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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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- Static Analysis
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  - 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: 2130 1D Damped Oscillator: Translation or Rotation

Test No. VM14Determine the frequency and damping rate of a 1D damped oscillator.

Definition

The material properties are:

Steel or rigid body, m = 0.00784998 [kg], k = 1[ N/m], c = 0.1 [N·s/m], I_zz = 1.30833e-07 [kg·m²] , k_rot = 1[N·m/rad], c_rot = 6.0e-04 [N·m·s/rad]

Figure 1. Translation motion

Figure 2. Rotational motion

Modeling and Results

The spring and damper is modeled with a bushing. To restrict motion to one dimension, sliding conditions are applied on two sides of the cube-shaped body for translational motion or on one side for rotational motion. Frequency and rate of damping are compared to the values from the analytical solution. The below results are for bushing.

Table 1.
Parameters	SimSolid, Steel, Translation	Analytical solution
Frequency, Hz	1.4830	1.48295
Damping rate, 1/s	6.3692	6.3694

Table 2.
Parameters	SimSolid, Steel, Rotation	Analytical solution^¹
Frequency, Hz	2.4582e+02	2.45815e+02
Damping rate, 1/s	2.2930e+03	2.2930e+03

¹ Kausel E., “Advanced Structural Dynamics”, Cambridge University Press, 2017, p.86.