Summing function Wm(time,a,b,c,d) from m=0 to m=n ?

[JBlackhole]

To all,

I am sure I saw something about how to do such thing but I cannot find it so needs some pointers

I have a function (see attached mcad sheet) Wm(t,am,bm,cm,dm) where t is time and a_m,b_m,c_m,d_m are coefficient valid for equation m

I need to do sum of W_m from m =0 to n: but I am struggling with indices in mcad

Coudl anyone refreshe my memory on this summation? It might be something with "dicretizing" the time 't' if I recall

Thanks

Regards

JXB

[MikeArmstrong]

Like the attached?

I have change t from a range variable to a vector and also removed the units s the program works.

[AlanStevens]

The attached should help.

Alan

Looks like Mike just beat me to it!

Edit: Just noticed that your original file was a .mcd, so I've added a .mcd version here.

Mike: In your file the definition of Wm still contains tdm < t > tdm+Nm/2fm. I suspect this should be tdm < t < tdm+Nm/2fm (though I could be wrong!).

[JBlackhole]

Hi Alan

Thanks for the help. Am I correct to say that the Sum only works for a specific t value and not a range of t. Using Mike suggested method, I reckon that one needs to use two range variables

i for the vectorised time t

m for the number of coefficient (a,b,c,d) to consider

[AlanStevens]

J B wrote:

Hi Alan

Thanks for the help. Am I correct to say that the Sum only works for a specific t value and not a range of t. Using Mike suggested method, I reckon that one needs to use two range variables

i for the vectorised time t

m for the number of coefficient (a,b,c,d) to consider

The sum as written only works for a specific value of t, but you could include this sum within another that summed over the values of t.

Alan

[Werner_E]

Am I correct to say that the Sum only works for a specific t value and not a range of t.

It depends on what you are hunting for. As I suppose from the inserted pic you want to define a function for the second derivative of x like shown below, but I may be wrong.

And of course you may "sum" over t by using an integral.

But to be honest its unclear to me what you are really after.

[JBlackhole]

Hi Werner

The function Wm is the wavelet function and as essentially 5 "variables", t(ime) and a,b,c,d coefficients. The idea is to define m sets of coefficients (a to d) and create a new function x2(t) which is the sum of all the Wm functions. A bit like a fourier series if you want

Will attach an updated mcad sheet based on all the inputs so far very shortly.

Regards

JXB

[MikeArmstrong]

AlanStevens wrote:

The attached should help.

Alan

Looks like Mike just beat me to it!

Edit: Just noticed that your original file was a .mcd, so I've added a .mcd version here.

Mike: In your file the definition of Wm still contains tdm < t > tdm+Nm/2fm. I suspect this should be tdm < t < tdm+Nm/2fm (though I could be wrong!).

Hi Alan,

I was a little unsure on this myself, but the tdm condition ' < t > tdm+Nm/2fm ' does return a few 'True' evaluations so I left it as it is. JXB can you clarify?

[AlanStevens]

Mike Armstrong wrote:

AlanStevens wrote:

The attached should help.

Alan

Looks like Mike just beat me to it!

Edit: Just noticed that your original file was a .mcd, so I've added a .mcd version here.

Mike: In your file the definition of Wm still contains tdm < t > tdm+Nm/2fm. I suspect this should be tdm < t < tdm+Nm/2fm (though I could be wrong!).

Hi Alan,

I was a little unsure on this myself, but the tdm condition ' < t > tdm+Nm/2fm ' does return a few 'True' evaluations so I left it as it is. JXB can you clarify?

It will evaluate to "true" only when t is greater than the larger of the two conditions.

Alan

[MikeArmstrong]

AlanStevens wrote:

Mike Armstrong wrote:

AlanStevens wrote:

The attached should help.

Alan

Looks like Mike just beat me to it!

Edit: Just noticed that your original file was a .mcd, so I've added a .mcd version here.

Mike: In your file the definition of Wm still contains tdm < t > tdm+Nm/2fm. I suspect this should be tdm < t < tdm+Nm/2fm (though I could be wrong!).

Hi Alan,

I was a little unsure on this myself, but the tdm condition ' < t > tdm+Nm/2fm ' does return a few 'True' evaluations so I left it as it is. JXB can you clarify?

It will evaluate to "true" only when t is greater than the larger of the two conditions.

Alan

Agree.

Which is does from row 951 onwards

I think the way you have it is the correct way, but confirmation by JXB would be beneficial.

[JBlackhole]

Clarification for < t > statment. I changed to an OR statment. Will attahced a ver2 of the mcad sheet soon

[Werner_E]

J B wrote:

Clarification for < t > statment. I changed to an OR statment. Will attahced a ver2 of the mcad sheet soon

OK, that changes the sum function, too, of coursed. I used Alans version in my previous answer.

You may alternatively define

Can you clarify your need concerning that sum?

[JBlackhole]

Werner

The sum of the Wm(t) functions creates a time signal/histort based on Shock Response Spectrum (SRS) specification. If one takes the time signal and convert it to an SRS (response of 1-DoF spring-mass system to the created time history) then one should get the "same-ish" SRS. The clever bit (which I haven't figures out!) is to create a (large enought) set of coefficients (a,b,c,d) to create this time history.

[Werner_E]

J B wrote:

Werner

The sum of the Wm(t) functions creates a time signal/histort based on Shock Response Spectrum (SRS) specification. If one takes the time signal and convert it to an SRS (response of 1-DoF spring-mass system to the created time history) then one should get the "same-ish" SRS. The clever bit (which I haven't figures out!) is to create a (large enought) set of coefficients (a,b,c,d) to create this time history.

Comparing the two plots I guess you got what you had asked for. You may consider adding units throughout. You simply have to type something like InputFreq:=InputFreq*Hz, etc. after you exctracted the values from your table.

[JBlackhole · Accepted solution]

Thanks to all for the help. Moving on to the next bit of the tool....