A square cantilever plate of 24 x 24 inches and 1 inch thick has weight density of 0.490 kip/ft3. The plate is fixed at its base. Determine the first five eigenvalues.

The plate model has 19 x 19 mesh. It consists of 400 joints and 361 plate elements. The in-plane action of the plate is restrained by eliminating X and Y translations and Z rotations for all the joints.

The properties of the plate are:

Plate Size = 24 x 24 inch

Modulus of Elasticity = 29,500 ksi

Poisson Ratio = 0.00

Shear Modulus = 14,750 psi

Weight Density = 0.000280 kip/in3 g = 386.4 in/sec2

Tested Features

Harris results are obtained using the Ritz method with beam mode shapes. The first, third and fourth modes are in good agreement with the results while the second and fifth modes are not in good agreement. This is because of a model approximating the plate with beam elements in Harris. The solutions of the same problem by SAP90 is also shown for comparison of results obtained by LARSA are in good agreement for all modes.

Sources

Harris, C.M. and Crete, C.E., "Shock and Vibration Handbook," McGraw-Hill, 1976.
Computers & Structures Inc., "SAP90 Structural Analysis Verification Manual", October, 1990.
LARSA 4D

Result Comparison

App Link:

https://openbrim.org/objidbufeqjiecfkzwe0djn15dc.project

Library Link:

https://openbrim.org/objidcrd7jaiutbc46z2gtes9j4.libobj

Model	Output Parameter	OpenBrIM	LARSA	Harris	SAP90	OpenBrIM vs LARSA
Square Cantilever Plate	f1(hz)	56.49	56.49	56.157	55.866	0.05%
	f2(hz)	155.13	155.18	154.229	136.61	0.04%
	f3(hz)	352.92	352.92	350.877	342.65	0.03%
	f4(hz)	451.80	451.97	449.236	438.596	2e-3%
	f5(hz)	538.88	539.16	535.618	497.512	4e-4%

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