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TEST CASE 2.4 NATURAL FREQUENCIES OF A SQUARE PLATE CLAMPED AROUND THE PERIMETER

Reference:

I.A. Birger, Ya.G. Panovko, Strength, Stability, Vibrations, Handbook in three volumes, Volume 3, Moscow, Mechanical engineering, 1968, p. 377.

 

Problem description:

Determine the natural frequencies of a square plate clamped around the perimeter.

 

Problem sketch:

Type of created problem:

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

 

Geometric characteristics:

a = 1 m; t = 0.01 m.

 

Material properties:

Elastic modulus: E = 2.1·1011 Pa;

Poisson’s ratio: μ = 0.3;

Density: γ = 7800 kg/m3.

 

Boundary conditions:

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

 

Loads:

Dead load.

 

Model description:

The system is modeled using 100 finite elements of thin plate (FE type is 19) with additional nodes. To solve the problem, a modal analysis was performed.

 

Analytical solution:

 

Calculation results:

Form №

Frequency, rad/sec

Deviation, %

Analytical solution

LIRA 10

1

560.1

557.80

0.41

2

1143.2

1137.57

0.49

3

1143.2

1137.57

0.49

4

1686.6

1677.33

0.55

5

2054.0

2039.12

0.72

6

2054.0

2048.76

0.26