Hi 

I work a lot on the Newmark method. 

The Newmark method can be used to solve structural dynamics problems in the time domain, of the form:

M (d^2x/dt^2) + C dx/dt + K x = F

This method performs direct integration on the mass, damping and stiffness matrices which may be fully-coupled.

Here is a Matlab script of the Newmark method with some examples.

I hope that I helped you, let us know if you have another questions or you need more details.

Best regards

Bonjour Aicha tu peux commencer par lire le livre A.K Chopra DYNAMICS OF STRUCTURES, je suis entrain de développer un programme MATLAB qui utilise la méthode Newmark beta pour une structure a plusieurs degrés de liberté

Hello Aicha you can take a look a A.K Chopra book titled DYNAMICS OF STRUCTURES actualley i'm develloping a Newmark Beta methode for calculation MDOF structures in Matlab

for more information you can contact me

best regards

Thank you, I'll start with 

Mes Remerciements, 

Try the program, If you need help pls let me know.

Bon courage!

function[At,V,D]=newm2(xm,hvec,s,beta,z,dt,ndev)

%newmark beta for MDOF

%xm: mass matrix

%hvec: each floor damping [h(n);h(n-1);...]

%s: stiffness matrix

%beta

%z: ground acceleration

%dt: time interval

%ndev: time interval division

siz=length(z);

nsiz=length(xm);

a(:,1)=zeros(nsiz,1)-z(1,1);

v(:,1)=zeros(nsiz,1);

d(:,1)=zeros(nsiz,1);

sa=zeros(nsiz,1);

sv=zeros(nsiz,1);

sd=zeros(nsiz,1);

temp=inv(xm)*s;

[vec,ei]=eig(temp);

h=zeros(nsiz,nsiz);

h=h+diag(hvec);

c=2*h*sqrt(ei)*xm;

for j=2:length(z)

dz=z(j,1)-z(j-1,1);

ddt=dt/ndev;

ddz=dz/ndev;

for k=1:ndev

% Newmark beta integration

ap=-xm*eye(nsiz,1)*ddz+xm*(v/(beta*ddt)+a/(2*beta))+c*(v/(2*beta)+(.25/beta-1)*a*ddt);

ak=s+c/(2*beta*ddt)+1/(beta*ddt*ddt)*xm;

dd=inv(ak)*ap;

dv=dd/(2*beta*ddt)-v/(2*beta)-(0.25/beta-1)*a*ddt;

da=dd/(beta*ddt*ddt)-v/(beta*ddt)-a/(2*beta);

%=============================

zz=z(j)+ddz*k;

d=d+dd;

v=v+dv;

a=a+da;

aa=a+zz;

At((j-1)*ndev+k,:)=aa';

D((j-1)*ndev+k,:)=d';

V((j-1)*ndev+k,:)=v';

end

end

Hi 

I work a lot on the Newmark method. 

The Newmark method can be used to solve structural dynamics problems in the time domain, of the form:

M (d^2x/dt^2) + C dx/dt + K x = F

This method performs direct integration on the mass, damping and stiffness matrices which may be fully-coupled.

Here is a Matlab script of the Newmark method with some examples.

I hope that I helped you, let us know if you have another questions or you need more details.

Best regards

Dear Ahmed and Ali,

I am working on Newmark's method and I am confused because I solved a problem from Prof. Naeem's book for verification of my matlab code but the answers are different.

So I tried the other codes for Newmark's method but each code made a totally different output (For example Ahmeds attached code). 

I used your code for the problem but the answer is different with the code that is suggested with Prof. Naeem. So I will be thankfull if you can help me to clarify the problem. 

I attached the My matlab code for newmark beta method and also the problem mass, stiffness, damping and load matrix that could be used in your code. 

The correct code and solution is also attached which is proposed with professor Naeem.

Please use datas.m for P load to use Ahmeds code because the code requires 2 column for P load (time,value).

In my code, I used P_hat=P(t+dt)+etc. but Prof. Naeem used dP in each step and I don't know the reason.

Best regards.