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Inconsistent dimensions for damping constants in AnalyticalLinearDamper #354

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sy-cui opened this issue Mar 30, 2024 · 0 comments
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bug Something isn't working discussion Topic that needs to be discussed. prio:high Priority level: high

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sy-cui commented Mar 30, 2024

The linear viscous damping forces and torques within the linear and angular momentum equations are given as follows (Gazzola 2018):
$$\mathbf{f}_v =-\gamma_t \mathbf{v}, ~~~~~~~~ \mathbf{c}_L^v = -\gamma_r \mathbf{\omega}_L $$
where the paper claims that the damping coefficients $\gamma_t$ and $\gamma_r$ can be set to equal. This statement is not strictly correct as they are dimensionally inconsistent:
$$[\gamma_t] = FL^{-1}T, ~~~~~~~ [\gamma_r] = FLT$$

The analytical linear damper assumes an eigenvalue problem with respect to the damping force, where the damped translational and angular velocities are respectively
$$v_{\text{damped}} = v_0 \exp \left(-\frac{\gamma_t}{m}t\right), ~~~~~~~ \omega_{\text{damped}} = \omega_0 \exp \left(-\frac{\gamma_r e}{J}t\right)$$
Current implementation assumes $\gamma = \gamma_t = \gamma_r$, and the input damping_constant corresponds to $\gamma / m$ where $m$ is the nodal / elemental mass. This includes a dimensional inconsistency and incurs problems in non-dimensional analysis.

Two possible remedies are proposed:

  1. The analytically rigorous approach is to include both $\gamma_t$ and $\gamma_r$ from user input, and compute the exponential coefficients based on these inputs and rod properties
  2. Assume that $k = \frac{\gamma_t}{m} = \frac{\gamma_r e}{J}$, with $k$ having inverse time dimension ($[k]= T^{-1}$). The damper class collects only one user input $k$ instead of two, and no access to kinematic/material properties is required.

The original implementation should be retained for the moment and possibly removed in a future update. If removal is expected, usage of the original approach should emit a deprecation warning.

@sy-cui sy-cui added bug Something isn't working prio:high Priority level: high labels Mar 30, 2024
@sy-cui sy-cui self-assigned this Mar 30, 2024
@bhosale2 bhosale2 added the discussion Topic that needs to be discussed. label Mar 30, 2024
@skim0119 skim0119 assigned skim0119 and unassigned sy-cui Jun 12, 2024
skim0119 added a commit to skim0119/PyElastica-mirror that referenced this issue Jun 12, 2024
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