SS-V: 2060 In-plane Vibration of Pin-ended Cross

Test No. VM07 Find the first eight modal frequencies for in-plane vibration of a cross with pin joints at the ends.

Definition

Figure 1.


Pins are simulated via zero displacements applied to a straight line. The front surface of the cross is fixed from out-of-plane displacements.

The units are SI.

The material properties are:
Properties
Value
Modulus of Elasticity
2e+11 N/m2
Poisson's Ratio
0.3
Mass density
8000 kg/m3

Results

The following table summarizes the modes.
Reference Solution SimSolid % Difference
Mode 1 [Hz] 11.336 11.316 -0.18%
Mode 2 [Hz] 17.709 17.813 0.59%
Mode 3 [Hz] 17.709 17.842 0.75%
Mode 4 [Hz] 17.709 17.843 0.76%
Mode 5 [Hz] 45.345 45.126 -0.48%
Mode 6 [Hz] 57.390 57.364 -0.05%
Mode 7 [Hz] 57.390 57.366 -0.04%
Mode 8 [Hz] 57.390 57.546 0.27%
1 NAFEMS, SBNFA (November 1987), Test 1.