Can anybody help me to implement caughey's equivalent linearization method for bilinear structure in MATLAB? I am not able to get the ductility(x/x0) vs frequency ratio(w/ws) plot.

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VAIBHAV PUJARI 2021-3-5

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https://ww2.mathworks.cn/matlabcentral/answers/763601-can-anybody-help-me-to-implement-caughey-s-equivalent-linearization-method-for-bilinear-structure-in

评论： VAIBHAV PUJARI 2021-3-7

These are some images from "Passive control of bilinear hysteretic structures by tuned mass damper

for narrow band seismic motions" Z. Zhang, T. Balendra.

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VAIBHAV PUJARI 2021-3-6

在 MATLAB Online 中打开

clc
clear all
result=zeros(1,300);
x_ax=(0:0.01:3);
aa=0; 
ws=sqrt(2.85e9/1.8e7); ms=1.8e7; k0=2.85e9; c0=0.015*2*sqrt(ms*k0); n=0.3; nu=0.02; x00=0.02; A=0.1*9.81;
ws=sqrt(2.85e9/1.8e7);
for w=x_ax*ws
% for w=ws
    aa=aa+1;
    x0=[1 1];
    [sol, fval]=fminunc(@(x)response(x,w, ms,k0,c0,n,nu,x00,A),x0);
    result(1,aa)=fval;
    ductility=result/x00;  
end
plot(x_ax,ductility,'r-*')
function DMF=response(x,w, ms,k0,c0,n,nu,x00,A)
wd=x(1,1); zid=x(1,2);
% ws=sqrt(2.85e9/1.8e7); ms=1.8e7; k0=2.85e9; c0=0.015*2*sqrt(ms*k0); n=0.3; nu=0.02; x00=0.02; A=0.1*9.81;
% ms=1.8e7; k0=2.85e6; c0=0.015*2*sqrt(ms*k0); n=0.3; nu=0.02; x00=0.02e-3; A=0.1;
md=nu*ms; kd=md*wd^2; cd=zid*2*md*wd;
    ke=k0; ce=c0; we=sqrt(ke/ms); zie=(ce/(2*ms*we));
    Z=md*(wd^2+2*1i*zid*wd*w)/(wd^2-w^2+2*1i*zid*wd*w);
    H=(ms+Z)/(ms*(we^2-w^2++2*1i*zie*we*w)-w^2*Z);     % should be multiplied by A*w^2
    RE=real(1/H);
    IM=imag(1/H);
    DMF=(1/sqrt(RE^2+IM^2))*ms*A/ke;
    tita=acos(1-2*x00/(DMF));    %%% Mistake: for inelastic, value of elastic DMF is being used 
                                            % see equation of ke, tita is
                                            % used
    if DMF<=x00
         disp('elastic')
        DMF
        
    else
        disp('inelastic')
        ke=(k0/pi)*((1-n)*tita+n*pi-0.5*(1-n)*sin(2*tita));
        we=sqrt(ke/ms);
        ce=c0+((k0/(pi*we))*(sin(tita))^2);
        zie=(ce/(2*ms*we));
        Z=md*(wd^2+2*1i*zid*wd*w)/(wd^2-w^2+2*1i*zid*wd*w);
        H=(ms+Z)/(ms*(we^2-w^2+2*1i*zie*we*w)-w^2*Z);   % should be multiplied by A*w^2
        RE=real(1/H); IM=imag(1/H);
        DMF=(1/sqrt(RE^2+IM^2))*ms*A/ke;
    end
end

darova 2021-3-7

It's too complicated for me. Sorry, can't help

VAIBHAV PUJARI 2021-3-7

ok.. Thanks.

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Can anybody help me to implement caughey's equivalent linearization method for bilinear structure in MATLAB? I am not able to get the ductility(x/x0) vs frequency ratio(w/ws) plot.

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Can anybody help me to implement caughey's equivalent linearization method for bilinear structure in MATLAB? I am not able to get the ductility(x/x0) vs frequency ratio(w/ws) plot.

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