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TEST CASE 2.5 EIGENFREQUENCIES OF CIRCULAR PLATE SIMPLY-SUPPORTED ALONG THE EDGE

Reference:

V.N. Chelomey, Vibration in technics, Handbook in six volumes;

V.V. Bolotin, Volume 1, The vibrations of linear systems, Moscow, Mechanical Engineering, 1978, p. 207.

Problem sketch:

Fig. 2.5

Type of created problem:

Flat plate or grillage ( Z , UX , UY).

Input data:

; ;

Material properties:

Isotropic elastic: ; ;

Boundary conditions:

Across perimeter: ;

Problem description:

System was modeled using finite elements of thin plate (FE 12, FE 19).

Mesh: R16xL72 FE - classic analysis; R8xL36 FE - analysis using finite elements with intermediate nodes.

Modal analysis has been performed to solve the problem.

Calculation results:

Table 2.5

# of mode

Frequency, rad/s

Deviation, %

Analytical solution

Solution results by LIRA 10.4

1

306

306(318.7)

0(4.15)

2, 3

861.8

861.8(875)

0(1.53)

4, 5

1588.2

1589.4(1603.3)

0.08(0.95)

6

1842.9

1843.1 (1858.8)

0.01 (0.86)

7, 8

2477.7

2481.4 (2494.8)

0.15 (0.69)

9, 10

3006.1

3008.1(3024.8)

0.07 (0.62)

11, 12

3524.6

3531.6 (3543.8)

0.2 (0.54)

13, 14

4347.8

4362 (4369.5)

0.33 (0.5)

15

4598.3

4597(4620.2)

0.03 (0.48)

- solution results using finite elements with intermediate nodes are specified within the brackets