Spring-dashpot coupling in 2 directions

[StavrosP]

Hello,

could you please help me model the concept that is described in the attached picture?

Eventually, A is the vector of a node from the axis of origin. Ax is the displacement in x-dir, Ay in y-dir. Single-dot above the vector is velocity and double-dot acceleration.

So I would like a coupling between the x and y dirs, which includes not only springs (with stiffness equal to omega^2) but also dashpots (with a coefficient equal to 2*omega). So, in x-dir for example, the calculated acceleration Ax_dot_dot should be affected by only Ay_dot and Ax.

Could the "sp" together with "CoupledZeroLength" commands do the trick?

I believe the attached equations describe precisely what I am after, but please let me know if the concept is not clear enough.

Stavros

[STKO Team]

It's not completely clear to me what you want to do here.
However the coupledZeroLength is used to create a sort of spherical yield-surface given a simple uniaxial material.

[StavrosP]

I will try to clarify more. There is a cross-coupling term in the system that I want to analyze - please see the equations that I posted in my first message. These equations are derived for an object (e.g. a beam node/element) moving in a rotating frame, with a constant angular velocity omega.

I want to model for example a beam element in the x-y plane. Under dynamic loading conditions (e.g. imposed displacement-controlled excitation in x-dir), the damping that is developed in the x-dir, due to the velocity Ax_dot, will need to have an effect on the y-dir, developing an acceleration Ay_dot_dot (y-dir equation), but no effect on the acceleration in the x-axis (x-dir equation).

Is there a way to model such cross-coupling in STKO?

Stavros

[STKO Team]

Let's see if this works:

There is a command in OpenSees that is not documented.
It's called equalDOF_Mixed, it's like the standard equalDOF, but you can couple a DOF (for example UX) to another (for example UY).

Format:
equalDOFmixed RnodeID? CnodeID? numDOF? RDOF1? CDOF1? ... ...

RnodeID = master
CnodeID = slave
numDOF = number of master-slave DOF pairs
RDOF1 = 1-st master DOF
CDOF1 = 1-st slave DOF
... (you can specify as many RDOF-CDOF pairs as numDOF)

For example if you want to couple the slave UY (dof = 2) of node 200 to the master UX (dof = 1) of node 100:
equalDOF_Mixed 100 200 1 1 2
equalDOF_Mixed 100(RNodeID) 200(CNodeID) 1(numDOF) 1(RDOF1) 2(CDOF1)

[kesavapraba]

Hello, I'm not entirely certain about your specific needs, but you could consider resolving these coupled second-order differential equations through various ODE solvers, such as those available in MATLAB or Python packages. I recommend attempting the ODE23 option in MATLAB; it seems to offer a straightforward and simpler solution compared to using a finite element (FE) program. For a basic illustration, please check Example 3 in the provided link (1st one below)

https://www.eng.auburn.edu/~tplacek/cou ... terloo.pdf

ODE23 Page from MathWorks:
https://in.mathworks.com/help/matlab/re ... 26e1089653