From 1e3bebb178b80d0c84f905ee724082f18201c93a Mon Sep 17 00:00:00 2001 From: "E. Cheynet" Date: Thu, 14 May 2020 16:48:28 +0200 Subject: [PATCH] Add files via upload --- CentDiff.m | 44 ++++++++++++++++++++++++++ Documentation.mlx | Bin 0 -> 187558 bytes NExT.m | 78 ++++++++++++++++++++++++++++++++++++++++++++++ RDT.m | 50 +++++++++++++++++++++++++++++ expoFit.m | 30 ++++++++++++++++++ 5 files changed, 202 insertions(+) create mode 100644 CentDiff.m create mode 100644 Documentation.mlx create mode 100644 NExT.m create mode 100644 RDT.m create mode 100644 expoFit.m diff --git a/CentDiff.m b/CentDiff.m new file mode 100644 index 0000000..96083dd --- /dev/null +++ b/CentDiff.m @@ -0,0 +1,44 @@ +function [y] = CentDiff(F,M,K,C,dt,x0,v0) +% [y] = CentDiff(F,M,K,C,dt,x0,v0)solves numerically the equation of motion +% of a damped system +% +% +% INPUT +% F : vector -- size: [1x N] -- Time series representinf the time history of the load. +% M : scalar -- size: [1 x 1] -- Modal mass +% K : scalar -- size: [1 x 1] -- Modal stifness +% C : scalar -- size: [1 x 1] -- Modal damping +% dt : scalar -- size: [1 x 1] -- time step +% x0 : scalar -- size: [1 x 1] -- initial displacement +% v0 : scalar -- size: [1 x 1] -- initial velocity +% +% OUTPUT +% y: time history of the system response to the load +% +% author: E. Cheynet - UiB - last updated: 14-05-2020 +% + +%% +% Initialisation +N = size(F,2); +% preallocation +y = zeros(size(F)); + +% initial acceleration +a0 = M\(F(1)-C.*v0-K.*x0); +% initialisation of y (first 2 values). +y0 = x0-dt.*v0+dt^2/2*a0; +y(:,1) = x0; +A = (M./dt.^2+C./(2*dt)); +B = ((2*M./dt.^2-K).*y(:,1)+(C./(2*dt)-M./dt.^2).*y0+F(:,1)); +y(:,2) = A\B; + +% For the rest of integration points +for ii=2:N-1 + A = (M./dt.^2+C./(2*dt)); + B = ((2*M./dt.^2-K).*y(:,ii)+(C./(2*dt)-M./dt.^2).*y(:,ii-1)+F(:,ii)); + y(:,ii+1) = A\B; +end + +end + diff --git a/Documentation.mlx b/Documentation.mlx new file mode 100644 index 0000000000000000000000000000000000000000..e5dac7132c23b6507c787991761b178678ff92fc GIT binary patch literal 187558 zcmV)fK&8J>O9KQH000080I_?nPc}3N+dlwJ9_Cwt0^3qzDA2fW{iks7irIt+rvCS;Z919Pi`^}8^f8hDR+4Hy?zcP(pv zv4@z^ue>~87xsMNGUDPn1j=Y7wk@qD?{9eYO~T5BXPvYazCl~t{&C4X5zPVP7h1V%w;4NAVp zz}a#!f5r|d_JpQ&fklW3k~c)|UWiaNs3Bz5p^23@>orh3`dT=sHc+D|^ZZu$QwC3& 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zrY0+Z)|ehT8SdDXW|;O7ui-W?UG0zoqk>^QdaPfloOeTyt9Ia*+K>*nBL@rT&o0n{9dYe>-+ z4rl^f;!M~RriLRlm4a~*HR>&S| z=jn>Bz~4*$13>t-d%$Q26F|3)4IuxQlCg;Y9{}nJbMyQ+^Z(RA{6YBNipNZ2{)^C*Xeo D;{JjV literal 0 HcmV?d00001 diff --git a/NExT.m b/NExT.m new file mode 100644 index 0000000..2b5d835 --- /dev/null +++ b/NExT.m @@ -0,0 +1,78 @@ +function [R,t] = NExT(y,dt,Ts,method) +% +% [R] = NExT(y,ys,T,dt) implements the Natural Excitation Technique to +% retrieve the free-decay response (R) from the cross-correlation +% of the measured output y. +% +% +% Synthax +% +% [R] = NExT(y,dt,Ts,1) calculates R with cross-correlation +% calculated by using the inverse fast fourier transform of the +% cross-spectral power densities without zero-padding(method = 1). +% +% [R] = NExT(y,dt,Ts,2) calculate the R with cross-correlation +% calculated by using the unbiased cross-covariance function (method = 2) +% +% Input +% y: time series of ambient vibrations: vector of size [1xN] +% dt : Time step +% method: 1 or 2 for the computation of cross-correlation functions +% T: Duration of subsegments (TN + y=y'; + [Nyy,N]=size(y); +end + +% get the maximal segment length fixed by T +M = round(Ts/dt); +switch method + case 1 + clear R + for ii=1:Nyy + for jj=1:Nyy + y1 = fft(y(ii,:)); + y2 = fft(y(jj,:)); + h0 = ifft(y1.*conj(y2)); + R(ii,jj,:) = h0(1:M); + end + end + % get time vector t associated to the R + t = linspace(0,dt.*(size(R,3)-1),size(R,3)); + if Nyy==1 + R = squeeze(R)'; % if Nyy=1 + end + case 2 + R = zeros(Nyy,Nyy,M+1); + for ii=1:Nyy + for jj=1:Nyy + [dummy,lag]=xcov(y(ii,:),y(jj,:),M,'unbiased'); + R(ii,jj,:) = dummy(end-round(numel(dummy)/2)+1:end); + end + end + if Nyy==1 + R = squeeze(R)'; % if Nyy=1 + end + % get time vector t associated to the R + t = dt.*lag(end-round(numel(lag)/2)+1:end); +end +% normalize the R +if Nyy==1 +R = R./R(1); +else +end + diff --git a/RDT.m b/RDT.m new file mode 100644 index 0000000..8fc2073 --- /dev/null +++ b/RDT.m @@ -0,0 +1,50 @@ +function [R,t] = RDT(y,ys,T,dt) +% +% [R] = RDT(y,ys,T,dt) returns the free-decay response (R) by +% using the random decrement technique (RDT) to the time serie y, with a +% triggering value ys, and for a duration T +% +% INPUT: +% y: time series of ambient vibrations: vector of size [1xN] +% dt : Time step +% ys: triggering values (ys < max(abs(y)) and here ys~=0) +% T: Duration of subsegments (T=dt*(numel(y)-1) + error('Error: subsegment length is too large'); +else + % number of time step per block + nT = round(T/dt); % sec +end + +if ys==0 + error('Error: ys must be different from zero') +elseif or(ys >=max(y),ys <=min(y)), + error('Error: ys must verifiy : min(y) < ys < max(y)') +else + % find triggering value + ind=find(diff(y(1:end-nT)>ys)~=0)+1; + +end + +% construction of decay vibration +R = zeros(numel(ind),nT); +for ii=1:numel(ind) + R(ii,:)=y(ind(ii):ind(ii)+nT-1); +end + +% averaging to remove the random part +R = mean(R); +% normalize the R +R = R./R(1); +% time vector corresponding to the R +t = linspace(0,T,numel(R)); +end + diff --git a/expoFit.m b/expoFit.m new file mode 100644 index 0000000..e1b8588 --- /dev/null +++ b/expoFit.m @@ -0,0 +1,30 @@ +function [zeta] = expoFit(y,t,wn,optionPlot) +% [zeta] = expoFit(y,t,wn) returns the damping ratio calcualted by fitting +% an exponential decay to the envelop of the free-decay response. +% +% Input: +% y: envelop of the free-decay response: vector of size [1 x N] +% t: time vector [ 1 x N] +% wn: target eigen frequencies (rad/Hz) : [1 x 1] +% optionPlot: 1 to plot the fitted function, and 0 not to plot it. +% +% Output +% zeta: modal damping ratio: [1 x 1] +% +% author: E. Cheynet - UiB - last updated: 14-05-2020 +% + +%% +% Initialisation +guess = [1,1e-2]; +% simple exponentiald ecay function +myFun = @(a,x) a(1).*exp(-a(2).*x); +% application of nlinfit function +coeff = nlinfit(t,y,myFun,guess); +% modal damping ratio: +zeta = abs(coeff(2)./wn); + +% alternatively: plot the fitted function +if optionPlot== 1, plot(t,myFun(coeff,t),'r'); end +end +