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TEST CASE 2.3 NATURAL FREQUENCIES OF A RECTANGULAR PLATE HINGED AROUND THE PERIMETER

Reference:

M.V. Barton, “Vibration of rectangular and skew cantilever plates”, Journal of Applied Mechanics, vol. 18, 1951, p. 129 – 134.

 

Problem description:

Determine the natural frequencies of a rectangular plate hinged around the perimeter.

 

Problem sketch:

Type of created problem:

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

 

Geometric characteristics:

a = 1.5 m; b = 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 = 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.

  

Calculation results:

Form №

Frequency, Hz

Deviation, %

Analytical solution

LIRA 10

1

35.63

35.624

0.02

2

68.51

68.506

0.01

3

109.62

109.600

0.02

4

123.32

123.305

0.01

5

142.51

142.474

0.03

6

197.32

197.267

0.03