A rectangular cantilever plate of uniform thickness has its own weight as the sole loading. The plate is 16 inches in span and 1 inch thick. The weight density of the plate is 0.281 lb/in3. The width of the plate is 4 inches. One four inch wide end of the plate is fixed. Determine the fundamental natural frequency.

This is a rectangular plate with one edge fixed. The model used has 4 x 2 mesh size and consists of 15 joints and 8 plate elements.

Modulus of Elasticity = 30,000,000 psi

Poisson's Ratio = 0.30

Shear Modulus = 11,538,461 psi

Weight Density = 0.281 lb/in3

Plate Thickness = 1 inch

Plate Width = 4 inches

Span Length = 16 inches g = 386.4 in/sec2

Tested Features

App

Object Link: https://openbrim.org/objidaq67y2os2b9v9kw5p6wys.project

Library

Object Link: https://openbrim.org/objid8r3swp3cbhc4yemiaux4f7.libobj

Results Comparison

Output Parameters	Independent (Timoshenko)	Larsa	OpenBrIM	Percent Difference (Larsa vs Independent)	Percent Difference (OpenBrIM vs Independent)
f1 (Hz)	128.09	128.16	126.78	0.05%	1.02%

Sources

Timoshenko, S., and Young,D.H., "Vibration Problems in Engineering 7quot;, 3rd Edition, D. Van Nostrand Co.,Inc., New York, 1955, p. 389.
LARSA 4D

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