequency when the system vibrating at its natural modes.

15. Beats
When two harmonic motions, with frequencies close to one another, are added, the resulting motion exhibits a phenomenon known as beats.
Octave
When the maximum value of a range of frequency is twice its minimum value, it is known as an octave band. E.g. 75 – 150 Hz, 150 – 300 Hz.
Decibel
A decibel (dB) is defined as a ratio of electric powers, P/Po, as
where Po is some reference value of power. Since electric power is proportional to the square of the voltage (X), the decibel can also be expressed as

16. VIBRATION ANALYSIS PROCEDURE
A vibratory system is a dynamic system for which the variables such as the excitations (inputs) and responses (outputs) are time-dependent.
Step 1: Mathematical Modeling
Step 2: Derivation of Governing Equations
Step 3: Solution of the Governing Equations
Step 4: Interpretation of the Results

17. Harmonic Motion
Periodic Motion: motion repeated after equal intervals of time
Harmonic Motion: simplest type of periodic motion
1) Vectorial representation of Harmonic Motion:
Displacement (x):
Velocity:
Acceleration:

18. Harmonic Motion Example: Scotch yoke mechanism
The similarity between cyclic
(harmonic) and sinusoidal motion.