Simulation > Simulation > Verification Guide—Creo Simulation Live and Creo Ansys Simulation > Verification Cases—Modal Analyses
Verification Cases—Modal Analyses
Cantilever Beam Modal Analysis
Problem Statement: Consider a cantilever beam of length l and a width w and height h. Compute the first three bending modes and natural frequencies. (Note that the simulation results include orthogonal bending, torsional and axial modes. The results comparison compares the first three bending modes from a closed form solution with the equivalent simulation results.)
References: W. T. Thompson, Theory of Vibration with Applications, 2nd Edition, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981, pg. 220
Material Properties
Geometric Properties
Young’s modulus E= 70e9 Pa
Poisson’s ratio ν = 0.35
Density ⍴ = 2700 kg/m^3
l = 4 m
w = 0.346 m
h = 0.346 m
Result Comparison—Simulation quality slider at default position
Results
Target
Creo Simulate
Ansys Discovery Live
Creo Simulation Live
Percent Error
Frequency Mode 1 (Hz)
17.8
17.88
17.8
17.8
0
Frequency Mode 3 (Hz)
111.5
110.03
108.3
108.2
3.05
Frequency Mode 6 (Hz)
312.1
320.22
288.6
288.8
8.06
Result Comparison for Creo Ansys Simulation (Default mesh)
Results
Target
Ansys AIM
Creo Ansys Simulation
Percent Error
Frequency Mode 1 (Hz)
17.8
17.788
17.76
0.22
Frequency Mode 3 (Hz)
111.5
107.71
107.646
3.58
Frequency Mode 6 (Hz)
312.1
287.07
287.239
8.79
Simply-Supported Beam Modal Analysis
Problem Statement: To determine the fundamental frequency of a simply-supported beam of length 80 in. and uniform cross-section A = 4 in​2 as shown below.
References: W. T. Thompson, Vibration Theory and Applications, 2nd Printing, Prentice-Hall, Inc.,Englewood Cliffs, NJ, 1965, pg. 18, ex. 1.5-1
Material Properties
Geometric Properties
Young’s modulus E = 3e7 psi
Poisson’s ratio ν = 0.3
Density ⍴= 0.2836 lb/in^3
l = 80 in
w = 2 in
h = 2 in
Result Comparison—Simulation quality slider at default position
(Simple support approximated by constraining 0.125 in imprinted faces.)
Results
Target
Creo Simulate
Ansys Discovery Live
Creo Simulation Live
Percent Error
Frequency Mode 1 (Hz)
28.766
28.67
36.88
36.20
20.5
Result Comparison for Creo Ansys Simulation (Default mesh)
Results
Target
Ansys AIM
Creo Ansys Simulation
Percent Error
Frequency Mode 1 (Hz)
28.766
28.561
29.4
2.15
Modal Analysis of an Annular Plate
Problem Statement: An assembly of three annular plates has cylindrical support (fixed in the radial, tangential, and axial directions) applied on the cylindrical surface of the hole. Determine the first six natural frequencies.
References: R. J. Blevins, Formula for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company Inc., 1979, Table 11-2, Case 4, pg. 247
Material Properties
Geometric Properties
Young’s modulus E = 2.9008e7 psi
Poisson’s ratio ν= 0.3
Density ⍴ = 0.28383 lb/in^3
Inner diameter of inner plate = 20 in.
Inner diameter of middle plate = 28 in
Inner diameter of outer plate = 34 in
Outer diameter of outer plate = 40 in
Thickness of all plates = 1 in
Result Comparison—Simulation quality slider at default position
Results
Target
Creo Simulate
Ansys Discovery Live
Creo Simulation Live
Percent Error
Frequency Mode 1 (Hz)
310.9
310.92
328.7
329.2
5.55
Frequency Mode 2 (Hz)
318.1
316.37
334.6
335.0
5.04
Frequency Mode 3 (Hz)
318.1
316.50
334.6
335.0
5.04
Frequency Mode 4 (Hz)
351.6
347.80
366.0
366.8
4.14
Frequency Mode 5 (Hz)
351.6
347.94
367.3
367.5
4.32
Frequency Mode 6 (Hz)
442.4
436.54
456.4
456.8
3.15
Result Comparison for Creo Ansys Simulation (Default mesh resolution)
Results
Target
Ansys AIM
Creo Ansys Simulation
Percent Error
Frequency Mode 1 (Hz)
310.9
310.16
312.296
0.45
Frequency Mode 2 (Hz)
318.1
315.47
317.835
0.083
Frequency Mode 3 (Hz)
318.1
315.59
317.847
0.079
Frequency Mode 4(Hz)
351.6
346.49
348.842
0.79
Frequency Mode 5 (Hz)
351.6
346.52
349.174
0.69
Frequency Mode 6 (Hz)
442.4
434.55
436.896
1.259
Modal Analysis of a Rectangular Plate
Problem Statement: Consider a rectangular plate with fixed supports where the dimensions of the plate are length = 6 in, width = 4 in and thickness = 0.063 in. Determine the natural frequency and mode shape.
References: R. Blevins, Formula for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company Inc., 1979, Table 11-6
Material Properties
Geometric Properties
Young’s modulus E = 1.0e7 psi
Poisson’s ratio ν = 0.33
Density ⍴ = 0.1 lbm/in^3
Length = 6 in
Width = 4 in
Thickness = 0.063 in
Result Comparison—Simulation quality slider at default position
Results
Target
Creo Simulate
Ansys Discovery Live
Creo Simulation Live
Percent Error
Frequency Mode 1 (Hz)
1016
1019.35
1123.9
1123
9.52
Results Comparison for Creo Ansys Simulation (Default mesh resolution)
Results
Target
Ansys AIM
Creo Ansys Simulation
Percent Error
Frequency Mode 1 (Hz)
1016
1024.2
1024.79
0.86