Calculate the natural frequencies of a square cantilever plate.

-Analysis Type

3-D eigenvalue analysis

-Unit System

in, kip

-Dimension

Length 24.0 in Width 24.0 in Thickness 1.0 in

Gravitational acceleration g = 386.4 in/sec²

-Element

Plate element (Thick type)

-Material

Modulus of elasticity E = 29.5 ×10³ksi

Poisson’s ratio ν = 0.3

Weight density γ = 2.835648 × 10^-4kips/in³

-Element Property

Element size a × b = 24.0/19 in × 24.0/19 in

Thickness t = 1.0 in

-Boundary Condition

Nodes 1 ~ 20 ; Constrain all DOFs.

All nodes ; Constrain Dx, Dy and Rz.

-Analysis Case

Self weight is converted to nodal masses automatically.

Number of natural frequencies to be computed = 5

App

Library

Sources

Harris, C. M. and Crede, C. E., “Shock and Vibration Handbook”, McGraw-Hill, 1976.
“SAP90, A Series of Computer Programs for the Finite Element Analysis of Structures,Structural Analysis Verification Manual”, Computer and Structures, Inc., 1992,Example 15.

Mode	Independent	SAP2000	MIDAS	OpenBrIM	Percent Difference (SAP2000 vs Independent)	Percent Difference (MIDAS vs Independent)	Percent Difference (OpenBrIM vs Independent)
Mode	Natural Period
1^st	0.01790	0.01781	0.01724	0.01723	-0.5028%	-3.6872%	-3.7430%
2^nd	0.00732	0.00648	0.00710	0.00701	-11.4754%	-3.0055%	-4.2350%
3^rd	0.00292	0.00285	0.00284	0.00282	-2.3973%	-2.7397%	-3.4247%
4^th	0.00228	0.00223	0.00223	0.00221	-2.1930%	-2.1930%	-3.0702%
5^th	0.00201	0.00187	0.00197	0.00194	-6.9652%	-1.9900%	-3.4826%