iMechanica - vibrations - Comments

related subject: Nonlinear Dynamics of Marriage!

Mike Ciavarella — Wed, 09 Nov 2011 03:39:41 -0500

The Mathematics of Marriage: Dynamic Nonlinear Models (Bradford Books)

The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one "marriage experiment," for example, the authors explored the effects of lowering or raising a couple?s heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions.Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well.

UPC is a very good place

Dibakar Datta — Thu, 27 Oct 2011 17:32:41 -0400

UPC is a very good place ... I studied there for six months.. But unfortunately many people do not know about this place... I strongly encourage the potential candidate to apply ...

Regards,
Dibakar Datta
Email : dibakar_datta@brown.edu
PhD Student ; Major : Solid Mechanics
Shenoy Research Group
Brown University
Providence 02912 , USA
Group Homepage : http://www.engin.brown.edu/faculty/shenoy/shenoygroup/

derivation of the pendulum eqt for happiness

Mike Ciavarella — Tue, 18 Oct 2011 05:44:26 -0400

From the love/hate model of R&J, the derivation of Dynamical Models of Happiness, is in short this.

dR/dt = aR + bJ
dJ/dt = cR + dJ

one can eliminate an eqt for Romeo's love alone
d2R/dt2 + beta dR/dt + omega2 R = 0

beta = -a - d (damping)
omega2 = ad - bc (frequency)

so notice that damping, which clearly is one of the key parameter,
depends only on the self/awareness factors, and not sensitivity to
partner. Manic depression for example may correspond to beta ~ 0.

H (your happiness)=dR/dt must average to zero (with positive damping)

But remember beta=-a-d, so generally speaking damping is high
with cautious lover and hermits, but not so for eager beavers
or narcissistic nerds which may have negative damping, i.e. have
either happiness very high or very low, forever!

See

1. The simplest model supposes that over a sufficiently long time,
people tend to acclimate to their circumstances and thus experience
equal amounts of happiness and unhappiness. Therefore, constant
happi-ness is an unrealistic and unobtainable goal.
2. Suicide is an irrational response to unhappiness, similar to
bailing out of the stock market at the bottom. The model predicts that
if you wait long enough, happiness will return, even if only by virtue
of acclimating whatever is causing the unhappiness.
3. Others tend to perceive less volatility in you than you feel since
they observe primarily your responses to external events (R) rather
than your true feelings (H), and therefore they often wrongly conclude
how happy you are.
4. Since individuals will tend to acclimate to their circumstances,
long prison terms may be ineffective if the goal is punishment rather
than deterrence or protection of society.
5. Individuals may be characterized by two parameters β (how rapidly
they return to equilibrium after a perturbing event) and ω (the
frequency with which their feelings change). These parameters may be
of diagnostic use in describing psychological health.
6. Healthy individuals may have β ~ 2ω, corresponding to critical
damping, while people with β < 0 exhibit bipolar behavior. A strongly
overdamped person (β » 2 ω) may be largely devoid of emotions and
unaffected by events, whether good or bad.
7. A reasonable goal of psychotherapy might be to alter the parameters
β and ω so that the patient responds to external events in a more
healthy manner. It is an open question the extent to which such
therapy is effective, since the parameters may be largely fixed by
one’s personality.

How to do this is left to the psychotherapists, I guess mechanics cannot do much more! :)

extension to love triangle dynamics

Mike Ciavarella — Tue, 18 Oct 2011 00:57:13 -0400

Consider a love triangle in which Romeo and Juliet love each other, but Romeo also loves his mistress Guinevere and she loves him. See http://numb3rs.wolfram.com/402/

there is even a mathematica demo of Romeo and Juliet's model

Mike Ciavarella — Mon, 17 Oct 2011 14:47:14 -0400

the code can be found at

demonstrations.wolfram.com/RomeoAndJuliet/

Thank you for your response

jgrzmmm — Mon, 08 Mar 2010 11:20:38 -0500

Thank you for your response Andras!

The results I need are the peak transient deflection and the stabilized response, which can be actually seen for the first 25ms.

It's true that the peak-to-peak amplitude is only about 0.00001 compared to the average residual deflection of 0.02426, so I will use this result in my report.

I was mainly concerned about choosing the right material and had doubts, that maybe the one I used, was causing such infinite vibrations. Your answer convinced me that it wasn't the main "problem".

I decided that I need only first 25-30ms of the simulation, it will surely save a lot of computational time!

Thank you for your help Andras, gave me a great insight into some matters I deal with in my simulations!

Best regards,
Julian

My thoughts

Andras Nelhiebel — Fri, 05 Mar 2010 18:10:35 -0500

Hello Julian!

I have some expertise on modeling blast loads, so please let me share some thoughts that came into my mind according to your question.

1. First I do not know what is your goal with the simulation, but my experience shows, that the important things happen in the first 10-25 ms when the response to blast loading is in focus. Your simulation shows the same pattern, so the time interval you concern is irrelevant (unless you investigate the rigid body motion - e.g. free falling - of the system)

2. The vibration you show is five orders of magnitude smaller than your maximal displacement. This is far less than any experimental uncertainity. If it would be 100 times bigger, it still would be within the engineering accuracy.

3. I think your problem is not connected to hourglassing rather a residual elastic vibration of the system, which leads directly to my next point.

4. Most materials in explicit FE codes do not contain material damping. This is no harm, since modeling blast loads take time in a few milliseconds where structural damping is irrelevant. The only thing that consumes energy is plasticity. All the plastic response occurs in the first 25 ms - according to your graph. As the plastic deformation takes place, your velocities - hence the force to deform your system - will get smaller and you fall back to the elastic region. From thet time you will have some elastic vibration in the system without anything to absorb the energy. It will stay like this forever.

5. Not to mention the fact that explicit codes ALWAYS have a vibration in them, since they do not solve the algebraic equations directly. Just build in a single element without any load or BC and let it run for 10-100 ms. You will get stresses at about 1e-5.

My advice would be, just simply forget the vibration and maybe as a result give an average value of the last 75 ms.

I hope I had some good ideas for your future analysis.

Regards, Andras