clear all; % constants f = linspace(1.25,4000,3200); roh = 2.3e3; % Density E = 2.6e10; % Young's modulus eta = 0.01; % loss factor h = 0.10; % thickness of the plate nue = 0.3; % Poisson's ratio lx = 2.8; ly = 2; x1 = 1.99; y1 = 1.27; x2 = x1; y2 = y1; w=(2*pi).*f; % max. frequency fmax=5000; %zeros of the gamma-functions yi = [7.8532 14.13716]; yj = [4.73004 10.9956]; groessef=size(f); Yf1z1zsummeges = zeros(1,groessef(2)); YMv1x1zsummeges = zeros(1,groessef(2)); YMv1y1zsummeges = zeros(1,groessef(2)); YfW1z1xsummeges = zeros(1,groessef(2)); YM1x1xsummeges = zeros(1,groessef(2)); YM1y1xsummeges = zeros(1,groessef(2)); YfW1z1ysummeges = zeros(1,groessef(2)); YM1x1ysummeges = zeros(1,groessef(2)); YM1y1ysummeges = zeros(1,groessef(2)); m = 1; n = 0; z = 0; %Zähler while (1) z = z + 1; if m == 0 Gx = 0; Hx = 0; Jx = 0; elseif m == 1 Gx = 1.506; Hx = 1.248; Jx = 5.017; else Gx = m+0.5; Hx = (m+0.5)^2*(1-4/((2*m+1)*pi)); Jx = (m+0.5)^2*(1+12/((2*m+1)*pi)); end if n == 0 Gy = 0; Hy = 0; Jy = 0; elseif n == 1 Gy = 1.506; Hy = 1.248; Jy = 5.017; else Gy = n+0.5; Hy = (n+0.5)^2*(1-4/((2*n+1)*pi)); Jy = (n+0.5)^2*(1+12/((2*n+1)*pi)); end qmn = sqrt(Gx^4+Gy^4*(lx/ly)^4+2*(lx/ly)^2*(nue*Hx*Hy+(1-nue)*Jx*Jy)); wmnr = sqrt(E*h^2/(12*roh*(1-nue^2)))*(pi/lx)^2*qmn; wmn(z) = wmnr*sqrt(1+j*eta); fmn(z) = wmn(z)/(2*pi); if m==0 phix1(z) = 1; phix1st(z) = 0; phix2(z) = 1; phix2st(z) = 0; else if m/2 == round(m/2); %Abfrage: m gerade Zahl ii = m/2; if ii > 2; yi(ii) = (4*ii+1)*pi/2; end kn = sin(0.5*yi(ii))/sinh(0.5*yi(ii)); phix1(z) = sqrt(2)*(sin(yi(ii)*(x1/lx-0.5))+kn*sinh(yi(ii)*(x1/lx-0.5))); %phi an der Stelle x1 phix1st(z) = sqrt(2)*(cos(yi(ii)*(x1/lx-0.5))*yi(ii)/lx+kn*cosh(yi(ii)*(x1/lx-0.5))*yi(ii)/lx); phix2(z) = sqrt(2)*(sin(yi(ii)*(x2/lx-0.5))+kn*sinh(yi(ii)*(x2/lx-0.5))); %phi an der Stelle x2 phix2st(z) = sqrt(2)*(cos(yi(ii)*(x2/lx-0.5))*yi(ii)/lx+kn*cosh(yi(ii)*(x2/lx-0.5))*yi(ii)/lx); else % n ungerade Zahl jj = (m+1)/2; if jj > 2; yj(jj) = (4*jj-1)*pi/2; end kn = -sin(0.5*yj(jj))/sinh(0.5*yj(jj)); phix1(z) = sqrt(2)*(cos(yj(jj)*(x1/lx-0.5))+kn*cosh(yj(jj)*(x1/lx-0.5))); phix1st(z) = sqrt(2)*(-sin(yj(jj)*(x1/lx-0.5))*yj(jj)/lx+kn*sinh(yj(jj)*(x1/lx-0.5))*yj(jj)/lx); phix2(z) = sqrt(2)*(cos(yj(jj)*(x2/lx-0.5))+kn*cosh(yj(jj)*(x2/lx-0.5))); phix2st(z) = sqrt(2)*(-sin(yj(jj)*(x2/lx-0.5))*yj(jj)/lx+kn*sinh(yj(jj)*(x2/lx-0.5))*yj(jj)/lx); end % der if Abfrage n gerade Zahl end if n == 0 phiy1(z) = 1; phiy1st(z) = 0; phiy2(z) = 1; phiy2st(z) = 0; else if n/2 == round(n/2); %Abfrage: n gerade Zahl ii = n/2; if ii > 2; yi(ii) = (4*ii+1)*pi/2; end kn = sin(0.5*yi(ii))/sinh(0.5*yi(ii)); phiy1(z) = sqrt(2)*(sin(yi(ii)*(y1/ly-0.5))+kn*sinh(yi(ii)*(y1/ly-0.5))); phiy1st(z) = sqrt(2)*(cos(yi(ii)*(y1/ly-0.5))*yi(ii)/ly+kn*cosh(yi(ii)*(y1/ly-0.5))*yi(ii)/ly); phiy2(z) = sqrt(2)*(sin(yi(ii)*(y2/ly-0.5))+kn*sinh(yi(ii)*(y2/ly-0.5))); phiy2st(z) = sqrt(2)*(cos(yi(ii)*(y2/ly-0.5))*yi(ii)/ly+kn*cosh(yi(ii)*(y2/ly-0.5))*yi(ii)/ly); else % m ungerade Zahl jj = (n+1)/2; if jj > 2; yj(jj) = (4*jj-1)*pi/2; end kn = -sin(0.5*yj(jj))/sinh(0.5*yj(jj)); phiy1(z) = sqrt(2)*(cos(yj(jj)*(y1/ly-0.5))+kn*cosh(yj(jj)*(y1/ly-0.5))); phiy1st(z) = sqrt(2)*(-sin(yj(jj)*(y1/ly-0.5))*yj(jj)/ly+kn*sinh(yj(jj)*(y1/ly-0.5))*yj(jj)/ly); phiy2(z) = sqrt(2)*(cos(yj(jj)*(y2/ly-0.5))+kn*cosh(yj(jj)*(y2/ly-0.5))); phiy2st(z) = sqrt(2)*(-sin(yj(jj)*(y2/ly-0.5))*yj(jj)/ly+kn*sinh(yj(jj)*(y2/ly-0.5))*yj(jj)/ly); end % der if Abfrage m gerade Zahl end psi1(z) = phix1(z)*phiy1(z); % psi an der Stelle 1 psi2(z) = phix2(z)*phiy2(z); % psi an der Stelle 2 psiX1(z) = phix1(z)*phiy1st(z); % psi x (m,n) an der Stelle 1 siehe (9.74) psiX2(z) = phix2(z)*phiy2st(z); % psi x (m,n) an der Stelle 2 psiY1(z) = -phix1st(z)*phiy1(z); % psi y (m,n) an der Stelle 1 psiY2(z) = -phix2st(z)*phiy2(z); % psi y (m,n) an der Stelle 2 Yf1z1zsumme(z,:) = psi1(z).*psi2(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YMv1x1zsumme(z,:) = psi2(z).*psiX1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YMv1y1zsumme(z,:) = psi2(z).*psiY1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YfW1z1xsumme(z,:) = psiX2(z).*psi1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YM1x1xsumme(z,:) = psiX2(z).*psiX1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YM1y1xsumme(z,:) = psiX2(z).*psiY1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YfW1z1ysumme(z,:) = psiY2(z).*psi1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YM1x1ysumme(z,:) = psiY2(z).*psiX1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); YM1y1ysumme(z,:) = psiY2(z).*psiY1(z)./(roh.*h.*lx.*ly.*(wmn(z).^2-w.^2)); Yf1z1zsummeges(1,:) = Yf1z1zsumme(z,:)+Yf1z1zsummeges(1,:); YMv1x1zsummeges(1,:) = YMv1x1zsumme(z,:)+YMv1x1zsummeges(1,:); YMv1y1zsummeges(1,:) = YMv1y1zsumme(z,:)+YMv1y1zsummeges(1,:); YfW1z1xsummeges(1,:) = YfW1z1xsumme(z,:)+YfW1z1xsummeges(1,:); YM1x1xsummeges(1,:) = YM1x1xsumme(z,:)+YM1x1xsummeges(1,:); YM1y1xsummeges(1,:) = YM1y1xsumme(z,:)+YM1y1xsummeges(1,:) ; YfW1z1ysummeges(1,:) = YfW1z1ysumme(z,:)+YfW1z1ysummeges(1,:); YM1x1ysummeges(1,:) = YM1x1ysumme(z,:)+YM1x1ysummeges(1,:) ; YM1y1ysummeges(1,:) = YM1y1ysumme(z,:)+YM1y1ysummeges(1,:); if (fmn(z) < fmax) m = m + 1; elseif (m > 0) n = n + 1; m = 0; z = z - 1; else break; end end YfRFree1z1z = abs(Yf1z1zsummeges(1,:).*j.*w); %YW,Fz YMvRFree1x1z = abs(YMv1x1zsummeges(1,:).*j.*w); %YW,Mx YMvRFree1y1z = abs(YMv1y1zsummeges(1,:).*j.*w); %YW,My YfWRFree1z1x = abs(YfW1z1xsummeges(1,:).*j.*w); %Y?x,Fz YMRFree1x1x = abs(YM1x1xsummeges(1,:).*j.*w); %Y?x,Mx YMRFree1y1x = abs(YM1y1xsummeges(1,:) .*j.*w); %Y?x,My YfWRFree1z1y = abs(YfW1z1ysummeges(1,:).*j.*w); %Y?y,Fz YMRFree1x1y = abs(YM1x1ysummeges(1,:) .*j.*w); %Y?y,Mx YMRFree1y1y = abs(YM1y1ysummeges(1,:).*j.*w); %Y?y,My loglog(f,YfRFree1z1z) grid on;