vibrations –basic definitionsfree vibration equilibrium pos. • when a system is initially...
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VIBRATIONS – Basic Definitions
Dr. S. K. PrasadProfessor of Civil EngineeringS. J. College of EngineeringMysuru [email protected]: +91-94496-21994
What is vibration?
• Vibrations are oscillations of a system about an equilbrium position.
VibrationIt is also an everyday phenomenon we meet on everyday life
Useful effect of Vibration
Harmful effect of vibration
Noise
Destruction
Compressor
Ultrasonic cleaning
Testing
Wear
Fatigue
Vibration
Vibration in our Lives
• Our heart beats
• Our lungs oscillate
• We hear because our ear drums vibrate
• Vibration makes us snore
• Light waves permit us to see
• Sound waves allow us to hear
• We move because of oscillation of legs
• We can not utter ‘vibration’ without the oscillation of larynges and vocal cords
• We limit our discussion to Mechanical Vibration
• Vibration of dynamic system of a structure
• It is the oscillations of a system that has mass and elasticity
Vibration in our Lives
Vibration – Friend or Foe
Vibration in
Machinery
Vibration in
Recreation
Vibration in
Defense
Vibration in
Transportation
Vibration in
Aerospace
Vibration in
Automobile
Vibration in
Health Care
Vibration in
Structures
Vibration during
Disasters
TYPES OF FORCES
Static or Monotonic
Dynamic
Periodic
Harmonic
Steady State
Transient
Non-Harmonic
Impulse Type
Random
Basic Definitions
Periodic Motion: A motion that repeats itselfafter equal interval of time.
Time Period: Time taken for one completecycle.
Simple Harmonic Motion: Motion of particlewith time that moves round a circle withuniform angular velocity. Trigonometricfunctions can be used to represent suchmotion.
Basic Definitions
Amplitude (Z or 2Z): The maximum displacement of avibrating body from its mean position. The amplitude caneither be single amplitude (Z) when the distance from meanposition to maximum displacement is measured or doubleamplitude (2Z) when the distance from negative maximum topositive maximum displacement (motion) is measured.
Frequency: It is the number of cycles per unit time.Frequency and time period are inversely proportional to eachother. A vibratory motion can have either a very highfrequency or a very low frequency. Frequency can beexpressed either as angular (circular) frequency (ω) oroscillatory frequency (f). ω is expressed in radians per secondand f is expressed in cycles per second or Hertz.
Basic Definitions
Free Vibration: Vibration of a systembecause of its own elastic property. Noexternal force is required for this vibration andonly initiation of vibration may be necessary.
Forced Vibration: A system that vibratesunder an external force at the samefrequency as that of external force.
Basic Definitions
Natural frequency: It is the frequency of freevibration of a system. It is constant for a system. Infact, it is an inherent property of a system. Itdepends on the elastic properties, mass andstiffness of the system.
Resonance: Vibration of a system when thefrequency of external force is equal to the naturalfrequency of the system. The amplitude of vibrationat resonance becomes excessive. Duringresonance, with minimum input, there will be amaximum output. Hence both displacement and thestresses in the vibrating body become very high.
Basic Definitions
Damping: It is the resistance to motion. It is also thesluggishness. Hence it is the delay in response to anyaction. Damping is observed only under fast loading, andnot during static loading.
Degree of freedom: The number of independentcoordinate systems required to specify a motion. If themotion is in one direction due to the vibration of a singlespring, then it is a Single degree of freedom system. If aparticle is likely to vibrate in space, it will have sixdegrees of freedom, namely three translations and threerotations along three axis. A continuum can have infinitedegrees of freedom.
Basic Definitions
Phase difference : The angle between two rotatingvectors representing Simple Harmonic Motion, In timedomain, it can be represented as the delay in one motioncompared with the other.
Wave : It is the vibratory motion of a body or a particlerepresented in time domain or space domain. Forrepresenting a one dimensional wave mathematically,the partial differential equation is given by,
2
22
2
2
x
uv
t
u
Basic Definitions
fT
12
vT
f
v
k
2
T = Time period (in sec)ω = Angular or Circular velocity (in rad/sec)f = Frequency of oscillations (in cycles/sec or Hz)λ = Wave length (in m)k = Wave number = ω/v (in rad/m)v = Wave velocity (in m/sec)
Basic Definitions
TYPES OF LOADING
CYCLIC OR REPETITIVELOADING
SLOWLOADING
RAPID OR TRANSIENT LOADING
STATIC LOADING
TIME
FO
RC
E
TYPES OF LOADING
CYCLIC OR REPETITIVELOADING
SLOW STATIC LOADING
RAPID OR TRANSIENT LOADING
STATIC LOADING
TIME
FO
RC
E
OSCILLATORY LOAD
Large Period Small Period
LOAD
Single Impulse Multiple Impulse
WHAT IS DYNAMIC FORCE ?
Time Time
Time Time
Actual Impulse
Typical Seismogram
• Random• Time Dependent• Cyclic
Start of PrimaryWaves
Start of SecondaryWaves
Start of Surface Waves
TraceAmplitude
Strong Motion
Time
SA
Acceleration
• PGA• Predominant Frequency• Duration of Strong Motion
No two earthquake motions are similar
Free vibration
Equilibrium pos.
• When a system is initially disturbed by a displacement, velocity or acceleration, the system begins to vibrate with a constant amplitude and frequency depending on its stiffness and mass.
• This frequency is called as natural frequency, and the form of the vibration is called as mode shapes
Forced VibrationIf an external force is applied to a system, the system will follow the force with the same frequency.
However, when the forcingfrequency is increased to the system’s natural frequency, amplitudes will dangerously increase in this region. This phenomenon called as“Resonance”
’
Vibration parameters
All mechanical systems can be modeled by containing three basic components:
spring, damper, mass
When these components are subjected to constant force, they react with a constant
displacement, velocity and acceleration
Newton’s Laws of Motion&
Earthquake Engineering
Newton’s First Law of Motion
Lesson: Wear your Seat BeltsLaw of Inertia
Every object continues to remain in its initial status unless acted upon by external force.
Newton’s Second Law of Motion
Lesson: Do not disturb Bad persons
Everyone unconsciously knows the second law that heavier objects require more force to move the same distance as lighter objects
F = m.a
Newton’s Third Law of Motion
Rockets Action: Push down on ground with powerful engine.
Reaction: Ground pushes the rocket upwards with equal force.
Lesson: If you hit some body, expect the same reaction.
For every action there is an equal and opposite reaction
∑FA = 0Statics
Dynamics∑FA - FI = 0
Dynamics is dangerous & action packed. But interesting
FI = m.a
Inertia ???
Effects of Earthquake
ACCELERATIONACCELERATION
DECELERATIONDECELERATION
Inertia Force F = m a
Building at RestBuilding at Rest Ground Accelerates to LeftGround Accelerates to Left
Ground Accelerates to RightGround Accelerates to Right Ground & Building at RestGround & Building at Rest
Period of Vibration
DAMPING AND RESONANCE
Effect of Damping
Effect of Resonance
Spring in vibration
F = C.V
c
Damper - Dashpot
Vibration System