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 11.312 -0.21%
Mode 2 [Hz] 17.709 17.810 0.57%
Mode 3 [Hz] 17.709 17.840 0.74%
Mode 4 [Hz] 17.709 17.840 0.74%
Mode 5 [Hz] 45.345 45.130 -0.47%
Mode 6 [Hz] 57.390 57.360 -0.05%
Mode 7 [Hz] 57.390 57.370 -0.03%
Mode 8 [Hz] 57.390 57.550 -0.28%
1 NAFEMS, SBNFA (November 1987), Test 1.