# SS-V: 2120 Two-body Symmetric Damped Oscillators System

Test No. VM13 Determine the frequency and damping rate of a 1D damped oscillator.

## Definition

The material properties are:

- Rigid body, m = 1 kg, k = 1 N/m, c
_{0}= 1 Ns/m, c_{1}= 0.1 Ns/m

## Modeling and Results

The spring and damper can be modeled with a shock absorber or a
bushing. To restrict motion to one dimension, sliding conditions are applied on two
sides of the cube-shaped bodies. Frequency and rate of damping are compared to the
values from the analytical solution.

Parameters | SimSolid | Analytical solution | % Difference | |
---|---|---|---|---|

Mode 1 | Frequency, Hz | 0.15876 | 0.158956 | 0.12% |

Mode 1 | Damping rate, 1/s | 0.049752 | 0.05 | 0.50% |

Mode 2 | Frequency, Hz | 0.2201 | 0.219236 | 0.39% |

Mode 2 | Damping rate, 1/s | 1.0476 | 1.05 | 0.23% |

^{1}Kausel E., “Advanced Structural Dynamics”, Cambridge University Press, 2017, Section 3: ”Multiple Degree of Freedom Systems” (general equations). Also see Additional Comments.