# Mechanical Vibrations Notes

Mohan Rao Chuck Van Karsen

Mechanical Engineering-Engineering Mechanics Michigan Technological University Copyright 2003

MEEM 3700

Lecture 1-Introduction

1

No Forces No Motion

Forces

Motion

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1

Force Linear Non-Linear Arbitrary motion Harmonic Motion Motion

Mechanical Vibrations Sound (Acoustics)

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Lecture 1-Introduction

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Dynamics and Kinematics (MEEM 2700) Strength of Materials (MEEM 2150) Thermodynamics (MEEM 2200) Differential Equations (MA3521)

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Lecture 1-Introduction

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2

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 cannot even say “Vibration” without vibration of larynges, vocal cord We move by oscillating our legs We limit out discussion to “MECHANICAL VIBRATION”… i.e. Vibration of Dynamic Systems What is a Dynamic System??? Any System that contain Mass and Elasticity.

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Lecture 1-Introduction

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Friend

•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.

Foe

•RESONANCE – RESONANCE – RESONANCE

Tacoma 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 MEEM 3700 6

Lecture 1-Introduction

3

Vibrations in Machinery

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Vibrations in Recreation

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4

Vibrations in Defense

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Vibrations in Transportation

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Vibrations in Aerospace

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Vibrations in Automobiles

NVH (Noise, Vibration, & Harshness) is a Top Priority for the BIG 3 Auto Industry. Several hundred million dollars have been invested in infrastructure & human resource development in this area over the past 10 years.

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Lecture 1-Introduction

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6

Sound/Noise in Automobiles

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Research in the Dynamic Systems Laboratory

Damping Characterization

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Research in the Dynamic Systems Laboratory

Nobeyama 45m Radio Telescope

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Lecture 1-Introduction

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Lecture 1-Introduction

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8

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Lecture 1-Introduction

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M K

Mass

Inertia (Kinetic Energy)

C

Spring

Storage (Potential Energy)

Damper

Dissipative (Energy Loss)

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Lecture 1-Introduction

18

9

Ct J Kt

Torsional Spring Rotating Inertia Torsional Damper

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Lecture 1-Introduction

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M

K

X

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Lecture 1-Introduction

20

10

M

X1

c

K

c

K X 2

Rear Suspension

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Lecture 1-Introduction

Front Suspension

21

M X1 X2

c Mt X3

K

K

c

Wheels/tires

K

Mt

K

X4

22

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Lecture 1-Introduction

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Ms X5

K

Seat

M X1 X2

c Mt X3

K

K

c Mt

K

K

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X4

23

Lecture 1-Introduction

Ms X5

K

Seat

θ

M X1

K K

c Mt X3

K

X6

c Mt

X2

K

MEEM 3700

X4

24

Lecture 1-Introduction

12

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Lecture 1-Introduction

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13

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