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Modeling Dynamic Systems. Basic Quantities From Earthquake Records Fourier Transform, Frequency Domain Single Degree of Freedom Systems (SDOF) Elastic Response Spectra Multi-Degree of Freedom Systems, (MDOF) Modal Analysis Dynamic Analysis by Modal Methods Method of Complex Response.

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modeling dynamic systems
Modeling Dynamic Systems
  • Basic Quantities From Earthquake Records
  • Fourier Transform, Frequency Domain
  • Single Degree of Freedom Systems (SDOF) Elastic Response Spectra
  • Multi-Degree of Freedom Systems, (MDOF) Modal Analysis
  • Dynamic Analysis by Modal Methods
  • Method of Complex Response
earthquake elastic response spectra

xt

x

m

m

x

c

c

k/2

k/2

k/2

k/2

xg

(a)

(b)

Earthquake Elastic Response Spectra
multi degree of freedom

x3

m3

c3

k3/2

k3 /2

x2

m2

c2

k2/2

k2/2

x1

m1

y3

y2

c1

y4

k1/2

k1/2

y1

y5

θ3

θ2

θ5

θ4

θ1

(a)

(b)

Multi-Degree of Freedom
slide16

Finite Elements

u1

u7

G1,ρ1,ν1

u2

u8

method of complex response
Method of Complex Response
  • Given earthquake acceleration vs. time, ü(t)
  • FFT => ω1, ω 2 , ω 3...ωn ; {p}1 ,{p}2 ,{p}3,{p}n
  • Recall that
  • Solve
  • FFT-1 => ü (t)
slide19

212,428 nodes, 189,078 brick elements and 1500 shell elements

Circular boundary to reduce reflections

slide22

Zoom 1

Zoom 2