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 2.6

# of mode	Frequency, rad/s		Deviation, %
	Analytical solution	Solution results by LIRA 10.4
1	633.5	634.6 (636.8)	0.17(0.52)
2, 3	1318.3	1321(1324.9)	0.2 (0.5)
4, 5	2162.7	2170 (2173.2)	0.34 (0.49)
6	2466.1	2469.9(2477.8)	0.15 (0.47)
7, 8	3164.3	3178.4 (3178.9)	0.45(0.46)
9, 10	3771.9	3780.6(3788.1)	0.23(0.43)
11, 12	4319.8	4324.2(4338.7)	0.1(0.44)
13, 14	5244.8	5275.1(5266.5)	0.58(0.41)
15	5525.2	5530.9(5546.5)	0.1(0.39)

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