VM66

VM66
Vibration of a Flat Plate

Overview

Reference: S. Timoshenko, D. H. Young, Vibration Problems in Engineering, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 338, article 53.
Analysis Type(s): Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):
Elastic Shell Elements (SHELL63)
3D Structural Solid Shell Elements (SOLSH190)
4-Node Finite Strain Shell Elements (SHELL181)
8-Node Finite Strain Shell Elements (SHELL281)
Input Listing: vm66.dat

Test Case

Determine the fundamental natural frequency of lateral vibration f of a flat rectangular plate. The plate is of uniform thickness t, width 2b, and length  .

Figure 91: Flat Plate Problem Sketch

Flat Plate Problem Sketch

Material PropertiesGeometric Properties
E = 30 x 106 psi
ρ = 0.000728 lb-sec2/in4
υ = 0
t = 1 in
b = 2 in
= 16 in

Analysis Assumptions and Modeling Notes

The problem is solved in four different ways:

  • Using Elastic Shell Elements (SHELL63)

  • Using 3D Solid Shell Elements (SOLSH190)

  • Using 4-Node Finite Strain Shell Elements (SHELL181)

  • Using 8-Node Finite Strain Shell Elements (SHELL281)

The area is meshed with 4 elements along the X axis and 2 elements along the Y axis. Poisson's ratio is assumed to be zero.

Results Comparison

TargetMechanical APDLRatio
SHELL63
f, Hz128.09128.411.002
SOLSH190
f, Hz128.09128.711.005
SHELL181
f, Hz128.09128.671.005
SHELL281
f, Hz128.09127.780.998