1

1Lecture 1

VibroVibro--AcousticsAcoustics--An OverviewAn Overview

2Lecture 1

Vibro-Acoustics

• What?• Why?• How ?

2

3Lecture 1

Harmonic Motion

Mechanical Vibrations

Sound (Acoustics)

Force

MotionLinearNon-Linear

Arbitrary motion

4Lecture 1

Our heart beat, our lungs oscillate, we hear because our ear drum vibrates…Vibration even makes us snore!!

The light waves which permit us to see & sound waves through which we hear entail vibration

We move by oscillating our legs

We cannot even say “Vibration” without vibration of larynges, vocal cord

We limit out discussion to “MECHANICAL VIBRATION & Noise”… i.e. Vibration & Acoustics of Dynamic Systems

What is a Dynamic System??? Any System that contain Mass and Elasticity.

3

5Lecture 1

FriendFriend

•Conveyors, Hoppers, Compactors, Pneumatic Drills, etc.

•Opening of a cork from a wine bottle

•Washing Machine

•Mechanical Shakers, Mixers, Sieves, Sorters, etc.

•Musical Instruments

•Clocks, Watches

•Medical Field – Massagers, etc.

FoeFoe•RESONANCE – RESONANCE – RESONANCE

Tacoma Narrows BridgeTacoma Narrows Bridge

•Similar problems in machine tools, vehicles, turbines, pumps, compressors, buildings, aircraft & spacecraft systems

•Excessive vibration leads to loosening on parts, noise & eventual failure

•Effects of vibration on human body: Discomfort, Fatigue, Loss of Efficiency

•Sound quality in products

6Lecture 1

Vibro-Acoustic Design Considerations

•Acoustic CriteriaNoise: Hearing Damage, AnnoyanceSpeech Intelligibility, Enjoyment of MusicSound Quality: Perception & Judgment of Product/Process QualityWarning Signals: Use of sound to determine safetyUse of Sound for Diagnostics & Health Monitoring

• Vibration & Dynamic Design CriteriaLocalized Damage, Fatigue, Human DiscomfortRoughness or Harshness of Operation & EnvironmentUse of Vibration for Diagnostics & Health MonitoringStructural Integrity & Crashworthiness

4

7Lecture 1

Automotive Noise & Vibration

Road Inputs (forces)

Powertrain Forces

Acoustic Response (drivers ear)

Vibration Response (steering column)

Aerodynamic Forces

8Lecture 1

Building Blocks: m, c, kThe fundamental building blocks of a physical system that undergoes dynamic behavior are;

m Mass elements, m

Energy dissipation elements (dampers), c

Energy storage elements (springs), k

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9Lecture 1

Real Structures (m, c, and k)

10Lecture 1

Basic System (SDOF)

ground

m

ck

X(t)

F(t)

m

X

spring damping force

applied force

Applying Newton's Law:

ForcesX∑ = mass * acceleration

spring force damping force applied force mass * acceleration+ + =

6

11Lecture 1

Free Vibration Response

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.015

-0.01

-0.005

0

0.005

0.01

0.015

time - seconds

ampl

itude

damped free vibration

Given an initial state of energy and no applied force, an exponentially decaying harmonic motion will result.

This motion is characteristic of the physical properties (M,C,K) of the system.

12Lecture 1

Fundamental Properties

MK Frequency Natural n =ω

KM2C Ratio Damping =ζ

n2

d 1 Frequency Natural Damped ωζ−=ω

ground

m

ck

X(t)

πω

=2

f (Hz) Frequency Natural nn

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13Lecture 1

Free Vibration Response

time - seconds0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.015

-0.01

-0.005

0

0.005

0.01

0.015am

plitu

dedamped free vibration

The free response of the system can be described in terms of the fundamental properties.

( )( )Θ+ω= ζω− tsinAe)t(x dtn

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

-1 . 5

-1

-0 . 5

0

0 . 5

1

1 . 5

2

0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1-2

-1 . 5

-1

-0 . 5

0

0 . 5

1

1 . 5

2

14Lecture 1

Forced Response

ground

m

ck

X(t)

F(t) )ft2cos(F)t(F π=

Am

plitu

de o

f For

ce

time

)ft2cos(X)t(x Response StateSteady

Φ+π=

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.5

-1

-0.5

0

0.5

1

1.5

tim e

Dis

plac

emen

t

-

X

F

X

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15Lecture 1

Forced Response

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 -1

10 0

10 1

fn

X F

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

20

40

60

80

100

120

140

160

180

90 degreesΦ

fn Freq.

Freq.

( ) ( )[ ] 21

222 CMK

1FX

ω+ω−=

ω−ω

=Φ −2

1

MKCtan

16Lecture 1

Effect of Damping on Forced Response

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 210

-1

100

101

102

zeta(ζ) 1% 2% 5% 10% 20% 50%

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0

20

40

60

80

00

20

40

60

80

zeta(ζ) 1% 2% 5% 10% 20% 50%

Freq.

Freq.

Φ

XF

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17Lecture 1

Regions of the FRF

0 2 4 6 8 10 12 14 16 18 2010

-2

10-1

100

Frequency Response Function

Frequency Hz

Log-

Mag

nitu

de

0 2 4 6 8 10 12 14 16 18 20-200

-150

-100

-50

0

Frequency Hz

Phas

e

damping controlled region

stiffness controlled region

mass controlled region

18Lecture 1

Total Response

0 1 2 3 4 5 6

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

time - seconds

X(t) transient

X(t) steady state

0 1 2 3 4 5 6 -0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

time - seconds

SDOF total response

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19Lecture 1

Real Structures

mode 1

m1

c1 k1

p(t)

mode 2

m2

c2 k2

p(t)

mode 3

m3

c3 k3

p(t)

20Lecture 1

Mode Shapes1 2 3

8

5

2

8

0-3

8-7

6

mode 1

mode 3

mode 2

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21Lecture 1

Source - Path - Receiver Concept

Source Path Receiver

Sources:

Engine, transmission, transfer case, prop-shaft,rotating components, chain drives, wind, pumps, road surface, etc.

Paths:

Structure-borne or airborne

Receiver:

Operators ear, steering column, seat, passengers ear/seat, pass-by observers.

22Lecture 1

Source, Path, Receiver CharacteristicsSource, Path, Receiver Characteristics

Source: Depends on the definition of the analysis

•Apparent “source of energy”, e.g. Electric motor

•Vector Quantity, e.g. rotating unbalance, acoustic energy

•Characterized by forces, moments, volume-velocities

•Operating System, e.g. IC engine, washing machine, AC compressor

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23Lecture 1

Sources and Paths

24Lecture 1

Characterizing Sources

• What is the best way to characterize NVH sources?– Time Domain?– Frequency Domain?– Order Domain?

• What are these different domains?

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25Lecture 1

Characterizing Sources

• What do we want to learn about a system to characterize it?– Amplitude?– Frequency?– Damping?– Natural Frequencies?– What are significant contributors to response?

• Intricate details about different contributors?

26Lecture 1

Time Domain Characterization

• What is the time domain?– Simply digitized signal from a transducer.

RESONANCES

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27Lecture 1

Time Domain Characterization

• What can we learn from the time domain?– Sometimes when an event occurs…

• Transients• Lightly damped resonances

– Peak amplitude of overall signal• Excellent for Sound Quality playback!• Basis for frequency and order domain

data!

28Lecture 1

Frequency Domain Characterization

• What is the frequency domain?– Fourier transform of digitized time domain

data.• What good is it?

– Decomposes time domain signals into individual frequency components.

• Does this help?– YES! - remember each source produces

different frequencies!!

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29Lecture 1

Frequency Domain Characterization

ORDERS - RADIAL LINES

RESONANCES - VERTICALLINES

30Lecture 1

Order Domain Characterization

• What is the order domain?– Order domain is when data are Fourier

transformed relative to the shaft position instead of time.

• What good is it?– Energy of an order is not smeared across the

spectrum.– Orders appears as vertical lines on colormaps!

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31Lecture 1

Path: Capable of transmitting energy from the source to the receiver

•Any “media”, steel, rubber, plastic, fluids, gases

•Directionality may be important, (X,Y,Z, Θx, Θy, Θz)

•Compliant Paths characterized by complex stiffness

•Characteristics described by Frequency Response Functions.

•Examples include: engine mounts, body mounts, bolted joints, springs, shock absorbers, air, water, any structural member

Source, Path, Receiver CharacteristicsSource, Path, Receiver Characteristics

32Lecture 1

Paths of InterestPaths of Interest

Source

Substructure

Structure borne paths

Air-borne pathsReceiver

Substructure

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33Lecture 1

Air-borne vs. Structure-borne

Tire/road interface energy travels through the “structure” of the vehicle to the steering column.

Tire/road interface energy travels through the air and leaks into the cabin through a small holein the door seal.

Air-borne Path

Structure-borne Path

34Lecture 1

Receiver: Responds to energy flowing through the paths

•Human or Human-structure interface

•Structural components

•Directionality may be important, (X,Y,Z, Θx, Θy, Θz)

•Can be affected by multiple paths at the same time

•Examples include: drivers right ear, steering column, seat, conversation in the house, Floor, cabinet, isolated hardware

Source, Path, Receiver CharacteristicsSource, Path, Receiver Characteristics

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35Lecture 1

Automotive “Receivers”

Driver’s Ear

Steering Column

Accelerator pedalSeat Track

Mirrors

Energy from the sources travels through both structure-borne and air-borne pathsto the receivers

36Lecture 1

Driver’s EarCharacterization of the NVH energy received at the Drivers Ear is done with a measurement of the Sound Pressure Level.