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## Elastic Wave Propagation (my 1st Post)

Hi All,

I'm new here so bear with me. I tried few searches but was not successful in finding what I was looking for.

Phi, Psi are functions (Helmholtz) in theta and r. J, H are Bessel, Hankel function of first kind.

The question is how can I factor A, B, C, D, E, F, G, H matrices? While I can not even conduct a simple differentiation. MathCad can not recognize that A, B, C...are unknowns to be found with boundary and initial conditions.

Thanks

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13 REPLIES 13

## Re: Elastic Wave Propagation (my 1st Post)

The attached might help.

Alan

NB The symbolic arrow comes from the symbolic keyword toolbar.

Message was edited by: AlanStevens Revised, corrected file attached, but note that the sums to infinity won't work in practice - the Bessel and Hankel functions won't calculate, and your E,F,G and H matrices have subscript n where n goes to infinity!!!

## Re: Elastic Wave Propagation (my 1st Post)

Thanks, The problem is a bit complicated than this. However, you have helped me in overcoming the 1st obstacle. A, B, C, D, E, F, G, H are unkowns (vectors of unkowns). Let's simply imagine that sigma-r (the stress) will have numeric values. Sigma-r is a lot complicated than what I wrote it will have phi differentiated w.r.t theta, r , theta-square, r-square and r-theta.

My objective was to use mathcad for symblically handling the equations. In other words, there will be more than 9 simultaneous equations with A, B, ...on both sides of the equation. I am trying to have Mathcad to factor these unknowns.

The interesting thing is some of these will have sigma squared.

## Re: Elastic Wave Propagation (my 1st Post)

If you are just interested in numerical evaluations of A , B etc then you probably don't need symbolic evaluations at all. If you are fitting to numerical data you'll need at least as many data points as you have unknowns. How big are the vectors A, B etc? If they have n rows you'll have 8n unknowns to fit. Look up Given ... Minerr in the Help files (or search this forum for examples).. However, this might not be what you're after, I can't really tell without more information. Try to construct a (possibly simplified) worksheet of the whole process you want to go through - perhaps we'll then be in a better position to help.

Alan

## Re: Elastic Wave Propagation (my 1st Post)

I'm including an example of how the equation of sigma-r would look like

The are two sigma-r both are funcitions in phi and Psi the unknowns that I was hoping to extract hopefully symbolically would be A, B,...

On a side note, I appreciate your help and so far you have given me ideas. I'm new here. I do not want to say my question was answered so it would neglected. I am not sure if I am not giving you enough credit by not marking these as answers.

## Re: Elastic Wave Propagation (my 1st Post)

 On a side note, I appreciate your help and so far you have given me ideas. I'm new here. I do not want to say my question was answered so it would neglected. I am not sure if I am not giving you enough credit by not marking these as answers.

As Alan has stated above most users do not help to acquire points. If you feel a post is helpful you can add a star by declaring the post a 'helpful'. Once you have the answer you can then declare the thread answered and indicate which post the answer came from. This helps other forum members, by saving time going through every thread if there only interested in the solution.

Mike

## Re: Elastic Wave Propagation (my 1st Post)

I'm positive that selecting the 'helpful answer' just allocates a star to that post to confirm it was helpful. There is another option to select the thread has been answered.

Mike

## Re: Elastic Wave Propagation (my 1st Post)

 Chad G. wrote:My objective was to use mathcad for symblically handling the equations. In other words, there will be more than 9 simultaneous equations with A, B, ...on both sides of the equation. I am trying to have Mathcad to factor these unknowns.The interesting thing is some of these will have sigma squared.

Usually, as the number of variables inbcrease, the problem becomes less and less solvable using symbolic methods.

One of the key difficulties is the lack of a method to direct and limit approximations so that say third order terms (and larger) are ignored.

You may be able to get a higher order solution but expect messages that say that it won't fit into the 'page' size, which is massive!

Sometimes it is a case of doing the substitution steps yourself so that you guide the approximation. Don't forgetr that you can name an expression e.g. Eqn1 := expression, and then pass the Eqn1 around (or whatever name you want), and you can have boolean equality in them.

Philip

## Re: Elastic Wave Propagation (my 1st Post)

Good point is it possible to use substitution for example instead of Hankel differentiation I can use Hp to represent this messy equation. Does the substitution variable has to have same arguments?

## Re: Elastic Wave Propagation (my 1st Post)

 Chad G. wrote:...I am thinking of ignoring the sum in Phi and Psi and see if I can still factor A, B, C,..... (the order m=1) in other words A, B would be 1 element instead of a vector of unkowns.Another idea just thought of it now is make sigma-r (from consti) - sigma-r (from physics) = 0.

Simplifying is definitely a good idea. Not only is it likely to help you to see the wood for the trees, but it will definitely help us!

You wrote: "I am not sure if I am not giving you enough credit by not marking these as answers." Don't worry about this - I'm not in it for the points!

Alan

## Re: Elastic Wave Propagation (my 1st Post)

Thanks just saw your reply. It would be easier to use substitution. I am including a file with your ideas.

## Re: Elastic Wave Propagation (my 1st Post)

Looking at the complexity of your equation, I do not think any symbolic math package would be able to solve for the coefficients. Even if that were possible, the solution to a system of equations that complicated would almost certainly (unless you got extremely lucky, and a lot of stuff canceled) be horrendously large and complicated. You need to be thinking about solving these numerically, not symbolically.

## Re: Elastic Wave Propagation (my 1st Post)

I'm totally new and do not know how things work in this forum or board. I want to give credit for any help without making the thread unnoticed or an answered. I totally understand where you coming from in regads to points. I just do not know how are things here. The very simple thing like even how to quote...therefore I do not want to be making mistakes.

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