Why matlab doesn't execute my int() sym hiperbolic function?
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I need to integrate the terms of a matrix that are in hyperbolic functions, but matlab gives me the result as a function of the integral. In other words, it is not integrating the function. When I use trigonometric functions (sin, cos..), it integrates normally. Any suggestion?
The first case that doesn't work:
syms k_theta k_v GA_c L eta Omega xi a b alpha x EI real
f=(eta^sym(2)*(a^2 + b^2)^2*(b^2*xi*cos(a*(2*L - x))*cosh(b*x) - a^2*xi*cosh(b*(2*L - x))*cos(a*x) + a^2*xi*cos(a*x)*cosh(b*x) - b^2*xi*cos(a*x)*cosh(b*x) + L^2*Omega*a^4*cos(a*x)*cosh(b*x) + L^2*Omega*b^4*cos(a*x)*cosh(b*x) + a*b*xi*sin(a*(2*L - x))*sinh(b*x) + a*b*xi*sinh(b*(2*L - x))*sin(a*x) - L^2*Omega*a^4*cosh(b*(2*L - x))*cos(a*x) - L^2*Omega*b^4*cos(a*(2*L - x))*cosh(b*x) + 2*a*b*xi*sin(a*x)*sinh(b*x) + 2*L^2*Omega*a^2*b^2*cos(a*x)*cosh(b*x) - L^2*Omega*a*b^3*sin(a*(2*L - x))*sinh(b*x) + L^2*Omega*a*b^3*sinh(b*(2*L - x))*sin(a*x) - L^2*Omega*a^3*b*sin(a*(2*L - x))*sinh(b*x) + L^2*Omega*a^3*b*sinh(b*(2*L - x))*sin(a*x) - L^2*Omega*a^2*b^2*cos(a*(2*L - x))*cosh(b*x) - L^2*Omega*a^2*b^2*cosh(b*(2*L - x))*cos(a*x))^2)/(a^2*xi^sym(2) + b^2*xi^sym(2) - b^2*cos(2*L*a)*(Omega*L^2*a^2 + Omega*L^2*b^2 - xi)^2 + L^4*Omega^sym(2)*a^6 + L^4*Omega^sym(2)*b^6 - a^2*cosh(2*L*b)*(Omega*L^2*a^2 + Omega*L^2*b^2 + xi)^2 + 3*L^4*Omega^sym(2)*a^2*b^4 + 3*L^4*Omega^sym(2)*a^4*b^2 + 2*L^2*Omega*a^4*xi - 2*L^2*Omega*b^4*xi)^2;
K_b=sym(zeros(1,1));
K_b(1,1)=int(f,x,0,L)
The second case that does work:
syms k_theta k_v GA_c L eta Omega xi r_1 r_2 alpha x EI real
f=(EI*(eta*r_1^2*r_2^2*sin(L*r_1)*sin(L*r_2)*cos(r_1*x)*(Omega*L^2*r_1^2 + xi) - eta*r_1^3*r_2*cos(r_1*x)*(Omega*L^2*r_2^2 + xi) - eta*r_1^2*r_2^2*cos(L*r_1)*sin(L*r_2)*sin(r_1*x)*(Omega*L^2*r_1^2 + xi) - eta*r_1*r_2^3*cos(r_2*x)*(Omega*L^2*r_1^2 + xi) - eta*r_1^2*r_2^2*cos(L*r_2)*sin(L*r_1)*sin(r_2*x)*(Omega*L^2*r_2^2 + xi) + eta*r_1^2*r_2^2*sin(L*r_1)*sin(L*r_2)*cos(r_2*x)*(Omega*L^2*r_2^2 + xi) + eta*r_1*r_2^3*cos(L*r_1)*cos(L*r_2)*cos(r_2*x)*(Omega*L^2*r_1^2 + xi) + eta*r_1^3*r_2*cos(L*r_1)*cos(L*r_2)*cos(r_1*x)*(Omega*L^2*r_2^2 + xi) + eta*r_1*r_2^3*cos(L*r_1)*sin(L*r_2)*sin(r_2*x)*(Omega*L^2*r_1^2 + xi) + eta*r_1^3*r_2*cos(L*r_2)*sin(L*r_1)*sin(r_1*x)*(Omega*L^2*r_2^2 + xi))^2)/(2*r_1*r_2*xi^sym(2) - sin(L*r_1)*sin(L*r_2)*(L^4*Omega^sym(2)*r_1^4*r_2^2 + L^4*Omega^sym(2)*r_1^2*r_2^4 + 4*L^2*Omega*r_1^2*r_2^2*xi + r_1^2*xi^sym(2) + r_2^2*xi^sym(2)) + 2*L^4*Omega^sym(2)*r_1^3*r_2^3 + 2*L^2*Omega*r_1*r_2^3*xi + 2*L^2*Omega*r_1^3*r_2*xi - 2*r_1*r_2*cos(L*r_1)*cos(L*r_2)*(Omega*L^2*r_1^2 + xi)*(Omega*L^2*r_2^2 + xi))^2;
K_b=sym(zeros(1,1));
K_b(1,1)=int(f,x,0,L)
I understand that "f" are differents in both cases, but the script that generates each "f" is the same and I can't understand why matlab doesn't execute the first one.
Thanks in advance.
1 个评论
Walter Roberson
2023-11-17
MATLAB does not seem to be able to integrate this.
Maple is able to integrate it. After simplification of the long result it gives, the result becomes
cg = (-2 * a * (L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 - xi) * (b ^ 2) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) * L * (a ^ 2) * b * cosh((2 * L * b)) + (-(L ^ 2 * Omega * a ^ 4) / 2 + ((-3 * L ^ 2 * Omega * b ^ 2 + xi) * a ^ 2) / 2 - (b ^ 2 * (L ^ 2 * Omega * b ^ 2 + xi))) * sinh((2 * L * b)) / 2 - ((L ^ 2 * Omega * a ^ 4 + (2 * L ^ 2 * Omega * b ^ 2 + 3 * xi) * a ^ 2 + b ^ 2 * (L ^ 2 * Omega * b ^ 2 - xi)) * b * L) / 2) * cos((2 * L * a)) + (((L ^ 2 * Omega * a ^ 4) + (3 / 2 * (L ^ 2) * Omega * (b ^ 2) - xi) * (a ^ 2) + (b ^ 2 * (L ^ 2 * Omega * b ^ 2 + xi)) / 2) * sin((2 * L * a)) + (a * (L ^ 2 * Omega * a ^ 4 + (2 * L ^ 2 * Omega * b ^ 2 + xi) * a ^ 2 + b ^ 2 * (L ^ 2 * Omega * b ^ 2 - 3 * xi)) * L)) * (a ^ 2) * (L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) * b * cosh((2 * L * b)) - a * (L * a * (b ^ 2) * (a - b) * (a + b) * (L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 - xi) * (L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) * sin((2 * L * a)) - (L ^ 4 * Omega ^ 2 * a ^ 8) / 2 - (L ^ 2 * Omega * (L ^ 2 * Omega * b ^ 2 + 2 * xi) * a ^ 6) / 2 + (3 / 2 * (L ^ 4) * (b ^ 4) * (Omega ^ 2) - (2 * L ^ 2 * b ^ 2 * xi * Omega) - (xi ^ 2) / 2 * (a ^ 4) + (5 / 2 * (L ^ 4) * (Omega ^ 2) * (b ^ 6) - (L ^ 2 * Omega * b ^ 4 * xi) + (b ^ 2 * xi ^ 2) / 2) * (a ^ 2) + (L ^ 4 * Omega ^ 2 * b ^ 8) - (b ^ 4 * xi ^ 2)) * sinh((2 * L * b)) - ((L ^ 4 * Omega ^ 2 * a ^ 8) + 5 / 2 * (L ^ 4) * (Omega ^ 2) * (a ^ 6) * (b ^ 2) + (3 / 2 * (L ^ 4) * (b ^ 4) * (Omega ^ 2) + (L ^ 2 * b ^ 2 * xi * Omega) - (xi ^ 2)) * (a ^ 4) - (b ^ 2 * (L ^ 4 * b ^ 4 * Omega ^ 2 - 4 * L ^ 2 * b ^ 2 * xi * Omega - xi ^ 2) * a ^ 2) / 2 - (b ^ 4 * (L ^ 2 * Omega * b ^ 2 - xi) ^ 2) / 2) * b * sin((2 * L * a)) - (a ^ 5) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) ^ 2) * sinh((4 * L * b)) / 4 - b * ((b ^ 4) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * sin((4 * L * a)) / 4 + (a * (L ^ 4 * Omega ^ 2 * a ^ 8 + 2 * L ^ 2 * Omega * (L ^ 2 * Omega * b ^ 2 + xi) * a ^ 6 + (2 * L ^ 4 * b ^ 4 * Omega ^ 2 + 2 * L ^ 2 * b ^ 2 * xi * Omega + xi ^ 2) * a ^ 4 + 2 * (L ^ 4 * Omega ^ 2 * b ^ 6 - L ^ 2 * Omega * b ^ 4 * xi - 2 * b ^ 2 * xi ^ 2) * a ^ 2 + b ^ 4 * (L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * L))) * eta ^ 2 * ((a ^ 2 + b ^ 2) ^ 2) / a / b / (-(b ^ 4) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 - xi) ^ 4) * cos((2 * L * a)) ^ 2 / 2 - ((a ^ 2) * cosh((2 * L * b)) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) ^ 2) - ((L ^ 4 * a ^ 4 * Omega ^ 2 + 2 * L ^ 2 * Omega * (L ^ 2 * Omega * b ^ 2 + xi) * a ^ 2 + (L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * (a ^ 2 + b ^ 2))) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * (b ^ 2) * cos((2 * L * a)) + (a ^ 2) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) ^ 2) * (L ^ 4 * a ^ 4 * Omega ^ 2 + 2 * L ^ 2 * Omega * (L ^ 2 * Omega * b ^ 2 + xi) * a ^ 2 + (L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * (a ^ 2 + b ^ 2) * cosh((2 * L * b)) - (a ^ 4) * ((L ^ 2 * Omega * a ^ 2 + L ^ 2 * Omega * b ^ 2 + xi) ^ 4) * cosh((4 * L * b)) / 4 - 3 / 4 * (L ^ 8) * (Omega ^ 4) * (a ^ 12) + ((-4 * L ^ 8 * Omega ^ 4 * b ^ 2 - 3 * L ^ 6 * Omega ^ 3 * xi) * a ^ 10) + 9 * (-(L ^ 6 * Omega ^ 3 * b ^ 2 * xi) - (L ^ 8 * Omega ^ 4 * b ^ 4) - (L ^ 4 * Omega ^ 2 * xi ^ 2) / 2) * (a ^ 8) + ((-11 * L ^ 8 * Omega ^ 4 * b ^ 6 - 7 * L ^ 6 * Omega ^ 3 * b ^ 4 * xi - 7 * L ^ 4 * Omega ^ 2 * b ^ 2 * xi ^ 2 - 3 * L ^ 2 * Omega * xi ^ 3) * a ^ 6) + ((3 * L ^ 6 * b ^ 6 * xi * Omega ^ 3) - 7 / 2 * (L ^ 4) * (b ^ 4) * (xi ^ 2) * (Omega ^ 2) - (3 * L ^ 2 * b ^ 2 * xi ^ 3 * Omega) - 3 / 4 * (xi ^ 4) - 31 / 4 * (L ^ 8) * (b ^ 8) * (Omega ^ 4)) * (a ^ 4) - 3 * (b ^ 2) * ((L ^ 4 * b ^ 4 * Omega ^ 2) + (xi ^ 2) / 3) * ((L ^ 2 * Omega * b ^ 2 - xi) ^ 2) * (a ^ 2) - (b ^ 4 * (L ^ 2 * Omega * b ^ 2 - xi) ^ 4) / 2) / 4;
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