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# Modal Transient Response (SOL 112) - Initial Conditions Not Working?

## Modal Transient Response (SOL 112) - Initial Conditions Not Working?

(OP)
Happy Friday all,

Sorry in advance for the long-winded explanation.

I'm dealing with an issue regarding SOL 112 (Modal Transient Response) which I'm hoping to receive some feedback on. I've made a simplified model (see attached) to test the behavior. The model looks like the letter "T" with the bottom of the T as my base input and the top outer-most edges of the T my eventual nodes of interest. I included a CBUSH at the T joint (in addition to the flexibility of the top T) for some added dynamics.

At its simplest, I'd like to have the entire model start at an initial angular velocity about the Z-axis and then, after some short period of time, apply an enforced angular acceleration (or velocity profile) to the base about Z in order to slow the model down over a short time period (~0.1s). I am interested in the dynamic response out on the ends of the "T" of the model during and after this transient event.

The trouble I run into is:
1) If I apply an enforced acceleration or velocity profile about Z at the base node, I must SPC the base node in DOF 6. This then eliminates the possibility of the base node being defined in the initial condition set.
2) If I forgo the initial condition and simply apply an enforced rotational velocity to the base node in addition to an enforced acceleration, the input node velocity vs. time looks correct, but the acceleration vs. time now starts from a very large number at t=0s and appears to "use" the first timestep to go from the large acceleration back to 0 acceleration (constant velocity) in order to what I can only assume is catch the rest of the model up to the initial t=0 velocity.

Perhaps there is a way to create a full 3d velocity (angular and translational) description for each node which would start the rest of the model in the correct dynamic state, but I have no idea how to do this (especially for a full-sized model).

For what it's worth, I am able to run the model with an initial velocity of 0rad/s and accelerate the model. What I miss out on is the added effect of the centripetal force due to the angular velocity which I would ideally like to capture. I am also able to run the model long enough that the initial acceleration response dies off and then I can input the deceleration at the correct angular velocity, but this seems crude.

The model takes seconds to run and there are three cases:
Case 1: Enforced velocity only (starts the model at the desired velocity then applies the correct velocity vs. time function to decelerate the model)
Case 2: Enforced velocity and acceleration (starts the model at the desired velocity then applied the enforced acceleration)
Case 3: Enforced acceleration only (starts the model with a velocity of 0rad/s, ignoring the added centripetal force effects)
Charts are prepared for all three cases once run.

Any help is greatly appreciated! If it is not possible to do what I am asking efficiently, then running the model long enough to stabilize the initial acceleration spike prior to performing the deceleration is OK, I'd just like to know that.

Thank you!

-CH

Blas Symbol Activated!

### RE: Modal Transient Response (SOL 112) - Initial Conditions Not Working?

You asked a question about Nastran, but posted a FEMAP file (as far as I can tell). I don't use FEMAP, so I can only help if you post a Nastran input file (the one containing the SOL 112 executive control command).

As some other food for thought, you appear to be wanting to simulate a rotating structure where differential stiffness due to the centripetal acceleration could be important - what about gyroscopic and circulation effects? Which version of Nastran are you using? MSC Nastran has a rotor dynamics capability which will handle rotor dynamics effects (centripetal, gyroscopic and circulation terms) in a direct transient response (SOL 109) or even nonlinear transient response (SOL 400) if you wanted to add things like the rotor hitting a casing or a nonlinear bearing.

DG

### RE: Modal Transient Response (SOL 112) - Initial Conditions Not Working?

(OP)
DG,

Fair point regarding the FEMAP .modfem file.

Attached is a .zip of the .bdf files for the following cases:
-Enforced rotational velocity only
-Enforced rotational velocity and acceleration
-Enforced acceleration only (0 starting velocity)

Yes, in general I'd like to be able to capture the effects of the centripetal acceleration due to the rotational velocity of the system prior to decelerating from the stop event.

I am using Simcenter Nastran 2019.1 (NX). So far, when using the direct transient analysis method, I've gotten results which do not appear to accurately capture the additional flexibility of the system (response looks more like a rigid body), but I will take another look at this with an eye towards rotor dynamics effects.

Thank you very much DG. Let me know if you have any further feedback!

CH

### RE: Modal Transient Response (SOL 112) - Initial Conditions Not Working?

When a structure is loaded, the displacement caused by the load can lead to a significant change in the apparent stiffness of the structure. If the load acts to extend the elements of the structure, like a guitar string, the apparent stiffness will increase - pluck the guitar string as you tension it and the frequency increases due to the apparent stiffness change; if the load acts to compress the elements of the structure, like a column, the apparent stiffness will decrease and the structure may even buckle. Both changes in apparent stiffness are due to the differential stiffness, sometimes called geometric stiffness because it is a function of the displaced shape.

In linear dynamic analysis (and I will include computation of normal modes in this), the change in stiffness may be computed by defining a static load case in the same input file as the dynamic load. The response to the static load yields the displaced shape from which the change in stiffness is computed. Those familiar with SOL 105 (linear buckling) will recognise the 2 SUBCASEs approach, the first with the applied load and the second where the distance to the buckling point is computed using an eigenvalue solution to yield a scale factor on the applied load. Stress stiffened normal modes may be computed in the same way using SOL 103 and 2 SUBCASEs, the first again with the applied load and the second this time that computes the stiffened natural frequencies. Forced response in SOL 108, 109, 111 and 112 all may use the same technique where a 2 SUBCASE job is defined and the first SUBCASE again applies the stiffening load and the second SUBCASE uses the static response as an initial condition, i.e. the structure is preloaded and its stiffness modified accordingly. So in SOL 112, to compute the stiffness change due to an angular velocity, you simply define 2 SUBCASEs, the first which references an RFORCE entry to define the angular velocity (and/or angular acceleration if needed) and the second which applies the transient load starting from the preloaded static condition.

The issue with this "linear dynamic" method for rotating structures is two-fold. Firstly, the angular velocity is a fixed speed, so the differential stiffness will be constant. If you want to decelerate the angular velocity over time in the second SUBCASE, the differential stiffness becomes progressively incorrect as it is not recomputed as the angular velocity slows. Secondly, there is no account for gyroscopic or circulation terms in the equation being solved. To get centripetal, gyroscopic and circulation terms, you must use a rotor dynamic analysis where (at least part of) the structure is defined as a rotor. In rotor dynamics, you do not need the first static SUBCASE as the differential stiffness is computed for a unit rotation speed for each rotor and then scaled by the actual speed of the rotor at each time step.

You can overcome the first issue by using a nonlinear dynamic analysis (even though there may be no other nonlinearities like contact or plasticity) where the solution recomputes the differential stiffness at each time step. However, the missing gyroscopic and circulation terms will produce an erroneous result which may be far from the true response. Much will depend on whether the elements of the structure precess or not (i.e. whether there is movement out of the plane of rotation), as only then will gyroscopic or circulation terms be generated. You may also define a nonlinear rotor dynamic analysis if you wanted to study something like a casing rub, but that's another story.

So, under the condition that your structure does not change angular velocity and there is no precession, you can use a SOL 112 or 109 job similar to the one you posted but with the addition of a first SUBCASE that defines a static load case referencing an RFORCE load to define the angular velocity from which the centrifugal force will allow the differential stiffness to be computed. In the second SUBCASE, the first SUBCASE is referenced with a STATSUB command to include the differential stiffness in the transient response. In this second SUBCASE, you will also need an IC= command to point to a set of TIC entries which specify the Time Initial Conditions for the rotating structure. For this you need to compute the R*omega force terms as tangential forces at the GRID points, plus the definition of the angular velocity that corresponds to the RFORCE angular velocity. The TIC entries will take care of the degrees of freedom that are NOT defined on SPCD entries for the enforced motion. In order to define an initial condition for the SPCD degrees of freedom, you need to use the VS0 field on the TLOAD1 entry (field 8).

As a final remark, be careful of the units; TIC rotation speed will be in radians per unit time but RFORCE angular velocity is defined in revolution per unit time for some strange reason.

I don't use NX Nastran so I can't advise you on how to define a rotor dynamics setup. I can do this for MSC Nastran if you have access to it.

I modified one of your input files with the above necessary entries for a job that defines an RFORCE load corresponding to 62.8319 RPM (10 radians/sec), TIC entries for 10 rads/s and a TLOAD1 entry with F=10. rads/s and VS0=10. rads/s. Like this, the job starts with the structure rotating at 10 rads/s and the enforced motion keeps it rotating at that speed; the displacement should be a uniform rotation with constant angular velocity and no acceleration. You can see that the modes have natural frequencies slightly higher than the modes of the stationary structure (in SOL 103 with a single SUBCASE) confirming the stress-stiffening effect of the RFORCE. To get the rotor slow down to give proper answers, you will need either nonlinear transient (no gyro effects) or rotor dynamics.

DG

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