BDC 4013 NOISE AND VIBRATION

LECTURE 1 FUNDAMENTAL OF

VIBRATION

DR SALIHATUN MD SALLEHFaculty of Mechanical & Manufacturing EngineeringUniversiti Tun Hussein Onn Malaysia

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.

DEFINITIONVibration :

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.

WHY STUDY VIBRATION?1. Vibrations can lead to excessive deflections and failure on

the machines and structures

2. To reduce vibration through proper design of machines and their mountings

3. To utilize profitably in several consumer and industrial applications (quartz oscillator for computers)

4. To improve the efficiency of certain machining, casting, forging & welding processes

5. To simulate earthquakes for geological research and conduct studies in design of nuclear reactors

BASIC CONCEPTSVibratory System consists of:

1) spring or elasticity2) mass or inertia3) damper

Involves transfer of potential energy to kinetic energy and vice versa

Minimum number of independent coordinates required to determine completely the positions of all parts of a system at any instant of timeExamples of single degree-of-freedom systems:

DEGREE OF FREEDOM (D.O.F)

Examples of two degree-of-freedom systems:

Examples of three degree-of-freedom systems:

CLASSIFICATION OF VIBRATION1. 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. oscillationarises 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 oscillations

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:

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.

pi

21

==f

AmplitudeThe maximum displacement of a vibrating body from its equilibrium position.

Period of OscillationThe time taken to complete one cycle of motion, denoted by .

Frequency of oscillationThe number of cycles per unit time, denoted by f.

Phase angle , .Consider two vibratory motion:

)sin(sin

22

11

+=

=

tAxtAx

These two harmonic motion are called synchronous because they have the same frequency or angular velocity, .

Natural frequencyNatural frequency is the frequency when the system vibrating at its natural modes.

=

0

log10PPdB

=

=

0

2

0

log20log10XX

XXdB

BeatsWhen two harmonic motions, with frequencies close to one another, are added, the resulting motion exhibits a phenomenon known as beats.

OctaveWhen 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.

DecibelA 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

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

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:

tAAx sinsin ==

tAdtdx

cos=

xtAdt

xd 222

2

sin ==

Example: Scotch yoke mechanism

The similarity between cyclic(harmonic) and sinusoidal motion.

Harmonic Motion