1D Newmark Using Matlab

Hi,

I am trying to solve example 5.1 in dynamic structure book by Anil K.Chopra page 168. But, I have a problem with the Matlab coding. Following are my coding:-

clc

m=0.2533;
k=10;
c=0.1592;
gam = 1/2 ;beta = 1/6 ;

%Initial Calculation
po=0;
u0=0;
udot0=0;
u2dot1 = 1/m*(po-k*u0-c*udot0);

% Time step
ti = 0. ;
tf = 4. ;
dt = 0.1 ;
t = ti:dt:tf ;
nt = fix((tf-ti)/dt) ;

kcap = k + gam/(beta*dt)*c + m/(beta*dt^2);
a = m/(beta*dt) + gam*c/beta;
b = 0.5*m/beta + dt*(0.5*gam/beta - 1)*c;
dp = diff(p);

for i = 1:nt
    deltaP = dp(i) + a*udot(i) + b*u2dot(i);
    du_i = deltaP/kcap;
    dudot_i = gam/(beta*dt)*du_i - gam/beta*udot(i) + dt*(1-0.5*gam/beta)*u2dot(i);
    du2dot_i = 1/(beta*dt^2)*du_i - 1/(beta*dt)*udot(i) - 0.5/beta*u2dot(i);
    u(i+1) = du_i + u(i);
    udot(i+1) = dudot_i + udot(i);
    u2dot(i+1) = du2dot_i + u2dot(i);
end

When i run the coding this warning appear

Undefined function or variable 'p'.
Error in (line 25)
dp = diff(p);

Why it happen and how to solve the problem?

Thank you.

[nur yusof]

Sorry.Attached the print screen of the question.

The example must be solved by using Newmark method. Given dt=0.1, m=0.2533, k=10, c=0.1592, u0=0,u0dot=0,p0=0 Hope anyone can help out.

[Chaudhary P Patel]

@nur yusof can you share the solution of this problem?

Answer 1

[Walter Roberson]

Poking around it appears likely that you are referring to "Dynamics of Structures: Theory and Application to Earthquake Engineering" by Anil K. Chopra, chapter 5, 5.1 Time-Stepping Methods . However you have not indicated which edition, with 4 known numbered editions, and with one named "International Edition". Or perhaps you are referring to "Dynamics of Structures: A Primer" by Anil K. Chopra, or to "Earthquake Dynamics of Structures: A Primer" by Anil K. Chopra and Barbara Zeiders.

The first of those has the most supporting evidence, but the edition matters because there might have been an error that got corrected in later versions.

Or if they do not give code in the book, then the error is in your introduction of p without defining it.

Have you considered using the implementation in the File Exchange ?

Answer 2

[Yasin]

Hello. I am looking at the code & the book you mentioned right now.

It seems that you didn't introduce the P function, which is:

P=10*sin((pi*t)/0.6))

Add the P function right under the u2dot line.