vibration of a rod using spectral element method

Question

Foil 2021-3-14

0
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https://ww2.mathworks.cn/matlabcentral/answers/772373-vibration-of-a-rod-using-spectral-element-method

评论： Foil 2021-3-14

Hi, everyone

I want to simulate the wave propagation in a rod with one side clamped, and another side experience a step force of duration 0.01s, as shown below. I have tried to write the matlab code but it didn’t work well. I have been puzzled by this problem for a long time. For the matlab code, it will be greatly appreciated if you could share some suggestions with me.

dt=0.0002; % time increment
N=5000;  % sample points 
tp=N*dt; % total time
t=0:dt:tp; % time discretization
F=1000e3*(stepfun(t,0)-stepfun(t,0.01)); % force duration= 0.01s
f=1/dt; % maximum frequency
fre=0:f/N:f;  % frequency discretization 
y=fft(F);  % FFT amplitude
A=0.01; % area
E=2.1e11; % Young’s modulus
rho=7850; % density
l=10;  % length
k=fre*2*pi*(rho/E)^0.5;  % wave number
u2f=y.*tan(k*l)./(E*A*k);  % displacement in frequency domain % solved by u1=y/k11
u2=ifft(u2f) % displacement in time domain