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

Test No. VM13Determine the frequency and damping rate of a 1D damped oscillator.

Definition

The material properties are:
  • Rigid body, m = 1 kg, k = 1 N/m, c0 = 1 Ns/m, c1 = 0.1 Ns/m
Figure 1.


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.
Table 1.
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).