CAE-Companion-2018-2019

966.7 800.0 633.3 466.7 300.0 133.3

Theory WISSEN CAE

RESPONSE GRAPH

8.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

6.

4.

*10 -3

2.

0.

X-DISPLACEMENT, FLANGE

-2.

1000.

1001.

1002.

1003.

1004.

1005.

Figure 9: Antenna model in various rotational positions using Bathe Method When using the Bathe method, the solution is obtained very accurately for many revolutions, whereas the Newmark time integration procedure fails before finishing the second revolution, see Figure 10 for the antenna rotation instability occurring in the solution. The numerical instability is also well seen when studying the axial forces in the antenna stabilizers, see Figure 10, and occurs quite suddenly. No physical damping, e.g. Rayleigh damping, is used in the model. This antenna rotation problemmay be seen as an extension of the problem of a rotating stiff pendulum[2].

*10 -2

TIME

Y

Y

TIME 10.02500

TIME 10.02500

DISP MAG 100.0

Z

X

Z

X

VELOCITY TIME 10.02500 TIME 10.02500

FE_PRESSURE RST CALC TIME 10.02500 DISP MAG 100.0

Y

36.08

ACCELERATION MAGNITUDE TIME 10.02500 X

Z

180000. 80000. -20000. -120000. -220000. -320000.

35.00 27.50 20.00 12.50 5.00

966.7 800.0 633.3 466.7 300.0 133.3

ACCELERATION MAGNITUDE TIME 10.02500

TIME 10.02500

X

RESPONSE GRAPH

8.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

Y Z

6.

0. Figure 7: Predicted response using Newmark method with numerical damping, (δ = 0.6, α = 0.3025) 2. 4. *10 -3

NODAL CONTACT STATUS TIME 10.02500

966.7 800.0 633.3 466.7 300.0 133.3

STICKING SLIPPING CLOSED

X-DISPLACEMENT, FLANGE

-2.

OPEN DEAD

1000.

1001.

1002.

1003.

1004.

1005.

*10 -2

TIME

RESPONSE GRAPH

8.

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

6.

4.

*10 -3

2.

0.

X-DISPLACEMENT, FLANGE

-2.

1000.

1001.

1002.

1003.

1004.

1005.

*10 -2

TIME

Y

Y

TIME 10.02500

TIME 10.02500

DISP MAG 100.0

Z

X

Z

X

VELOCITY TIME 10.02500

FE_PRESSURE RST CALC TIME 10.02500

36.05

ACCELERATION MAGNITUDE TIME 10.02500

180000. 80000. -20000. -120000. -220000. -320000.

35.00 27.50 20.00 12.50 5.00

966.7 800.0 633.3 466.7 300.0 133.3

TIME 10.02500

X

RESPONSE GRAPH

8.

Y Z

X-DISPLACEMENT, FLANGE X-DISPLACEMENT, SUPPORT_PLATE X-DISPLACEMENT, TOP

6.

0. Figure 8: Predicted response using Bathe method, no physical damping 2. 4. *10 -3 X-DISPLACEMENT, FLANGE

NODAL CONTACT STATUS TIME 10.02500

STICKING SLIPPING CLOSED

-2.

OPEN DEAD

1000.

1001.

1002.

1003.

1004.

1005.

*10 -2

TIME

Another example solution pertains to the rotation of a heavy antenna structure, with focus on high accuracy of the anten- na positioning and orientation. In this application, we see very large displacements over long time ranges in the transient analysis, and numerical stability can be difficult to achieve. Figure 9 shows the model of the antenna, which is rotated with various angular velocities using the classical trapezoidal rule and the Bathe method for time integration.

Figure 10: Predicted transient response of antenna using Newmark and Bathe Method

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