Modeling and Analysis Lab Problem-12 solution: Modal analysis of cantilever beam using ANSYS

1. • Simple Modal Analysis of a cantilever beam as shown below.
• Objective is to get the frequency and different modes of
vibration.
• E=2e11 N/m2
• I = 8.33e-06 m4
• Area A = 0.01 m2
• Density = 7830 Kg/m3

2. Kg-Sec2/m47.982E+02ρs =S-Density
Kg/m7.830E+01ρl =Density/L
m48.33333E-06I =M.I
m20.01A =Area
3.143π =PIE
m/Sec29.810g =Aceln due to gravity
Kg/m37.830E+03ρ =Density
N/m22.00E+11E =Young's Modulus
m0.1D =Depth
m0.1B =Breath
m1L =Length
Given Data
To Determine the Natural Frequencies of a Cantilever Beam

3. 4485.4759ωn3/2π =fn3 =
1599.3593ωn2/2π =fn2 =
255.89749ωn1/2π =fn1 =Natural Frequencies
2.819E+04(β3l)2√(EI)/(ρl4)ωn3 =
1.005E+04(β2l)2√(EI)/(ρl4)ωn2 =
1.608E+03(β1l)2√(EI)/(ρl4)ωn1 =
Circular Frequency
61.7022.003.52
(β3l)2(β2l)2(β1l)2
Beam Constant

12. The Density 7830 Kg/m3 should be divided by 9.81 m/sec2. This gives the software density
798.16 Kg–sec2/m4. This new value should be used as density Value in ansys.

14. Key points are specified in the given coordinate box
KP1 (0,0)
KP2 (1,0)

29. General Postprocessor

38. 1432.1012783
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Theory (Frequency)FEM (Frequency)Mode