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solving coupled system of second order differential equations

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aakash dewangan
aakash dewangan 2021-5-25
评论： aakash dewangan 2021-5-30
Hello everyone,
I want to solve a "second order coupled ordinary differential equation". I searched a lot but could not find the solution.
Please suggest me how can I solve this.
The structure of my equation is given below,
[M]{x''} + [K]{x} = {F}
where [M], [K] are the matrices, which contain time dependent terms.
{x} vector of unknown dependent variables.
{x''} is the second derivative of the vector {x} with respect to time.
Please note that [M], [K] contains time varying terms
Looking forward for your the response.
Thanks for your time..
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Paul
Paul 2021-5-28
Do you have a simple example for M, K, and F? Preferably one that you know what that solution should be?
aakash dewangan
aakash dewangan 2021-5-30
M, K and F contains sinusoidal terms, which depend on time. Diagonal terms of M and K are in the form of a+sin(nwt), and non diagonal terms are like sin(nbt)*sin(nct). Where a,b,c,n are some constant parameters, and t is time.

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采纳的回答

Sulaymon Eshkabilov
Hi,
You can employ ode solvers (ode23, ode23tb, ode45, ode113, etc) as suggested or write scripts using function handles or anonymous functions by apply Euler or Runge-Kutta methods.
  2 个评论
aakash dewangan
aakash dewangan 2021-5-28
Thanks Sulaymon,
But I am looking for Analytical solution. Can you suggest me how I can solve this using Analytical approach?
Sulaymon Eshkabilov
Sulaymon Eshkabilov 2021-5-28
Should you need to obtain an analytical solution, then dsolve() of Symbolic MATH toolbox needs to be employed. E..g.:
syms x(t) Dx(t) DDx(t)
Dx = diff(x, t);
DDx = diff(Dx, t);
M = [??];
K = [??];
EQN = DDx==inv(M)*(F-K*x);
SOL = dsolve(EQN, x(0)==??, Dx(0)==??)
Good luck

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