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 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 12, FE 19).

Mesh: R16xL72 FE - classic analysis; R8xL36 FE - analysis using finite elements with intermediate nodes.

Modal analysis has been performed to solve the problem.

Calculation results:

Table 2.5

# of mode	Frequency, rad/s		Deviation, %
	Analytical solution	Solution results by LIRA 10.4
1	306	306(318.7)	0(4.15)
2, 3	861.8	861.8(875)	0(1.53)
4, 5	1588.2	1589.4(1603.3)	0.08(0.95)
6	1842.9	1843.1 (1858.8)	0.01 (0.86)
7, 8	2477.7	2481.4 (2494.8)	0.15 (0.69)
9, 10	3006.1	3008.1(3024.8)	0.07 (0.62)
11, 12	3524.6	3531.6 (3543.8)	0.2 (0.54)
13, 14	4347.8	4362 (4369.5)	0.33 (0.5)
15	4598.3	4597(4620.2)	0.03 (0.48)

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