Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated!Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated! Hi All,
I am trying to perform a definite integration in X (length axis) to calculate some beam modeshapes, following this the variables will be passed into a time integration using ode45. In the integration there are beam modeshape terms (W) which are a function of x and there are time dependent terms (qw) which are not. Crucially the qw terms are not commutable so cannot be factored out of the integrals. I need the answer to W6 to be given in terms W6=Y1*qw1+Y2*qw2… where Y1 and Y2 are numerical coefficients.
Here is my code:
clear all
clc
syms x qw1 qw2
L=0.52;
qw=[qw1; qw2];
%Bending Mode
Landa=[1.875104069 4.694091133];% 7.854757];% 10.99554];
for j=1:length(Landa)
SIGMA(j)=(cos(Landa(j))+cosh(Landa(j)))/(sin(Landa(j))+sinh(Landa(j)));
W(j)=cosh(Landa(j)*x/L)-cos(Landa(j)*x/L)-SIGMA(j)*(sinh(Landa(j)*x/L)-sin(Landa(j)*x/L));
end
% Integration in X over length of beam
W6=(vpaintegral(W*diff(diff(W,x,1)*qw*diff(diff(W,x,1)*qw*diff(W,x,2)*qw,x,1),x,1),0,L));

The value W6 is left as symbolic without the integrals being solved, this means that when I pass the W6 term into the time integration in a separate script and solve for qw terms the time integration is much slower because it is computing the spatial integration in X for each time of the 1000 time-steps.
I have tried using the ‘double’,’simplify’ and ‘collect’ commands but I have not been able to get the result in the form I want it. So what I’m asking is, is there a way to "force" matlab to do the integrations with the symbolic coefficients attahced. Any help would be much appreciated! definite integration, symbolic toolbox, simplifying MATLAB Answers — New Questions

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