1 Dr. Peter Avitabile Modal Analysis & Controls Laboratory 22.451 Dynamic Systems – Introduction Course Introduction Dynamic Systems 22.451 Peter Avitabile Mechanical Engineering Department University of Massachusetts Lowell j ω σ UNSTABLE STABLE TIME FRF FRF TIME FRF TIME FRF TIME TIME TIME > 1.0 ζ = 1.0 ζ = 0.7 ζ = 0.3 ζ = 0.1 ζ = 0 ζ TRANSFER FUNCTION ) S ( F ) S ( H ) S ( Y • = LAPLACE DOMAIN IMPULSE ) t ( f ) t ( h ) t ( y ⊗ = ∫ τ τ − τ = t 0 d ) t ( f ) ( h ) t ( y TIME DOMAIN FRF ) j ( F ) j ( H ) j ( Y ω • ω = ω FREQUENCY DOMAIN RESPONSE MODELS
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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