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Simplify three equations and write them in a matrix form?

vin Bha
Posted 4 years ago

research work

I want simply last three equation interms of Amn, Bmn, Cmn and also want to write in a matrix form.

Attaching herewith the expected solution image.enter image description here
POSTED BY: vin Bha
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1) Rohit's solution is perfectly correct.

2) Amn is zero, Bnm and Cmn are functions of x and y! So they have different values for different values of x and y. I don't see how one could avoid that

3)Again, what do you mean by "get rid of"?

4) Are you sure that your model is correct? Looking at the plots at the end of the notebook it seems they are somewhat strange.

Attachments:
research work.nb
POSTED BY: Hans Dolhaine

Vin,

I showed you how to remove the Sin and Cos terms using Assuming on this other thread BUT you must be certain they are not zero (or if they are zero that it does not matter to your solution).

https://community.wolfram.com/groups/-/m/t/1856471?p_p_auth=L9dN9FO4

Did you try that solution?
POSTED BY: Neil Singer

What do you mean by "get rid of"? For me Sin and Cos contain essential information, and they have rarely the same value. You could try

cM /. Sin[ m_ (Pi x_)/a_] :> s[m/a] /. Cos[ m_ (Pi x_)/a_] :> c[m/a]

See the notebook attached (at the very end)

Did you mean that?

Attachments:
research work.nb
POSTED BY: Hans Dolhaine
vin Bha
vin Bha
Posted 4 years ago

Sir In the present work value of x and y is unknown so somehow i want to eliminate term containing x and y variable from all three equation. I am finding free vibration frequency of a plate using the assumed solution but the problem is x and y is unknown and so i want equation without x and y term.
POSTED BY: vin Bha
Bill Nelson
Bill Nelson
Posted 4 years ago

Can you use this method to get what you need?

{4,Sin[m Pi x/a], 2 Sin[n Pi y/b],m*Cos[m Pi x/a], Pi b Cos[n Pi y/b]}/.{Sin[__]->1,Cos[__]->1}

which replaces each Sin and Cos with 1 and returns

{4, 1, 2, m, b Pi}
POSTED BY: Bill Nelson

Did you mean this? (See notebook)

But it won't give Matrix.{Amn,Bmn,Cmn} ==0, because there are terms containing Dqx ans Dqy

But look at

pp = cM.{Amn, Bmn, Cmn} - {0, Dqx \[Psi]xmn, Dqy \[Psi]ymn};
pp[[1]] - e1 // Simplify
pp[[2]] - e2 // Simplify
pp[[3]] - e3 // Simplify
Attachments:
research work.nb
POSTED BY: Hans Dolhaine
vin Bha
vin Bha
Posted 4 years ago

Sir thank you for reply I got all the coefficient of Amn, Bmn and Cmn, but now I want to get rid of x and y terms from all three equation. I mean to say want to get rid of Sin and Cos terms which contains x and y variables i.e. Sin(mpix/a), Sin(npiy/b), Cos(mpix/a), Cos(npiy/b) from all three equation. Kindly help me out.
POSTED BY: vin Bha

What was wrong with the result posted by Rohit Namjoshi ?
POSTED BY: Daniel Lichtblau
vin Bha
vin Bha
Posted 4 years ago

Can anybody solve the above equation???

POSTED BY: vin Bha
vin Bha
vin Bha
Posted 4 years ago

I am attaching herewith the code.

Attachments:
research work.nb
POSTED BY: vin Bha
Rohit Namjoshi
Rohit Namjoshi
Posted 4 years ago

Please post code, not images, or attach a notebook with the code.
POSTED BY: Rohit Namjoshi
vin Bha
vin Bha
Posted 4 years ago

Attaching herewith the code

Attachments:
research work.nb
POSTED BY: vin Bha
Rohit Namjoshi
Rohit Namjoshi
Posted 4 years ago

Without any constraints on the various constants in the equations, one solution is

{Amn -> 0, 
 Bmn -> -((Dqx ?xmn Csc[(n ? y)/b] Sec[(m ? x)/a])/(h ? ?mn^2)), 
 Cmn -> -((Dqy ?ymn Csc[(m ? x)/a] Sec[(n ? y)/b])/(h ? ?mn^2))}

I do not see how these relate to the matrix you have.
POSTED BY: Rohit Namjoshi
vin Bha
vin Bha
Posted 4 years ago

Thank you sir for your reply. i am having three equation which consists of three terms namely Amn, Bmn and Cmn which needs to be sorted out and write in matrix form.

In all three equation sin and cos terms are common through out the equation and thus can be eliminated and that is why sin and cos terms are not mentioned in the given matrix.!enter image description here

First i want to simplify those three equation by removing common terms( Sin and Cos terms). Second I want to convert those simplified equation in terms of matrix form with Amn, Bmn and Cmn in 3*1 matrix.

[3 x 3 matrix ][ 3 x 1 matrix ]=0.
POSTED BY: vin Bha
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