# 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·m^{2}] , k_{rot}= 1[N·m/rad], c_{rot}= 6.0e-04 [N·m·s/rad]

## 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.

Parameters | SimSolid, Steel, Translation | Analytical solution |
---|---|---|

Frequency, Hz | 1.4836 | 1.48295 |

Damping rate, 1/s | 6.3694 | 6.3694 |

Parameters | SimSolid, Steel, Rotation | Analytical solution^{1} |
---|---|---|

Frequency, Hz | 2.4582e+02 | 2.45815e+02 |

Damping rate, 1/s | 2.2931e+03 | 2.2930e+03 |

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