Waves mode summation for a string

Question

Andi 2022-1-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1633085-waves-mode-summation-for-a-string

评论： KSSV 2022-1-21

采纳的回答： KSSV

在 MATLAB Online 中打开

I required to computer code for mode summation for a string with a length of 20, wave velocity of 3.

Here is my attempt:

clear all
clc
xs=8; % source position 
v=3; % wave velocity
L=20; % length of string
ta=0.2; % tension of string
n=20; % number of nodes (we need to perform the summition for first 40 and 80 nodes. 
% here i fixed the nodes for the seek of simplicity)
t=1; % time after the spring plucked,
omga=n*pi*v/L;  % input source factor 
F=exp(-((omga*ta).^2)/4); % force 
x=0:0.01:20; % waves amplitude for distnace vary form 0 to 20
%x=x';
for i=1:length(x)
    u(i)=sin(n*pi*xs/L)*F*sin(n*pi*x(i)/L)*cos(omga*t);
end
plot(x,u)

The above script produce this plot for n=20

This script works perfectly to generate the wave for a single node value (above figure). I required to generate the waves for node values varies between 1 to 40. For this i modifiy teh script as follows:

clear all
clc
xs=8;
v=3;
L=20;
ta=0.2;
t=1;
n=1:1:40;
x=0:0.1:20;
for j=1:length(n)
    omga(j)=n(j)*pi*v/L;
    F(j)=exp(-((n(j)*pi*v*ta).^2)/4);
    for i=1:length(x)
        u(i)=sin(n(j)*pi*xs/L)*F(j)*sin(n(j)*pi*x(i)/L)*cos(omga(j)*t);
    end
end
plot(x,u)

This output produce a single line where i required to plot all (x,u) for n=1:40. along with a summiation plot of all the waves nodes (bold one in the attched figure)

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

KSSV 2022-1-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1633085-waves-mode-summation-for-a-string#answer_878770

在 MATLAB Online 中打开

xs=8;
v=3;
L=20;
ta=0.2;
t=1;
n=1:1:40;
x=0:0.1:20;
omga = zeros(1,length(n)) ; 
F = zeros(1,length(n)) ; 
u = zeros(length(n),length(x)) ; 
for j=1:length(n)
    omga(j)=n(j)*pi*v/L;
    F(j)=exp(-((n(j)*pi*v*ta).^2)/4);
    u(j,:)=sin(n(j)*pi*xs/L)*F(j)*sin(n(j)*pi*x/L)*cos(omga(j)*t);    % no loop needed
end
us = sum(u) ; 
plot(x,us)

2 个评论
显示无隐藏无

Andi 2022-1-21

The output (attached figure) of your proposed script is only valid for n=1.

Where the required output should be like this:

KSSV 2022-1-21

The code given by you is edited to get the sum. It is your job to check what you have missed in the code. The other mode number values are very less. You have to check your formula and the constant values given.

请先登录，再进行评论。