dettimo1.m

利用matalab编制的转子动力学计算软件。其中模型利用有限元建模

function t0=dettimo(lambda,L,A,Gs,E,Iy,rho)
% t0=dettimo(lambda,L,A,Gs,E,Iy,rho)
%
%  eigenvalue equation for a free-free beam
      s1 = -pow(lambda,4.0)*pow(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*( ...
rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E...
*E+4.0*E*Gs*Gs*A)),2.0)*exp(sqrt(2.0)*L*(sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs...
+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*...
lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-sqrt(-E*Iy*Gs*(lambda*...
rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*...
lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda))/E/Iy/Gs)...
/16;
      s4 = pow(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)),2.0);
      s8 = sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(...
rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E...
*E+4.0*E*Gs*Gs*A))))*sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*...
rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*...
lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)*exp(-sqrt(2.0)*L*(3.0*sqrt(-E*Iy*Gs*lambda*...
(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*...
rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-sqrt(-E*Iy...
*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs...
-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda...
))/E/Iy/Gs/2);
      s10 = sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*...
(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*...
E*E+4.0*E*Gs*Gs*A))))*sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*...
rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*...
lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)*exp(-3.0/2.0*sqrt(2.0)*L*(sqrt(-E*Iy*Gs*...
lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs);
      s11 = lambda*lambda*E*E*Iy*Iy*Gs*rho*exp(-sqrt(2.0)*L*(3.0*sqrt(-E*Iy*Gs*...
lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs/2);
      s9 = s10+s11;
      s7 = s8+s9;
      s8 = s7-lambda*lambda*E*E*Iy*Iy*Gs*rho*exp(-3.0/2.0*sqrt(2.0)*L*(sqrt(-E*...
Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A))))-sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*...
lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*...
E*Gs*Gs*A)))*lambda))/E/Iy/Gs);
      s9 = s8;
      s11 = -lambda*lambda*E*Iy*Iy*Gs*Gs*rho*exp(-3.0/2.0*sqrt(2.0)*L*(sqrt(-E*...
Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A))))-sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*...
lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*...
E*Gs*Gs*A)))*lambda))/E/Iy/Gs);
      s12 = lambda*lambda*E*Iy*Iy*Gs*Gs*rho*exp(-sqrt(2.0)*L*(3.0*sqrt(-E*Iy*Gs...
*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs/2);
      s10 = s11+s12;
      s6 = s9+s10;
      s8 = s6-4.0*sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(...
Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*...
lambda*E*E+4.0*E*Gs*Gs*A))))*sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-...
sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*...
lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)*exp(-sqrt(2.0)*L*(sqrt(-E*Iy*Gs*...
lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs);
      s9 = s8;
      s11 = sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*...
(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*...
E*E+4.0*E*Gs*Gs*A))))*sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*...
rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*...
lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)*exp(-sqrt(2.0)*L*(sqrt(-E*Iy*Gs*lambda*(...
lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*...
rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-sqrt(-E*Iy...
*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs...
-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda...
))/E/Iy/Gs/2);
      s12 = sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*...
(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*...
E*E+4.0*E*Gs*Gs*A))))*sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*...
rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*...
lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)*exp(-sqrt(2.0)*L*(-3.0*sqrt(-E*Iy*Gs*(...
lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*...
rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)+...
sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*...
lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*...
E*Gs*Gs*A)))))/E/Iy/Gs/2);
      s10 = s11+s12;
      s7 = s9+s10;
      s8 = s7-lambda*lambda*E*Iy*Iy*Gs*Gs*rho*exp(-sqrt(2.0)*L*(sqrt(-E*Iy*Gs*...
lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs/2);
      s9 = s8+lambda*lambda*E*Iy*Iy*Gs*Gs*rho*exp(-sqrt(2.0)*L*(-3.0*sqrt(-E*Iy...
*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs...
-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda...
)+sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*...
lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*...
E*Gs*Gs*A)))))/E/Iy/Gs/2);
      s10 = s9;
      s12 = -lambda*lambda*E*E*Iy*Iy*Gs*rho*exp(-sqrt(2.0)*L*(sqrt(-E*Iy*Gs*...
lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*...
Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A))))-...
sqrt(-E*Iy*Gs*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*...
lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs...
*A)))*lambda))/E/Iy/Gs/2);
      s13 = lambda*lambda*E*E*Iy*Iy*Gs*rho*exp(-sqrt(2.0)*L*(-3.0*sqrt(-E*Iy*Gs...
*(lambda*rho*Iy*Gs+lambda*rho*Iy*E-sqrt(Iy*rho*(rho*Iy*lambda*lambda*Gs*Gs-2.0*...
rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*E*Gs*Gs*A)))*lambda)+...
sqrt(-E*Iy*Gs*lambda*(lambda*rho*Iy*Gs+lambda*rho*Iy*E+sqrt(Iy*rho*(rho*Iy*...
lambda*lambda*Gs*Gs-2.0*rho*Iy*lambda*lambda*Gs*E+rho*Iy*lambda*lambda*E*E+4.0*...
E*Gs*Gs*A)))))/E/Iy/Gs/2);
      s11 = s12+s13;
      s5 = s10+s11;
      s3 = s4*s5;
      s4 = 1/pow(E,6.0)/pow(Iy,6.0)/pow(Gs,6.0);
      s2 = s3*s4;
      t0 = s1*s2;