COOLER DYNAMIC ANALYSIS 1 - Cooler Input

COOLER DYNAMIC ANALYSIS 1 - Cooler Input

RPM

_EA16

 750 rpm  RPM

_EA15

 1470 rpm 

ω

cooler_EA16

RPM

_EA16

78.54 rad

 s



 ω

cooler_EA15

RPM

_EA15

153.938 rad

 s





f

cooler_EA16

ω

cooler_EA16

2 π   12.5 Hz 

 f

cooler_EA15

ω

cooler_EA15

2 π   24.5 Hz 



2 - Supporting Beam Input

E  210 GPa  A

_b

 113 cm  ² I

_y

 18260 cm  ⁴ I

_z

 6310 cm  ⁴ L

_b

 5.70 m 

3 - Mass Coordinates

Mass relative span:

L

₁

 1.0 m  L

₂

 2.0 m  L

₃

 2.0 m 

Mass absolute distance:

x

₁

 L

₁

 1 m x

₂

 x

₁

 L

₂

 3 m x

₃

 x

₂

 L

₃

 5 m L

₄

 L

_b

 x

₃

 0.7m

check_1 "YES" if L

₄

 0

"NO" otherwise

"YES"





4 - Load input

W

₁

 100 kN  W

₂

 50 kN  W

₃

 30 kN 

m

₁

W

₁

g  1.02 10  ⁴ kg



m

₂

W

₂

g  5.099 10  ³ kg



m

₃

W

₃

g  3.059 10  ³ kg



5 - Local Matrix

I  I

_y

 1.826 10  ^{ 4} m ⁴

K

_{1_LOC}

2.373 10  ⁹ 0 0 2.373

  10 ⁹ 0 0

0 4.602 10  ⁸ 2.301 10  ⁸

0 4.602

  10 ⁸ 2.301 10  ⁸

0 2.301 10  ⁸ 1.534 10  ⁸

0 2.301

  10 ⁸ 7.669 10  ⁷

2.373

  10 ⁹ 0 0 2.373 10  ⁹

0 0

0 4.602

  10 ⁸ 2.301

  10 ⁸ 0 4.602 10  ⁸

2.301

  10 ⁸

0 2.301 10  ⁸ 7.669 10  ⁷

0 2.301

  10 ⁸ 1.534 10  ⁸

 

 

 

 

 



 

 

 

 

 





K

_{2_LOC}

1.187 10  ⁹ 0 0 1.187

  10 ⁹ 0 0

0 5.752 10  ⁷ 5.752 10  ⁷

0 5.752

  10 ⁷ 5.752 10  ⁷

0 5.752 10  ⁷ 7.669 10  ⁷

0 5.752

  10 ⁷ 3.835 10  ⁷

1.187

  10 ⁹ 0 0 1.187 10  ⁹

0 0

0 5.752

  10 ⁷ 5.752

  10 ⁷ 0 5.752 10  ⁷

5.752

  10 ⁷

0 5.752 10  ⁷ 3.835 10  ⁷

0 5.752

  10 ⁷ 7.669 10  ⁷

 

 

 

 

 



 

 

 

 

 





K

_{3_LOC}

1.187 10  ⁹ 0 0 1.187

  10 ⁹ 0 0

0 5.752 10  ⁷ 5.752 10  ⁷

0 5.752

  10 ⁷ 5.752 10  ⁷

0 5.752 10  ⁷ 7.669 10  ⁷

0 5.752

  10 ⁷ 3.835 10  ⁷

1.187

  10 ⁹ 0 0 1.187 10  ⁹

0 0

0 5.752

  10 ⁷ 5.752

  10 ⁷ 0 5.752 10  ⁷

5.752

  10 ⁷

0 5.752 10  ⁷ 3.835 10  ⁷

0 5.752

  10 ⁷ 7.669 10  ⁷

 

 

 

 

 



 

 

 

 

 





K

_{4_LOC}

3.39 10  ⁹ 0 0

 3.39  10 ⁹ 0 0

0 1.342 10  ⁹ 4.695 10  ⁸

0 1.342

  10 ⁹ 4.695 10  ⁸

0 4.695 10  ⁸ 2.191 10  ⁸

0 4.695

  10 ⁸ 1.096 10  ⁸

 3.39  10 ⁹ 0 0 3.39 10  ⁹

0 0

0 1.342

  10 ⁹ 4.695

  10 ⁸ 0 1.342 10  ⁹

4.695

  10 ⁸

0 4.695 10  ⁸ 1.096 10  ⁸

0 4.695

  10 ⁸ 2.191 10  ⁸

 

 

 

 

 



 

 

 

 

 





6 - Global Matrix

C

₁

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

 

 

 

 



 

 

 

 



 C

₂

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

 

 

 

 



 

 

 

 





C

₃

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

 

 

 

 



 

 

 

 



 C

₄

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

0 1 0 0 0 0

0 0 1 0 0 0

0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 0 0 1

 

 

 

 



 

 

 

 





K

₁

 C

₁^T

 K

_{1_LOC}

 C

₁

K

₂

 C

₂^T

 K

_{2_LOC}

 C

₂

K

₃

 C

₃^T

 K

_{3_LOC}

 C

₃

K

₄

 C

₄^T

 K

_{4_LOC}

 C

₄

K

_TOT

 K

₁

 K

₂

 K

₃

 K

₄

OC 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0 0 0 0

0 0 1 0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0 0 0 0

0 0 0 0 1 0 0 0 0 0 0

0 0 0 0 0 1 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0

0 0 0 0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0 1 0 0

0 0 0 0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



K

_RID

 OC K 

_TOT

 OC

^T

7 - Load Vector

W

_L

0 0  W

₁

N 0 0  W

₂

N 0 0  W

₃

N 0 0

 



 

 

W

_L

^{0 1 2 3 4 5 6 7}

0 0 0 -1·10

⁵

0 0 -5·10

⁴

0 ...



8 - Eigen Values

OC

_DYN

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 1 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1

 

 

 

 

 



 

 

 

 

 





Dynamic Matrix:

K

_DYN

 OC

_DYN

 K

_TOT

 OC

_DYN^T

K

_DYN

1.534 10  ⁸ 2.301

  10 ⁸ 7.669 10  ⁷

0 0 0 0 0

2.301

  10 ⁸ 5.177 10  ⁸

1.726

  10 ⁸ 5.752

  10 ⁷ 5.752 10  ⁷

0 0 0

7.669 10  ⁷ 1.726

  10 ⁸ 2.301 10  ⁸

5.752

  10 ⁷ 3.835 10  ⁷

0 0 0

0 5.752

  10 ⁷ 5.752

  10 ⁷ 1.15 10  ⁸

0 5.752

  10 ⁷ 5.752 10  ⁷

0

0 5.752 10  ⁷ 3.835 10  ⁷

0 1.534 10  ⁸

5.752

  10 ⁷ 3.835 10  ⁷

0

0 0 0 5.752

  10 ⁷ 5.752

  10 ⁷ 1.399 10  ⁹

4.12 10  ⁸ 4.695 10  ⁸

0 0 0 5.752 10  ⁷ 3.835 10  ⁷ 4.12 10  ⁸ 2.958 10  ⁸ 1.096 10  ⁸

0 0 0 0 0 4.695 10  ⁸ 1.096 10  ⁸ 2.191 10  ⁸

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Mass Matrix:

M

_DYN

1 0 0 0 0 0 0 0

0 m

₁

kg 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 m

₂

kg 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 m

₃

kg 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 0 0 0 0 0 0 0

0 1.02 10  ⁴

0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 5.099 10  ³

0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 3.059 10  ³

0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

 

 

 

 

 

 



 

 

 

 

 

 







Modal Matrix:

M

_modal

 M

_DYN

^{ 1}  K

_DYN

Eigenvalues:

Λ ^ sort eigenvals M  

_modal

 

^T

Natural Frequencies:

ω

₀

Λ

^T

rad

 s

34.636 124.096 283.357 9.763 10  ³ 1.127 10  ⁴ 1.289 10  ⁴ 1.689 10  ⁴ 1.945 10  ⁴

 

 

 

 

 

 

 

 

 

 

 

 

 

 

rad

 s



 f

₀

ω

₀

2 π 

5.512 19.75 45.098 1.554 10  ³ 1.794 10  ³ 2.051 10  ³ 2.688 10  ³ 3.096 10  ³

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 Hz



 T

₀

f

₀

^{ 1}

0.181 0.051 0.022 6.436 10  ^{ 4} 5.573 10  ^{ 4} 4.876 10  ^{ 4} 3.72 10  ^{ 4} 3.23 10  ^{ 4}

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 s



9 - Hysteretic Damping matrix

α  0 β  0.04

C

_H

^  α M 

_DYN

 β K 

_DYN



C

_H

6.135 10  ⁶ 9.203

  10 ⁶ 3.068 10  ⁶

0 0 0 0 0

9.203

  10 ⁶ 2.071 10  ⁷

6.902

  10 ⁶ 2.301

  10 ⁶ 2.301 10  ⁶

0 0 0

3.068 10  ⁶ 6.902

  10 ⁶ 9.203 10  ⁶

2.301

  10 ⁶ 1.534 10  ⁶

0 0 0

0 2.301

  10 ⁶ 2.301

  10 ⁶ 4.602 10  ⁶

0 2.301

  10 ⁶ 2.301 10  ⁶

0

0 2.301 10  ⁶ 1.534 10  ⁶

0 6.135 10  ⁶

2.301

  10 ⁶ 1.534 10  ⁶

0

0 0 0 2.301

  10 ⁶ 2.301

  10 ⁶ 5.596 10  ⁷ 1.648 10  ⁷ 1.878 10  ⁷

0 0 0 2.301 10  ⁶ 1.534 10  ⁶ 1.648 10  ⁷ 1.183 10  ⁷ 4.382 10  ⁶

0 0 0 0 0 1.878 10  ⁷ 4.382 10  ⁶ 8.765 10  ⁶

 

 

 

 

 

 

 

 

 

 

 

 

 

 



10 - Harmonic Forces

F

_{h_EA15}

 20 kN  f

cooler_EA15

 24.5 Hz  F

_{h_EA16}

 10 kN  f

cooler_EA16

 12.5 Hz 

F

_{DYN_EA15}

( ) f F

_{h_EA15}

N

2 π   f

  ²

2 π   f

cooler_EA15

  ²





F

_{DYN_EA16}

( ) f F

_{h_EA16}

N

2 π   f

  ²

2 π   f

cooler_EA16

  ²





F

DYN_EA15_SS

( ) f ^  0 F

_{DYN_EA15}

( ) 0 0 0 0 0 0 f 

F

DYN_EA16_SS

( ) f ^  0 0 0 F

_{DYN_EA16}

( ) 0 F f

_{DYN_EA16}

( ) 0 0 f 

0 20 40 60 80 100 2 10 

⁵

4 10 

⁵

6 10 

⁵

8 10 

⁵

HARMONIC FORCES

[Hz]

[N]

F_{DYN_EA15}

( )

f F_{DYN_EA16}

( )

f

f

11 - Direct integration of motion equations

Κ

_DYN

( ) f  K

_DYN

  C 1 

_H

  2 π   f  ²  M

_DYN

 

 

Dynamic displacements calculation:

U

_EA15

( ) f  Κ

_DYN

( ) f ^{ 1}  F

DYN_EA15_SS

( ) f

^T

U

_EA16

( ) f  Κ

_DYN

( ) f ^{ 1}  F

DYN_EA16_SS

( ) f

^T

Dynamic displacements under bearing points:

u

_{EA15_1}

( ) f U

_EA15

( ) f

 1

u

_{EA15_2}

( ) f U

_EA15

( ) f

 3

u

_{EA15_3}

( ) f U

_EA15

( ) f

 5

u

_{EA16_1}

( ) f U

_EA16

( ) f

 1

u

_{EA16_2}

( ) f U

_EA16

( ) f

 3

u

_{EA16_3}

( ) f U

_EA16

( ) f

 5

f  0 0.01   100

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1.4 10 

^4

2.8 10 

^4

4.2 10 

^4

5.6 10 

^4

7 10 

^4

8.4 10 

^4

9.8 10 

^4

1.12 10 

^3

1.26 10 

^3

1.4 10 

^3

DYNAMIC RESPONSE - EA15

[Hz]

[m]

u_{EA15_1}

( )

f u_{EA15_2}

( )

f u_{EA15_3}

( )

f

f

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 8 10 

^4

1.6 10 

^3

2.4 10 

^3

3.2 10 

^3

4 10 

^3

4.8 10 

^3

5.6 10 

^3

6.4 10 

^3

7.2 10 

^3

8 10 

^3

DYNAMIC RESPONSE - EA16

[Hz]

[m]

u_{EA16_1}

( )

f u_{EA16_2}

( )

f u_{EA16_3}

( )

f

f

12 - AMPLITUDE OF VIBRATIONS - RMS

u

_{RMS_1}

( ) f  u

_{EA15_1}

( ) f ²  u

_{EA16_1}

( ) f ² u

_{RMS_2}

( ) f  u

_{EA15_2}

( ) f ²  u

_{EA16_2}

( ) f ² u

_{RMS_3}

( ) f  u

_{EA15_3}

( ) f ²  u

_{EA16_3}

( ) f ²

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 8 10 

^4

1.6 10 

^3

2.4 10 

^3

3.2 10 

^3

4 10 

^3

4.8 10 

^3

5.6 10 

^3

6.4 10 

^3

7.2 10 

^3

8 10 

^3

AMPLITUDE OF VIBRATIONS - RMS

[Hz]

[m]

u_{RMS_1}

( )

f u_{RMS_2}

( )

f u_{RMS_3}

( )

f

f

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 4.5 10 

^4

9 10 

^4

1.35 10 

^3

1.8 10 

^3

2.25 10 

^3

2.7 10 

^3

3.15 10 

^3

3.6 10 

^3

4.05 10 

^3

4.5 10 

^3

NODE 1

[Hz]

[m]

u_{RMS_1}

( )

f

u_{EA15_1}

( )

f u_{EA16_1}

( )

f

f

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 7 10 

^4

1.4 10 

^3

2.1 10 

^3

2.8 10 

^3

3.5 10 

^3

4.2 10 

^3

4.9 10 

^3

5.6 10 

^3

6.3 10 

^3

7 10 

^3

NODE 2

[Hz]

[m]

u_{RMS_2}

( )

f

u_{EA15_2}

( )

f u_{EA16_2}

( )

f

f

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 8 10 

^4

1.6 10 

^3

2.4 10 

^3

3.2 10 

^3

4 10 

^3

4.8 10 

^3

5.6 10 

^3

6.4 10 

^3

7.2 10 

^3

8 10 

^3

NODE 3

[Hz]

[m]

u_{RMS_3}

( )

f

u_{EA15_3}

( )

f u_{EA16_3}

( )

f

f