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# Modal Transient Response (SEMTRAN -- SOL112) with acceleration base excitation

Innovator
Hello Experts!,
I want to study the transient response to a base acceleration Accel +Y=3G applied at the base of a simply steel cantilever beam of length L=1000 mm and cross section 50x50 mm using the Modal Transient Response Analysis (SOL112) of NX NASTRAN to compute the behavior of a structure in the time domain.

INPUT DATA&colon;
• EX=206E3 MPa,
• NUXY=0.3,
• DENS=7.85E-9 Tons/mm3,
• Total Mass Beam = 0.019625 Tons

A modal damping of 2% is used for all modes.

LINEAR STATIC ANALYSIS (SOL101) RESULTS
===================================
As a reference here you are the results of the basic linear static analysis to a gravity load = 3G = 3*10e3 mm/s2:
• Beam EndA Max Comb Stress = 14.13 MPa
• Maximum displacement = 0.688 mm
• Reaction force in the fully constrained base node T2 Constraint Force = 588.75 N

MODAL TRANSIENT RESPONSE ANALYSIS
==================================

The Enforced motion is used to specify the acceleration at the base grid point #1 for transient response. In this example there are no applied loads. Instead the base of the beam undergoes an enforced acceleration time history in the +Y axis direction using the SPC/SPCD Method (not LARGE MASS method):

Modal transient response analysis (SOL 112) is run with 2% critical damping used for all modes. Modes up to 20 are computed with the Lanczos method using mass formulation = coupled. A time step of 0.001 second is used, and the analysis is run for 0.5 second (number of steps = 500). The following picture shows the modal mass in the X, Y and Z directions for the first 20 modes. Generally, the number of modes considered must contribute to a total mass participation factor of at least 80% of the system mass in the direction of the base motion.

4 REPLIES

# Re: Modal Transient Response (SEMTRAN -- SOL112) with acceleration base excitation

Innovator
ANIMATION OF RESPONSE
===================

The following picture shows the animation of Resultant Displacement of ALL the output sets resulting from the analysis (using increment 5.0 to reduce file size). Please explain why the model exhibid a rigid body motion when the base grid node is fully constrained.

The following pictures shows the displacement, velocity and acceleration response at grid points 1 (base) and 21 (tip).
XYPLOT OF RESPONSES AT BASE NODE #1
=================================

The displacement vs. time of base node #1 is incrising & increasing, how to understand this behaviour?. The total value at time = 0.5 sec. is 145.5 mm. This linearly increasing displacement result need to be explained by NX NASTRAN guys ...

The velocity vs. time of base node #1 seems to reach a constant value = 300 mm/sec. at the end of the acceleration shock base motion.

The acceleration vs. time of base node #1 seems correct, is exactly the input prescribed to grid node#1.

And finally here you are the reaction force at base constrained node#1: very insteresting this plot, it shows a maximum value of 656.9 N, then if compared with the linear static reaction force of 588.75 N it SHOWS A DYNAMIC MAGNIFICATION FACTOR of 656.9/588.75 = 1.12. In my opinion this is a reasonable answer: 1st eigenvalue has a value of 41.3 Hz, then the structre a quite rigid, not flexible (cutting frequency is around 33 Hz), so dynamic magnification factor must be relatively small.

# Re: Modal Transient Response (SEMTRAN -- SOL112) with acceleration base excitation (PART III)

Innovator
XYPLOT OF "DISPLACEMENT" RESPONSE AT TIP NODE #21
============================================

And finally here you are the X-Y Plot dynamic responses of displacement, velocity and acceleration vs. Time at the tip node of the cantilever beam.
Again appear the rigid body movement of displacement, the value is useless, anybody from NX NASTRAN EXPERTS should explain this extrange behaviour.

XYPLOT OF "VELOCITY" RESPONSE AT TIP NODE #21
============================================

The resultant velocity vs. time shows a maximum value of 545.4 mm/s and the average damped value tends to 300 mm/s

XYPLOT OF "ACCELERATION" RESPONSE AT TIP NODE #21
============================================

The resultant acceleration vs. time shows a maximum value of 6.27e4 mm/s2 and the average damped value tends to 5796 mm/s2

DYNAMIC TRANSIENT RESPONSE OF BEAM STRESS
============================================

The MAXIMUM transient dynamic response of beam stresses is at time t=0.02 sec and has a value of Beam EndA Max Comb Stress = 19.3 MPa, giving a DYNAMIC MAGNIFICATION FACTOR of 19.3/14.13 = 1.36

Well, that's all I wanted to share with you all, any comments from NX NASTRAN experts are welcome to validate the metodoly folowed & results obtained when performing an Enforced base Motion with Modal Transient Response Analysis (SEMTRAN SOL112) and try to explain this extrange results of displacement vs. time -- thanks!.

Best regards,
Blas.

# Re: Modal Transient Response (SEMTRAN -- SOL112) with acceleration base excitation (PART III)

Innovator
Hello!,
I forgot to include the NX NASTRAN file input for your revision.

Also, here you the X-Y plot of dynamic transient Beam EndA Max. Combined stress response for element#1 vs. time:

Best regards,
Blas.

# Re: Modal Transient Response (SEMTRAN -- SOL112) with acceleration base excitation (PART III)

Innovator
Hello!,
Well, I will answer my own question.
After investigating, the main problem was the following:

The key here was to obtain the response of relative displacement, instead of absolute displacement generated by default.
Displacements and accelerations are different, because answers computed by using the absolute acceleration enforced motion contain the rigid body drift contribution, whereas answers computed by using the relative displacement enforced motion do not contain the rigid body drift contribution. Displacement and acceleration responses can be made equal regardless of which spectra was used by using PARAM,LFREQ,0.01 (or some other small number) to remove the rigid body mode contribution from the answers.
Stresses and other element quantities are unaffected by the contribution of any rigid body modes.

Then with the arrival of new FEMAP V11.1 release a new option exist in the NASTRAN Output Request GUI that allows to define the relative displacements response results for dynamic enforced motion. Simply activating this option now results seems reasonable.

Here you are both the INPUT excitation of T2 acceleration of 3G prescribed to the base (node#1) together with the OUTPUT T2 acceleration response in the tip node of the beam (node#21):

Also, here you are the response of vertical T2 displacement vs. time, supperposed over the linear static maximum displacement results.

And finally the resultant reaction force (N) vs. Time:

That´s explain everything.
Best regards,
Blas.