Question 4.8: Represent the ramp function shown in Figure 4.14 in terms of...
Represent the ramp function shown in Figure 4.14 in terms of Fourier series using MATLAB.
The MATLAB code for ramp function is written in the following parts:
Main module DOS4_2 calls MATLAB function ‘quad’. The function ‘quad’ numerically evaluates an integral using Simpson rule.
Function curve2 calculates the constant term a_{0}
Function curve2c calculates the a_{n} coefficients of cosine terms
Function curve2s calculates the b_{n} coefficients of sine terms
The Fourier representation of the ramp function with 15 terms is shown in Figure 4.15
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CODE DOS4_2 RAMP Function
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% Dynamics of Structures by Ashok K. Jain I. I. T. Roorkee
% DOS4_2
% Fourier representation of a periodic force: Ramp function
% Calls: curve2, curve2c and curve2s
% curve2c: cosine constants; curve2s: sine constants
% The program calls function “quad” to integrate and find Fourier constants
% N: total number of terms to be included
% T: period of periodic force
% P: Amplitude of periodic force
%
close all;
clear all;
clc;
P = 10;
T = 2;
fprintf(‘Amplitude of periodic force = %.3g N\n’,P);
fprintf(‘Period of force = %.3g sec\n’,T);
a0 = quad(@(t)curve2(t,T,P),0,T,1e-9);
for N=1:15
for n=1:N
a(n) = quad(@(t)curve2c(t,n,T,P),0,T,1e-9);
b(n) = quad(@(t)curve2s(t,n,T,P),0,T,1e-9);
end
Outp = 0;
x=1;
for t=0:0.05:T*4
c=0;
s=0;
for n=1:N
c=c+a(n)*cos(t*2*pi*n/T);
s=s+b(n)*sin(t*2*pi*n/T);
end
Outp(x)=s+c+a0;
x=x+1;
end
plot(0:0.05:T*4,Outp,’.-’)
pause(1);
end
grid on;
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CODE CURVE2
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% curve2
% Called by: DOS4_2
% Fourier representation of a periodic force: Ramp function
%
function a = curve2(t,T,P)
%
% Ramp function
%
w = 2*pi/T;
for d=1:length(t)
if t(d)<=T
p1(d) = t(d)*P/T;
else
p1(d) = 0;
end
end
a = (1/T)*p1;
end
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CODE CURVE2C
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% curve2c
% Called by: DOS4_2
% Fourier representation of a periodic force: Ramp function
% Computes constants for cosine terms
%
function a = curve2c(t,n,T,P)
w = 2*pi/T;
for d=1:length(t)
if t(d)<=T
p1(d) = t(d)*P/T;
else
p1(d) = 0;
end
end
a = (2/T)*p1.*cos(w*t*n);
end
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CODE CURVE2S
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% curve2s
% Called by: DOS4_2
% Fourier representation of a periodic force: Ramp function
% Computes constants for sine terms
%
function b = curve2s(t,n,T,P)
w = 2*pi/T;
for d=1:length(t)
if t(d)<=T
p1(d) = t(d)*P/T;
else
p1(d) = 0;
end
end
b = (2/T)*p1.*sin(w*t*n);
end