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  • ¸½¼þ 1 : clamped_coefficient.m
  • 2015-11-17 08:43:57, 1.84 K
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2Â¥2015-11-17 08:44:05
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  • ¸½¼þ 1 : clamped_coefficient.m
  • 2015-11-17 16:03:10, 1.95 K
3Â¥2015-11-17 16:03:17
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function [orthogonality, coefficient_all]=clamped_coefficient(c)
format long
clear all
G=8.0e10;
K=1.2;
E=2.06e11;
P=7.9e3;
l=4;
D=0.6;
H=0.2;
k=1/K;
I=D*(H^3)/12;
A=D*H;
              
figure;
coefficient_all = [];

r=sqrt(I/A);
s=sqrt(E*I/(k*A*G));
syms x ;
syms c;
frequency=[405.35308 1093.84137  2087.15447  3341.29751];

for ii=1:length(frequency)
  b=sqrt(P*A/(E*I))*frequency(ii);

  alfa=b*sqrt(-(r^2+s^2)+sqrt((r^2-s^2)^2+4./(b^2)))/sqrt(2);
  beta=b*sqrt(r^2+s^2+sqrt((r^2-s^2)^2+4./(b^2)))/sqrt(2);
  y=cosh(alfa*x)+(alfa*(beta^2-b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2)).*sinh(alfa*x)...,
      -cos(beta*x)-(beta*(alfa^2+b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2)).*sin(beta*x);
  y_int=int(y^2,0,l);

  fai=(alfa^2+b^2*s^2)/alfa*sinh(alfa*x)+(alfa*(beta^2-b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2))*(alfa^2+b^2*s^2)/alfa*cosh(alfa*x)...,
      -(b^2*s^2-beta^2)/beta*sin(beta*x)-(beta*(alfa^2+b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2))*(b^2*s^2-beta^2)/beta*cos(beta*x);
  fai_int=int(fai^2,0,l);

  orthogonality=c^2*y_int+c^2*r^2*fai_int-1/(P*A);
coefficient_result=solve(orthogonality,c) ;
coefficient_results=vpa(coefficient_result,6);
coefficient = abs(coefficient_results(1));
coefficient_all = [coefficient_all; coefficient];
x_shuzhi=0:0.01:4;
y_shuzhi=cosh(alfa.*x_shuzhi)+(alfa*(beta^2-b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2)).*sinh(alfa.*x_shuzhi)...,
      -cos(beta.*x_shuzhi)-(beta*(alfa^2+b^2*s^2)*(cos(beta*l)-cosh(alfa*l)))/((beta^2-b^2*s^2)*alfa*sinh(alfa*l)-beta*sin(beta*l)*(alfa^2+b^2*s^2)).*sin(beta.*x_shuzhi);
  
  hold on; h(ii) = plot(x_shuzhi,y_shuzhi);

end
5Â¥2015-11-17 16:15:45
ÒÑÔÄ   »Ø¸´´ËÂ¥   ¹Ø×¢TA ¸øTA·¢ÏûÏ¢ ËÍTAºì»¨ TAµÄ»ØÌû
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