VM54

VM54
Vibration of a Rotating Cantilever Blade

Overview

Reference:

W. Carnegie, "Vibrations of Rotating Cantilever Blading", Journal Mechanical Engineering Science, Vol. 1 No. 3, 1959, pg. 239

Analysis Type(s):

Static Analysis (ANTYPE = 0)

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:

vm54.dat

Test Case

A blade is cantilevered from a rigid rotating cylinder. Determine the fundamental frequency of vibration of the blade, f, when the cylinder is spinning at a rate of Ω .

Figure 78: Rotating Cantilever Blade

Material Properties

Geometric Properties

E = 217 x 10⁹ Pa

ρ = 7850 kg/m³

υ = 0.3

r = 150 mm

= 328 mm

b = 28 mm

t = 3mm

Ω = 100π rad/sec

Analysis Assumptions and Modeling Notes

The problem is solved in four different ways:

Using Elastic Shell Elements (SHELL63).
3D Solid Shell Elements (SOLSH190) using linear perturbation analysis.
Low order Finite Strain Shell Elements (SHELL181) using linear perturbation analysis.
High order Finite Strain Shell Elements (SHELL281) using linear perturbation analysis.

Since the cylinder is rigid, the base of the blade has its displacements constrained. A static prestress analysis is performed to include the inertial effects resulting from the rotation of the cylinder.

Results Comparison

	Target	Mechanical APDL	Ratio
SHELL63
f, Hz	52.75	52.01	0.986
SOLSH190
f, Hz	52.75	51.87	0.983
SHELL181
f, Hz	52.75	51.87	0.983
SHELL281
f, Hz	52.75	51.92	0.984