Wave Propogation Anti-symmetric and Symmetric mode propogation
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Hi all,
I'm working on quite some time to improve the code which I've written for better visualization of A0 mode. In my code everything looks good even I'm able to track the properties of the wave like out-of-plane and in-plane displacement but it is only evident and observable only at the extreme edges of the x (defined window). I'm attaching my code below. Any idea will be greatly appreciated. I'm also attaching the link of reference video which I'm trying to achieve or atleast anything close to it.
"freq = 2.5; %% KHz
Cpasym = 2.8953; %%phase velocity
d = 1; %% thickness of AL plate
Cl = 6.350; %% longitudnal velocity in the Al
Ct = 3.130; %% transverse velocity in the AL
zrange = -0.5:0.01:0.5;
shape = zeros(length(zrange),3);
for i = 1:length(zrange)
z = zrange(i);
shape(i,1) = z;
%% Mode shape in plane
Uasym = (2*pi*freq/Cpasym)*((sinh(sqrt(1/Cpasym^2-1/Cl^2)*2*pi*freq*z)/cosh(sqrt(1/Cpasym^2-1/Cl^2)*2*pi*freq*0.5*d))-(2*((2*pi*freq)^2*(1/Cpasym^2-1/Cl^2)^0.5*(1/Cpasym^2-1/Ct^2)^0.5)/((2/Cpasym^2-1/Ct^2)*(2*pi*freq)^2))*(sinh(sqrt(1/Cpasym^2-1/Ct^2)*2*pi*freq*z)/cosh(sqrt(1/Cpasym^2-1/Ct^2)*2*pi*freq*0.5*d)));
%% Mode shape out of plane
Wasym = (sqrt(1/Cpasym^2-1/Cl^2)*2*pi*freq)*((cosh(sqrt(1/Cpasym^2-1/Cl^2)*2*pi*freq*z)/cosh(sqrt(1/Cpasym^2-1/Cl^2)*2*pi*freq*0.5*d))-(2*(2*pi*freq/Cpasym)^2/((2/Cpasym^2-1/Ct^2)*(2*pi*freq)^2))*(cosh(sqrt(1/Cpasym^2-1/Ct^2)*2*pi*freq*z)/cosh(sqrt(1/Cpasym^2-1/Ct^2)*2*pi*freq*0.5*d)));
shape(i,2) = real(Uasym);
shape(i,3) = real(Wasym);
end
%% Normalizing the Mode shape
shape(:,2) = shape(:,2)/max(abs(shape(:,2)));
shape(:,3) = shape(:,3)/max(abs(shape(:,3)));
tvec = 0:0.01:10;
xvec = 0:0.01:9.5;
[X, Z] = meshgrid(xvec, zrange);
UAsym3D = zeros(length(zrange),length(xvec), length(tvec));
WAsym3D = zeros(length(zrange),length(xvec), length(tvec));
%% propogation governing equation
for i = 1:length(tvec)
for k = 1:length(xvec)
%for j = 1:length(zrange)
Ux = shape(:,2).*sin((2*pi*freq/Cpasym)*xvec(k)-(2*pi*freq*tvec(i)));
UAsym3D(:,k,i) = Ux;
Wz = shape(:,3).*cos((2*pi*freq/Cpasym)*xvec(k)-(2*pi*freq*tvec(i)));
WAsym3D(:,k,i) = Wz;
%end
end
end
% Normalize to [-1, 1]
UAsym3DN = UAsym3D / (max(abs(UAsym3D(:))));
WAsym3DN = WAsym3D / (max(abs(WAsym3D(:))));
% Create a VideoWriter object
videoFile = 'wave_motionAsym.avi'; % Output file name
writerObj = VideoWriter(videoFile , 'Motion JPEG AVI');
writerObj.FrameRate = 7; % Frames per second
open(writerObj);
hFig = figure('units','normalized','outerposition',[0 0 1 1]);
axis tight manual;
set(gca, 'NextPlot', 'replacechildren');
xlabel('x');
ylabel('z');
title('Resultant Displacement Anti-symmetric(A0) mode');
colormap(jet);
numTimeSteps = size(UAsym3DN, 3);
frames(numTimeSteps) = struct('cdata',[],'colormap',[]);
% Loop through each time step and create frames
for t = 1:size(UAsym3DN, 3)
% Get displacement at current time step
X_new = X + UAsym3DN(:,:, t); % Extract displacement at time t
Z_new = Z+ WAsym3DN(:,:, t); % Extract displacement at time t
scatter(X_new(:), Z_new(:), 5, 'filled');
%quiver(X(:), Z(:), Usym3DN(:,:, t),Wsym3DN(:,:, t), 'k','LineWidth',1);
xlabel('x'); ylabel('z');
axis([min(xvec)-1 max(xvec)+1 min(zrange)-1 max(zrange)+1]);
axis equal;
grid on;
drawnow;
pause(0.002);
frame = getframe(gcf);
frames(t) = frame;
writeVideo(writerObj, frame);
end
% Close the VideoWriter object
close(writerObj);
disp(['Movie saved as ', videoFile]);
implay('wave_motionAsym.avi');"
