Free Vibrations of a Compressor Blade

This test lets you check analysis free vibrations results for a compressor blade in the context of a modal (or frequency) case. You will use 2D meshes.

Reference:

  • OLSON,M.D.,LINDBERG,G.M., Vibration analysis of cantilevered curved plates using a new cylindrical shell finite element, 2nd Conf. Matrix Methods in Structural Mechanics, WPAFB, Ohio 1968.
  • OLSON,M.D.,LINDBERG,G.M., Dynamic analysis of shallow shells with a doubly curved triangular finite element, JSV, Vol. 19, No 3, pp 299-318, 1971.
 

Specifications

Geometry Specifications

Length:
L = 304.8 mm

Radius:
R = 609.6 mm

Thickness:
th = 3.048 mm

Angle:
A = 28.6479 deg  
(or 0.5 rad)
 

Analysis Specifications

Young Modulus (material):
E = 2.0685e+011 N_m2

Poisson's Ratio (material):
ν = 0.3

Density:

ρ = 7857.2 Kg/m3

Mesh Specifications:
11 x 11 nodes

Restraints:
BC straight edge is free
AD straight edge is clamped
 

Results

The table below presents the frequencies of the first six modes (mesh specifications: 11 x 11 nodes).

Mode
 

Reference value
[Hz]

Computed value [Hz]

Linear triangle
(TR3)

Parabolic triangle
(TR6) 

Linear quadrangle
(QD4)

Parabolic quadrangle
(QD8)

 1

85.6

87.68

85.34

84.10

85.90

2

134.6

143.05

138.2

136.3

138.6

3

259.0

251.3

246.4

252.4

246.1

4

351.0

349.6

339.8

338.0

341.3

5

395.0

394.4

383.3

382.5

384.1

6

531.0

544.0

527.9

547.3

528.8

To Perform the Test:

The Free_vibrations_compressor_blade_QD8.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of parabolic and quadrangular elements (QD8).

To compute the case with linear quadrangle (QD4), linear triangle (TR3) and parabolic triangle (TR6) elements, proceed as follow:

  1. Open the CATAnalysis document.

  2. In the Advanced Meshing Tools workbench, replace the mesh specifications as indicated above.

  3. In the Generative Structural Analysis workbench, compute the case.