# Equations of motion of TMD (StrucCtrl module)

Dear @Jason.Jonkman

I was reading the equation of motion in 4.2.12.2. Theory Manual for the Tuned Mass Damper Module in OpenFAST β OpenFAST v3.5.1 documentation

I understand that point P is the origin point of the non-inertial reference frame fixed to the component where the TMD is desired to be installed.

However, the position of the TMD with respect to P has the coordinates [x, y, z] as written in the table of definitions: 4.2.12.2. Theory Manual for the Tuned Mass Damper Module in OpenFAST β OpenFAST v3.5.1 documentation

When the equations of motion are written, the variables y and z are set to zero : 4.2.12.2. Theory Manual for the Tuned Mass Damper Module in OpenFAST β OpenFAST v3.5.1 documentation

For me, is is not necessary to be zero. In fact, they depend on TMD position at time equals zero. This will affect the equations of motion in particular the centrifugal acceleration. Am I right ?

What do you think ? Please if you could clarify.

Best Regards,

Iβm not sure I fully understand your question. Are you referring to the second equation in the section for TMD_X, where the y and z displacements of the TMD are zero?

The y and z displacements are set to zero for the x-based TMD. Likewise, the x and z displacements are zero for the y-based TMD and the x and y displacements are zero for the z-based TMD. Effectively, when `StC_DOF_MODE` = 1, the x-, y-, and z-based TMDs are completely independent from each other.

Best regards,

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Dear @Jason.Jonkman ,

Yes, you are right. I am referring to the second equation in the section for TMD_X.

I think I am kind confused between the point P and the origin point of the non-inertial reference frame fixed to the component where the TMD is desired to be installed. In fact, these two points are different and are not the same.

The coordinates of point P are the position of the TMD at time equals zero and the TMD position (the unknown x in a case of unidirectional TMD) is measured with respect to point P and not measured with respect to the origin point of the non-inertial reference frame. Right ?

Indeed, when we set a simulation including a TMD, the position of point P is an input in StrucCtrl input file and this is how OpenFAST knows the coordinates of point P. Moreover, the stroke of the TMD placde in the substructure (position of the TMD given by the output called βSStCXQβ) is measured with respect to P. Right ?

Best Regards,

I think I am kind confused between the point P and the origin point of the non-inertial reference frame fixed to the component where the TMD is desired to be installed. In fact, these two points are different and are not the same.

What the Structural Control documentation refers to as point P, i.e., the βorigin point of non-inertial reference frame fixed to component (blade, nacelle, tower, substructure) where TMDs are at restβ is the location defined via `StC_P_X`, `StC_P_Y`, `StC_P_Z` in the Structural Control input file. For the nacelle, setting `StC_P_X` = `StC_P_Y` = `StC_P_Z` = 0 would place point P at the yaw bearing; otherwise, nonzero `StC_P_X`, `StC_P_Y`, and/or `StC_P_Z` define point P to be offset relative to the yaw bearing.

The coordinates of point P are the position of the TMD at time equals zero and the TMD position (the unknown x in a case of unidirectional TMD) is measured with respect to point P and not measured with respect to the origin point of the non-inertial reference frame. Right ?

I agree except for your statement about time equals zero given that the user can specific nonzero initial conditions of the TMD (e.g., via Structural Control input `StC_X_DSP` for the x-based TMD).

Indeed, when we set a simulation including a TMD, the position of point P is an input in StrucCtrl input file and this is how OpenFAST knows the coordinates of point P. Moreover, the stroke of the TMD placde in the substructure (position of the TMD given by the output called βSStCXQβ) is measured with respect to P. Right ?

Correct.

Best regards,

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