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

Problem sketch:

Type of created problem:

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

Input data:

; ;

Material properties:

Isotropic elastic: ; ;

Boundary conditions:

AB side: ;

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:

Table 2. 2

# of mode	Frequency, Hz		Deviation, %
	Analytical solution	Solution results by LIRA 10.4
1	8.7266	8.6741 (8.6747)	0.60 (0.59)
2	21.3042	21.2576 (21.2577)	0.22 (0.22)
3	53.5542	53.2113 (53.1853)	0.64 (0.69)
4	68.2984	67.9355 (67.9581)	0.53 (0.5)
5	77.7448	77.3499 (77.3504)	0.51 (0.51)
6	136.0471	135.2213 (135.3838)	0.61 (0.49)

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