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:

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:

Table 2.3

# of mode	Frequency, Hz		Deviation, %
	Analytical solution	Solution results by LIRA 10.4
1	35.63	35.573 (35.624)	0.16 (0.02)
2	68.51	68.327 (68.506)	0.27 (0.01)
3	109.62	109.381 (109.600)	0.22(0.02)
4	123.32	122.933 (123.305)	0.32(0.01)
5	142.51	141.665 (142.474)	0.6 (0.03)
6	197.32	195.591 (197.267)	0.88 (0.03)

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