matlab直接刚度法计算结构频率
syms E I K r l x c
ja1=-E*I*K*r^3*(cos(x)*sinh(x)+sin(x)*cosh(x))
jc1=-E*I*K*r^2*sin(x)*sinh(x)
je1=E*I*K*r*(cos(x)*sinh(x)-sin(x)*cosh(x))
je2=4*E*I*K*r*(cos(0.7825*x*2)*sinh(0.7825*x*2)-sin(0.7825*x*2)*cosh(
0.7825*x*2))
jf2=4*E*I*K*r*(sin(0.7825*x*2)-sinh(0.7825*x*2))
A=[ja1 -jc1;-jc1 je1+je2+jf2]
B=det(A)
simplify(B)
B=-E^2*I^2*K^2*r^4*(cos(x)^2*cosh(x)^2 +
4*sin((313*x)/200)*cos(x)*sinh(x) +
4*sin((313*x)/200)*cosh(x)*sin(x) -
4*sinh((313*x)/200)*cos(x)*sinh(x) -
4*sinh((313*x)/200)*cosh(x)*sin(x) +
4*cos((313*x)/200)*sinh((313*x)/200)*cos(x)*sinh(x) +
4*cos((313*x)/200)*sinh((313*x)/200)*cosh(x)*sin(x) -
4*cosh((313*x)/200)*sin((313*x)/200)*cos(x)*sinh(x) -
4*cosh((313*x)/200)*sin((313*x)/200)*cosh(x)*sin(x) - 1)
ezplot x-x , grid on , hold on
ezplot('(cos(x)^2*cosh(x)^2 + 4*sin((313*x)/200)*cos(x)*sinh(x) +
4*sin((313*x)/200)*cosh(x)*sin(x) -
4*sinh((313*x)/200)*cos(x)*sinh(x) -
4*sinh((313*x)/200)*cosh(x)*sin(x) +
4*cos((313*x)/200)*sinh((313*x)/200)*cos(x)*sinh(x) +
4*cos((313*x)/200)*sinh((313*x)/200)*cosh(x)*sin(x) -
4*cosh((313*x)/200)*sin((313*x)/200)*cos(x)*sinh(x) -
4*cosh((313*x)/200)*sin((313*x)/200)*cosh(x)*sin(x) - 1)')
%得到零点x=5.4994476为解
%(2)
%正对称
syms l t x;
v1=1-cos(pi*x/(2*l))
v2=sin(pi*x/(2*l))
v3=v1
d2v1=diff(v1,x,2)
d2v2=diff(v2,x,2)
d2v3=diff(v3,x,2)
A=int((d2v1)^2,x,0,l)+4*int((d2v2)^2,x,0,2*l)+int((d2v3)^
2,x,0,l)
%反对称
syms l t x
v1=1-cos(pi*x/(2*l))
v2=sin(2*pi*x/(2*l))
v3=-v1
d2v1=diff(v1,x,2)
d2v2=diff(v2,x,2)
d2v3=diff(v3,x,2)
A=int((d2v1)^2,x,0,l)+4*int((d2v2)^2,x,0,2*l)+int((d2v3)^
2,x,0,l)
B=(0.5*(1-cos(pi/4))^2*2+1*(1-cos(pi/2))^2*2+1.5*sin(pi/2
))*m*l