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E05: Rectangular Cantilever Plate Eigenvalues

E05: Rectangular Cantilever Plate Eigenvalues

Owned by Gokhan Alkan (Unlicensed)

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 ParametersIndependent
(Timoshenko)		LarsaOpenBrIMPercent Difference (Larsa vs Independent)Percent Difference (OpenBrIM vs Independent)
f1 (Hz)128.09128.16126.780.05%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