I writing program for rung kutta th4 now i have a problem who can help me?
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% clear;
clc;
%% precision of work
n=100; %steps
dr=1/n; %minimum step radius
r=1/n:dr:1+1/n; %0=<r=<1 radius
%%
vdc=2.4; %max voltage(v)
dv=0.001; %step voltage(v)
%% capasitor properties
R=500e-6; %max radius plate(m)
h=1e-6; %thickness plate(m)
g=2e-6; %Initial gap capasitor(m)
%% material properties
E=150e9; %Young’s modulus (pa)
e0=8.854e-12; %Electrical permittivity of air
nu=0.06; %Poisson ratio
rho=2300; %Density (kg/m^3)
%% Fixed functions
D=(E*h^3)/(12*(1-nu^2)); %flexural strength
%tstar=R^2*sqrt((rho*h)/D);
%betha2=(c*R^4)/(D/tstar);
alpha=(e0*R^4)/(2*D*g^3);
%% mode shape
phi=cos((pi*r)/2).^2;
phi1=-cos(pi.*r/2).*pi.*sin(pi.*r/2);
phi2=((pi^2*sin(pi*r/2).^2)/2)-((cos(pi.*r/2).^2*pi^2)/2);
phi3=pi^3*sin(pi.*r/2).*cos(pi.*r/2);
phi4=((pi^4*cos(pi*r/2).^2)/2)-((pi^4*sin(pi*r/2).^2)/2);
%%
ws=zeros(1,n+1); %zeros matrix for ws
wprim=zeros(1,n+1);
V=0; %first voltage
zita=0.01; %Damping ratio=C/C(critical) %C(critical)=2*sqrt(k*m)
%% time option
T=1;
dt=0.01; %step time
t=0; %first time
y1=zeros(1,(T/dt)+1); y1=0;
y2=zeros(1,(T/dt)+1); y2=0;
%% loop
for i=1:vdc/dv
%% static
Tstr=((E*h)/2*R*(1-nu^2)).*sum((wprim.^2)*dr); %stretching force
betha1=Tstr.*(g^2*R)/D;
Fs=sum(((2*alpha.*V.*dv.*phi)./(1-ws).^2)*dr);
kelec=sum(((2*alpha.*V.^2.*phi.^2)./((1-ws).^3))*dr);
kmech=sum(((phi).*(phi4+(2./r).*phi3-((1./r.^2).*phi2)+((1./r.^3).*phi1)+...
(betha1.*(phi2+((1./r).*phi1))))).*dr);
keq=kmech-kelec;
as=Fs/keq;
psi=as*phi;
ws=ws+psi;
for j=1:n
wprim=(ws(j+1)-ws(j))/dr; %dw
end
V=V+dv;
wss(i)=ws(1);
VV(i)=V;
%% dynamic
m=sum((phi.^2)*dr);
k=sum(((phi).*(phi4+(2./r).*phi3-((1./r.^2).*phi2)+((1./r.^3).*phi1)+...
(betha1.*(phi2+((1./r).*phi1))))).*dr);
c=2*zita*sqrt(k*m);
end
%% runge kutta loop
for a=1:T/dt
% first
F=sum(((alpha.*(V.^2).*phi)./(1-(y1.*phi)).^2)*dr);
s1=y2;
p1=(1/m)*(F-(c*y2)-(k*y1));
% second
F=sum(((alpha.*(V.^2).*phi)./(1-((y1+(dt/2)*s1).*phi)).^2)*dr);
s2=y2+(dt/2)*p1;
p2=(1/m)*(F-(c*(y2+(dt/2)*p1))-(k*(y1+(dt/2)*s1)));
% third
F=sum(((alpha.*(V.^2).*phi)./(1-((y1+(dt/2)*s2).*phi)).^2)*dr);
s3=y2+(dt/2)*p2;
p3=(1/m)*(F-(c*(y2+(dt/2)*p2))-(k*(y1+(dt/2)*s2)));
% fourth
F=sum(((alpha.*(V.^2).*phi)./(1-((y1+(dt*s3)).*phi)).^2)*dr);
s4=y2+(dt*p3);
p4=(1/m)*(F-(c*(y2+(dt*p3)))-(k*(y1+(dt*s3))));
y1=y1+(dt/6)*(s1+(2*s2)+(2*s3)+s4);
y2=y2+(dt/6)*(p1+(2*p2)+(2*p3)+p4);
t=t+dt;
tt(a)=t;
y1(a)=y1;
y2(a)=y2;
end
%%
%plot(tt,y1.*phi)
%plot(tt,y2.*phi)
plot(y1.*phi,y2.*phi)
%plot(VV,1-wss)
grid on
1 comentario
Walter Roberson
el 4 de Feb. de 2021
for j=1:n
wprim=(ws(j+1)-ws(j))/dr; %dw
end
That overwrites all of wprim each iteration of the loop.
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