How to Solve a second order differential equation for variable eta in time domain- with a contained integral over another dummy variable (tau)-
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Vignesh Kumar
am 30 Okt. 2015
Kommentiert: sivabalan sitti
am 12 Nov. 2018
Hello All,
I am new to Matlab and I am trying to solve the attached 'Cummins Equation'. It is an equation of motion in time domain for the variable (eta). All other parameters in the equation M,A,B,C,F,h have been found over a period of interest from time 0 to time t. eta is to be found as function of t.
I have to integrate the contained integral over a dummy tau (convolution of both functions h and etadot) and then solve the resulting ODE. With a known h and an unknown etadot, could I still use conv2 function and continue to solve the ODE?
Will a time marching Runge Kutta method (ode45) work?
I would sincerely appreciate any help in this direction as I have hit a roadblock. Thanks in advance.
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Torsten
am 30 Okt. 2015
Bearbeitet: Torsten
am 30 Okt. 2015
Consider the different numerical methods for Cummins equation explained in
In any case, you will have to spend some effort in the solution method. A simple application of a standard tool like ODE45 won't work.
Best wishes
Torsten.
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ben howey
am 21 Mai 2018
Hi, I am trying to do the same thing. I have used a BEM code to calculate the IRF, inf added mass and frequency dependant excitation force and want to calculate the time dependant float position. Have you had any luck in solving this? I dont see how you can solve the convolution integral with the trapz method if z dot is unknown!
Any help or code that I can look through would be much appreciated!!
Thanks
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sivabalan sitti
am 12 Nov. 2018
There is an open source code available to solve cummins equ,u can try that https://wec-sim.github.io/WEC-Sim/getting_started.html
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