
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
299318, 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_m^{2} 

Poisson's Ratio (material):
ν
= 0.3 
Density:
ρ
= 7857.2 Kg/m^{3} 
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 
84.2461 
82.8426 
83.6888 
85.7079 
2 
134.5 
141.824 
136.908 
136.16 
138.555 
3 
259.0 
248.017 
242.163 
252.195 
245.927 
4 
351.0 
341.879 
333.202 
337.331 
340.94 
5 
395.0 
380.636 
373.174 
381.633 
382.989 
6 
531.0 
538.508 
517.818 
546.994 
527.982 


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:

Open the CATAnalysis document.

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

In the Generative Structural Analysis
workbench, compute the case.
