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Modal Analysis
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.

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Verification Problems
Solved verification models.
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- Static Analysis
- Modal Analysis
  - SS-V: 2000 Free Vibration of a Wedge
    Test No. VM01 Determine the first fundamental frequency and vibration mode of a wedge constrained at the wide end.
  - SS-V: 2010 In-plane Vibration of a Cantilever Plate
    Test No. VM01 Find the fundamental frequency for in-plane vibration of a cantilevered plate.
  - SS-V: 2020 Cylindrical Shell
    Test No. VM03 Find the fundamental frequency of a cantilever cylindrical shell.
  - SS-V: 2030 Free Thin Square Plate
    Test No. VM04 Determine the first fourteen modal frequencies for a free thin square plate.
  - SS-V: 2040 Thick Skewed Plate
    Test No. VM05 Find the fundamental frequency of a thick clamped skewed plate.
  - SS-V: 2050 Thick Square Plate
    Test No. VM06 Determine the first twelve modes and frequencies for a simply supported thick square plate.
  - 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.
  - SS-V: 2070 Cantilever Beam
    Test No. VM08 Perform normal mode dynamic analysis of a cantilevered beam.
  - SS-V: 2080 Circular Ring - In-plane and Out-of-plane Vibration
    Test No. VM09 Perform normal mode dynamic analysis of an unconstrained circular ring.
  - SS-V: 2090 Triangular Wing - Fixed Vibration
    Test No. VM10 Perform a normal mode dynamic analysis of a fixed right triangular plate.
  - SS-V: 2100 Cantilevered Tapered Beam
    Test No. VM11 Shear behavior of a cantilevered tapered beam.
  - SS-V: 2110 Cantilever with Off-Center Remote Mass
    Test No. VM12 Find the frequencies of a cantilever with off center remote masses at the free end.
  - SS-V: 2120 Two-body Symmetric Damped Oscillators System
    Test No. VM13Determine the frequency and damping rate of a 1D damped oscillator.
  - SS-V: 2130 1D Damped Oscillator: Translation or Rotation
    Test No. VM14Determine the frequency and damping rate of a 1D damped oscillator.
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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

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.