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

Problem sketch:

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.