1 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Course Introduction

DynamicSystems22.451

Peter AvitabileMechanical Engineering DepartmentUniversity of Massachusetts Lowell

jω

σ

UNSTABLESTABLE

TIME

FRF

FRF

TIME

FRF

TIME

FRF

TIME

TIME

TIME

> 1.0ζ

= 1.0ζ

= 0.7ζ

= 0.3ζ

= 0.1ζ = 0ζ

TRANSFER FUNCTION

)S(F)S(H)S(Y •=

LAPLACE DOMAIN

IMPULSE

)t(f)t(h)t(y ⊗=

∫ ττ−τ=t

0d)t(f)(h)t(y

TIME DOMAIN

FRF

)j(F)j(H)j(Y ω•ω=ω

FREQUENCY DOMAIN

RESPONSEMODELS

2 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

What you have learned thus far in other courses

Math & Science RelatedCalculusOrdinary Differential EquationsPhysics

Engineering RelatedStatics & DynamicsStrength of Materials & Applied StrengthMachine Design I & IIMathematical Methods

Why didn’t you tell us ???

3 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Text Book and References

Palm textbook has just been released.Excellent treatment of material for course.

Two other good texts

Vu & Esfandiari Ogata

4 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Overview of this course

5 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Overview of this course

6 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Overview of this course

7 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Overview of this course

Lectures and homework assignments

8 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Overview of this course

Lectures and homework assignments

9 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

http://faculty.uml.edu/pavitabile/22.451/ME22451_PDF_downloads.htm

Course Webpage is your source of information

10 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Peter Avitabile’s Webpage is tag to all course pages

http:// pavitabile.caeds.eng.uml.edu

11 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Why study Dynamic Systems ?

Static systems are rarely observed – but are often used as an approximation for design

Just about everything moves !

Must be able to predict dynamic response of systems for many applications.

Source: Thelen - UWISC

12 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

What are some Dynamic Systems ?

13 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Some systems are of personal interest

Source: Thelen - UWISC

14 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Some systems are inherently fun

Just how much does the bungee stretch ?

ANIMATE

15 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Some systems are technically challenging

response due to shock

ANIMATE

high speed videoshowing drop load

ANIMATE

16 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Some systems need performance enhancements

96.9 3 0.7 0.1 0.3 0.4 0.3 43 0.4 0.3 3.6 2.1 18.2 0.3 14 0.30.2 64.1 1.6 0.1 3.2 3.3 2.7 0.3 2.6 2.7 0.3 2 0.3 1.2 0.5 0.21.8 0.5 3.8 0.7 11.4 1.5 13.2 1.4 12.7 15.7 3.8 2.7 1.6 1.8 1.1 0.40.2 0.6 1.2 96.4 5.1 9.4 0.5 0 0.3 8.7 5.8 0 0 6.9 0 0.10.2 0.8 0.5 0.6 98.3 4.7 48.8 2.2 49.5 24.7 0.9 14.5 0.1 2.4 0.9 0.90.8 4.2 0.7 5.2 22.8 85.5 16.6 0.5 17.5 7.4 12.9 12.5 0.4 5.1 0.8 3.91.9 0.3 0.4 0.5 47.7 2.4 98.4 0.1 57 25.6 11.1 7.1 2 2.7 0.3 1.50.8 0.6 1.4 0.7 50.9 3 59 1.6 97.9 76.9 3.8 9.2 0.4 3.5 0 4.50.2 0.1 2.3 17.2 18.6 0.8 17.8 0.6 66.5 88.4 4.8 5 0.1 16.2 0.3 15.52.3 0.1 0.1 0.3 3.7 0.8 1.1 8.9 2.1 1.1 6.6 8.4 9.8 11.2 15.7 0.5

12.6 2.2 0.8 0.1 1 0.8 0 55.5 0.5 0.4 5.4 23 86.9 2.8 97.4 0.40.3 2 10.1 1 0.2 1.7 4.1 0.2 10.5 17.8 14.6 0.6 0.2 22.7 1 92.8

17 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

Some systems are technically challenging

missile launch responseANIMATE

AIRFRAME

WING

PYLON

MISSILE

TYPICAL CONFIGURATION

18 Dr. Peter AvitabileModal Analysis & Controls Laboratory22.451 Dynamic Systems – Introduction

What needs to be considered to evaluate a system?

Applied Force(speed bump)

Free body Diagram

Dynamic characteristics

Response Specification