铝板频散曲线（A0、S0）.rar_carbonpdm_overfem_导波频散曲线_能量 谱图_超声信号

function dispersion %绘制平板频散曲线 %tic clc;clear; cl=5850; %材料纵波波速（铝板） cs=3127; %材料横波波速（铝板） dfd=0.01*1e3; fd0=(0.01:dfd/1e3:20)*1e3; %频厚积（MHz*mm） d_lv=2.5; cps_min=0; cpa_min=0; cp_max=10000; mode=2; %绘制的模式数 precision=1e-8; cpa=zeros(length(fd0),mode); cps=zeros(length(fd0),mode); for i=1:length(fd0) fd=fd0(i); [cp12, n]=ss(cps_min,cp_max,fd,cl,cs,mode); for j=1:n cp1=cp12(j,1); cp2=cp12(j,2); cps(i,j)=serfen(cp1,cp2,fd,cl,cs,precision); end [cp12, n]=aa(cpa_min,cp_max,fd,cl,cs,mode); for j=1:n cp1=cp12(j,1); cp2=cp12(j,2); cpa(i,j)=aerfen(cp1,cp2,fd,cl,cs,precision); end end h=zeros(mode,2); %绘制相速度 figure(1) for j=1:2 if j==1 cp=cps; %对称 color='b'; else cp=cpa; %反对称 color='r'; end for i=1:mode cpp=cp(:,i); ind=find(cpp==0); if ~isempty(ind) h(i,j)=plot((fd0(ind(end)+1:end))/d_lv,cpp(ind(end)+1:end),color); else h(i,j)=plot(fd0/d_lv,cpp,color); end hold on end if j==2 xlabel('f/(KHz)') ylabel('C_{p}/(km?s^{-1})') title('5mm铝板 相速度频散曲线') set(gca,'xtick',(0:0.6:20)*1e3/d_lv,'xticklabel',(0:0.6:20)*1e3/d_lv) xlim([0, 1000]);% set(gca,'ylim',[0 cp_max],'ytick',(0:cp_max/1e3)*1e3,... 'yticklabel',0:cp_max/1e3) grid on hSGroup = hggroup;%要在子对象构建之后构建，构建后立即使用，否则将失效 hAGroup = hggroup; set(h(:,1),'parent',hSGroup) set(h(:,2),'parent',hAGroup) set(get(get(hSGroup,'Annotation'),'LegendInformation'),... 'IconDisplayStyle','on'); set(get(get(hAGroup,'Annotation'),'LegendInformation'),... 'IconDisplayStyle','on'); legend('对称模式','反对称模式') end end % %绘制群速度 % figure(2) % for j=1:2 % if j==1 % cp=cps; % color='b'; % else % cp=cpa; % color='r'; % end % for i=1:mode % cpp=cp(:,i); % ind=find(cpp==0); % if ~isempty(ind) % fd=fd0(ind(end)+1:end)'; % cpp=cpp(ind(end)+1:end); % else % fd=fd0'; % end % dcdf=diff(cpp)/dfd; %diff是二阶差分变换 % cg=cpp(1:end-1).^2./(cpp(1:end-1)-fd(1:end-1).*dcdf); % h(i,j)=plot(fd(1:end-1)/d_lv,cg,color); % hold on % end % if j==2 % xlabel('f/(KHz)') % ylabel('C_{g}/(km?s^{-1})') % title('5mm铝板 群速度频散曲线') % set(gca,'xtick',(0:0.6:20)*1e3/d_lv,'xticklabel',(0:0.6:20)*1e3/d_lv) % xlim([0, 1000]);% % set(gca,'ylim',[0 5.5]*1e3,'ytick',(0:0.5:5.5)*1e3,'yticklabel',0:0.5:5.5) % grid on % hSGroup = hggroup;%要在子对象构建之后构建，构建后立即使用，否则将失效 % hAGroup = hggroup; % set(h(:,1),'parent',hSGroup) % set(h(:,2),'parent',hAGroup) % set(get(get(hSGroup,'Annotation'),'LegendInformation'),... % 'IconDisplayStyle','on'); % set(get(get(hAGroup,'Annotation'),'LegendInformation'),... % 'IconDisplayStyle','on'); % legend('对称模式','反对称模式') % end % end % %toc end % % %对称模式 function [cp0, n]=ss(cp_min,cp_max,fd,cl,cs,mode) %确定方程解的区间 cp2=cp_min; deter=33; %步长 cp0=zeros(mode,2); n=0; while cp2<cp_max&&n<mode cp1=cp2; cp2=cp1+deter; y1=smode(cp1,fd,cl,cs); y2=smode(cp2,fd,cl,cs); while y1*y2>0&&cp2<cp_max cp1=cp2; cp2=cp1+deter; y1=smode(cp1,fd,cl,cs); y2=smode(cp2,fd,cl,cs); end if y1*y2<0 n=n+1; cp0(n,:)=[cp1 cp2]; else if y1==0&&y2~=0 n=n+1; cp0(n,:)=[cp1 cp1]; elseif y2==0&&y1~=0 n=n+1; cp0(n,:)=[cp2 cp2]; cp2=cp2+1; elseif y1==0&&y2==0 n=n+1; cp0(n,:)=[cp1 cp1]; n=n+1; cp0(n,:)=[cp2 cp2]; cp2=cp2+1; end end end end function fs=smode(cp,fd,cl,cs) p=abs(sqrt((cp/cs)^2-1)); q=abs(sqrt((cp/cl)^2-1)); if cp<=cs%p和q都是复数 fs=-4*p*q*sinh(pi*fd/cp*q)*cosh(pi*fd/cp*p)+(-p^2-1)^2*sinh(pi*fd/cp*p)*cosh(pi*fd/cp*q); elseif cp>cs&&cp<=cl%p是实数，q是复数 fs=-4*p*q*sinh(pi*fd/cp*q)*cos(pi*fd/cp*p)+(p^2-1)^2*sin(pi*fd/cp*p)*cosh(pi*fd/cp*q); else fs=4*p*q*sin(pi*fd/cp*q)*cos(pi*fd/cp*p)+(p^2-1)^2*sin(pi*fd/cp*p)*cos(pi*fd/cp*q); end end function cp=serfen(cp1,cp2,fd,cl,cs,precision) while cp2-cp1>precision y1=smode(cp1,fd,cl,cs); y2=smode(cp2,fd,cl,cs); cp0=(cp1+cp2)/2; y0=smode(cp0,fd,cl,cs); if y1*y0<0 cp2=cp0; elseif y2*y0<0 cp1=cp0; elseif y0==0 break elseif y1==0 cp2=cp1; break elseif y2==0 cp1=cp2; break end end cp=(cp2+cp1)/2; end %反对称模式 function [cp0 n]=aa(cp_min,cp_max,fd,cl,cs,mode) cp2=cp_min; deter=0.2; cp0=zeros(mode,2); n=0; while cp2<cp_max&&n<mode cp1=cp2; cp2=cp1+deter; y1=amode(cp1,fd,cl,cs); y2=amode(cp2,fd,cl,cs); while y1*y2>0&&cp2<cp_max cp1=cp2; cp2=cp1+deter; y1=amode(cp1,fd,cl,cs); y2=amode(cp2,fd,cl,cs); end if y1*y2<0 n=n+1; cp0(n,:)=[cp1 cp2]; else if y1==0&&y2~=0 n=n+1; cp0(n,:)=[cp1 cp1]; elseif y2==0&&y1~=0 n=n+1; cp0(n,:)=[cp2 cp2]; cp2=cp2+1; elseif y1==0&&y2==0 n=n+1; cp0(n,:)=[cp1 cp1]; n=n+1; cp0(n,:)=[cp2 cp2]; cp2=cp2+1; end end end end function fs=amode(cp,fd,cl,cs) p=abs(sqrt((cp/cs)^2-1)); q=abs(sqrt((cp/cl)^2-1)); if cp<=cs%p和q都是复数 fs=-4*p*q*sinh(pi*fd/cp*p)*cosh(pi*fd/cp*q)+(-p^2-1)^2*sinh(pi*fd/cp*q)*cosh(pi*fd/cp*p); elseif cp>cs&&cp<=cl%p是实数，q是复数 fs=4*p*q*sin(pi*fd/cp*p)*cosh(pi*fd/cp*q)+(p^2-1)^2*sinh(pi*fd/cp*q)*cos(pi*fd/cp*p); else fs=4*p*q*sin(pi*fd/cp*p)*cos(pi*fd/cp*q)+(p^2-1)^2*sin(pi*fd/cp*q)*cos(pi*fd/cp*p); end end function cp=aerfen(cp1,cp2,fd,cl,cs,precision) while cp2-cp1>precision y1=amode(cp1,fd,cl,cs); y2=amode(cp2,fd,cl,cs); cp0=(cp1+cp2)/2; y0=amode(cp0,fd,cl,cs); if y1*y0<0 cp2=cp0; elseif y2*y0<0 cp1=cp0; elseif y0==0 break elseif y1==0 cp2=cp1; break elseif y2==0 cp1=cp2; break end end cp=(cp2+cp1)/2; end