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TEST CASE 2.4 EIGENFREQUENCIES OF RECTANGULAR PLATE CLAMPED ON ALL EDGES

Reference: I.A. Birger, Y.G. Panovko, Strength, stability, vibrations, Handbook in three volumes, Volume 3, Moscow, Mechanical Engineering, 1968, p. 377.

Problem sketch:

Fig. 2.4

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 19).

Mesh: 20x20 FE - classic analysis; 10x10 FE - analysis using finite elements with intermediate nodes.

Modal analysis has been performed to solve the problem.

Calculation results has been compared to analytical solution using Rayleigh-Ritz method.

Calculation results:

Table 2. 4

# of mode

Frequency, rad/s

Deviation, %

Analytical solution

Solution results by LIRA 10.4

1

560.1

556.38 (557.80)

0.66 (0.41)

2

1143.2

1133.68 (1137.57)

0.83 (0.49)

3

1143.2

1133.68 (1137.57)

0.83 (0.49)

4

1686.6

1663.98 (1677.33)

1.34 (0.55)

5

2054.0

2031.91 (2039.12)

1.07 (0.72)

6

2054.0

2042.13 (2048.76)

0.58 (0.26)

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