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%% function to calculate total suspension thermal noise depending on frequency % calling frequency, constants from list_constants.m %% funciton total_sus_therm function [total_sus_therm] = total_sus_therm(freq) list_constants; T = T_mir; % temperature m = M4; % mass suspension L = F_l; % length suspension rad1 = L4_rad1; %for 40kg %radius of thick section of fibre (to cancel thermoelastic) rad2 = L4_rad2; %for 40kg %radius of thin section of fibre Y = constants.Y; rho = constants.rho; C = constants.C; kB = constants.kB; kappa = constants.kappa; % thermal conductivity alpha = constants.alpha; % thermal expansion coefficient silica beta = constants.beta; % Young's modulus variation of silica (1/Y dY/dT) Iarea = pi.*rad1^4/4; % second moment of areafor bending region hphi_s=6.15e-12; % surface loss phi_weld=5.8e-7; % weld loss weld_energy=7e-2; % weld energy tension=(m/4).*9.81; % tension kl=m.*9.81/L; % longitudinal spring constant kv=Y.*pi.*(rad2)^2/L; % vertical spring constant wl=sqrt(9.81/L); % longitudinal w wv=sqrt(2).*sqrt(kv/(m/4)); % vertical w (sqrt(2) higher as both masses free, assumes masses identical=> need to change % violin mode (just fundamental mode) % mass per unit length mu=pi.*rad2^2.*rho; mass_fibre=mu.*L; speed=sqrt(tension/mu); fviolin1=(speed/(2.*L)); wviolin1=2.*pi.*fviolin1; %factor=0.5; % half dilution for bending at both ends %FEA=1/3; % factor to account for variation between analytical and FEA (about 1.8) %dilution_l=2.*L.*sqrt(tension/(Y.*Iarea)).*factor.*FEA % ideal dilution for longitudinal %dilution for L4=1.2m if val==0 dilution_l=91 else if m==40 dilution_l=269.1269*(L/1.2) %40kg %dilution_l=91; elseif m==60 dilution_l=217.7803*(L/1.2) %60kg elseif m==80 dilution_l=187.5951*(L/1.2) %80kg elseif m==100 dilution_l=166.6399*(L/1.2) %100kg elseif m==120 dilution_l=151.736*(L/1.2) %120kg elseif m==140 dilution_l=140.3183*(L/1.2) %140kg elseif m==160 dilution_l=139.6907*(L/1.2) %160kg elseif m==180 dilution_l=123.7676*(L/1.2) %180kg elseif m==200 dilution_l=117.6563*(L/1.2) %200kg end end cross_coupling=1/1000; % "dilution" for vertical => cross coupling of 0.1% dilution_violin=0.5.*L.*sqrt(tension/(Y.*Iarea)) % ideal dilution for violin (approximate solution, needs checking) % define frequency points freq=frequency; % freq = logspace(log10(fmin),log10(fmax),N); would be another interesting option omega=2.*pi.*freq; % assume idealistic loss and that all energy is stored in the 800um region phi_surf=(8.*hphi_s/(2.*rad1)); % phi surface phi_weld=(phi_weld).*weld_energy; % phi weld % phi thermoelastic tau1=1/(4.32.*pi).*rho.*C.*rad1^2/kappa; sigma1=tension/(pi.*(rad1)^2); val1=(Y.*T)/(rho.*C).*(alpha-sigma1.*(beta/Y))^2; %-------------------------------------------------------------------- n=length(freq) for j.html">j=1:n % phi thermoelastic phi_thermo=(omega(j.html">j)*tau1)/(1+(omega(j.html">j)*tau1)^2)*val1; % phi bulk phi_bulk=4.1e-12*freq(j.html">j)^0.77; % longitudinal loss phi_term_l=(phi_bulk+phi_thermo+phi_surf+phi_weld)/dilution_l; % vertical loss (no thermoelastic, surface/2) phi_term_v=(phi_bulk+phi_surf/2); % violin loss (2* undiluted longitudinal) phi_term_violin1=2*(phi_term_l*dilution_l)/dilution_violin; phi_total_l(j.html">j)=phi_term_l; phi_total_v(j.html">j)=phi_term_v; phi_total_violin1(j.html">j)=phi_term_violin1; phi_total_surf(j.html">j)=phi_surf; phi_total_bulk(j.html">j)=phi_bulk; phi_total_thermo(j.html">j)=phi_thermo; phi_total_weld(j.html">j)=phi_weld; % calculate longitudinal thermal displacement noise xthermal(j.html">j)=sqrt((4*kB*T*phi_total_l(j.html">j)*wl^2)/((m*omega(j.html">j))*((wl^2-omega(j.html">j)^2)^2+(phi_total_l(j.html">j)*wl^2)^2))); % calculate vertical thermal displacement noise zthermal(j.html">j)=cross_coupling*sqrt((4*kB*T*phi_total_v(j.html">j)*wv^2)/((m*omega(j.html">j))*((wv^2-omega(j.html">j)^2)^2+(phi_total_v(j.html">j)*wv^2)^2))); % calculate fundamental violin mode thermal displacement noise v1_thermal(j.html">j)=sqrt((8*kB*T*mass_fibre*phi_total_violin1(j.html">j)*wviolin1^2)/((pi^2*m^2*omega(j.html">j))*((wviolin1^2-omega(j.html">j)^2)^2+(phi_total_violin1(j.html">j)*wviolin1^2)^2))); total(j.html">j)=sqrt(xthermal(j.html">j)^2+zthermal(j.html">j)^2+v1_thermal(j.html">j)^2); total_sus_therm(j.html">j) = total(j.html">j); x_therm(j.html">j) = xthermal(j.html">j); z_therm(j.html">j) = zthermal(j.html">j); v_therm(j.html">j) = v1_thermal(j.html">j); end