VM62

VM62
Vibration of a Wedge

Overview

Reference: S. Timoshenko, D. H. Young, Vibration Problems in Engineering, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 392, article 62.
Analysis Type(s): Mode-frequency Analysis (ANTYPE = 2)
Element Type(s):

Elastic Shell Elements (SHELL63)

4-Node Finite Strain Shell Elements (SHELL181)

8-Node Finite Strain Shell Elements (SHELL281)

Input Listing: vm62.dat

Test Case

Determine the fundamental frequency of out-of-plane vibration f of a wedge-shaped plate of uniform thickness t, base 2b, and length .

Figure 86: Wedge Vibration Problem Sketch

Wedge Vibration 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 first using "plate" elements (SHELL63 with bending stiffness only) and then using "shell" elements (SHELL63 with bending and membrane stiffness). Two symmetric areas are created to ensure model symmetry about the plate centerline. Each area is meshed with 4 elements along the X axis and 1 element along the Y axis. Poisson's ratio is assumed to be zero.

The model is then solved using SHELL181 and SHELL281 elements using bending and membrane stiffness option.

Results Comparison

 TargetMechanical APDLRatio
Plate Elements SHELL63 f, Hz259.16261.081.007
Shell Elements SHELL63 f, Hz259.16261.081.007
Shell Elements SHELL181 f, Hz259.16256.990.992
Shell Elements SHELL281 f, Hz259.16258.970.999