Sign in /
Register
   

TEST CASE 2.6 NATURAL FREQUENCIES OF THE ROUND PLATE CLAMPED ALONG THE CONTOUR

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 description:

Determine the natural frequencies of the round plate clamped along the contour.

 

Problem sketch:

Type of created problem:

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

 

Geometric characteristics:

r = 0.5 m; t = 0.01 m.

 

Material properties:

Elastic modulus: E = 2.06·1011 Pa;

Poisson’s ratio: μ = 0.3;

Density: γ = 7850 kg/m3.

 

Boundary conditions:

On the perimeter: Z = UX = UY = 0.

 

Loads:

Dead load.

 

Model description:

The system is modeled using 288 finite elements of thin plate with additional nodes (FE type is 19), splitting in the radial direction with a step of 0.0625 m and in the tangential with a step of 10°. To solve the problem, a modal analysis was performed.

 

Analytical solution:

Jn, In – Bessel functions.

 

Calculation results:

Form №

Frequency, rad/sec

Deviation, %

Analytical solution

LIRA 10

1

633.5

636.8

0.52

2, 3

1318.3

1324.9

0.50

4

2162.7

2173.1

0.48

5

2162.7

2173.2

0.49

6

2466.1

2477.8

0.47

7, 8

3164.3

3178.8

0.46

9, 10

3771.9

3788.1

0.43

11

4319.8

4338.6

0.44

12

4319.8

4338.7

0.44

13, 14

5244.8

5266.5

0.41

15

5525.2

5546.5

0.39