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Modal Analysis
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.

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Verification Problems
Solved verification models.
- Introduction
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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.
- Thermal Analysis
- Thermal Loading
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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.

Definition

The units are SI.

The material properties are:

Properties: Value
Modulus of Elasticity: 2e¹¹ N/m²
Poisson's Ratio: 0.3
Mass density: 8000 kg/m³

Results

The following table summarizes the modes.


	Reference	SimSolid	% Difference	NAFEMS	% Difference
Mode 7, 8 out-of-plane	51.850	51.484	-0.71%	52.290	-1.55%
Mode 9, 10 in-plane	53.380	53.153	-0.43%	53.970	-1.51%
Mode 11, 12 out-of-plane	148.800	146.740	-1.38%	149.700	-1.98%
Mode 13, 14 in-plane	151.000	149.490	-1.00%	152.400	-1.91%
Mode 15 out-of-plane	287.000	280.660	-2.21%	288.300	-2.65%
Mode 16 in-plane	289.500	280.660	-3.05%	288.300	-2.65%

¹ NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C. Selected Benchmarks for Natural Frequency Analysis, Test No. 6. Glasgow: NAFEMS, Nov, 1987.