[Python] Python solver returns no values upon running the code

I need to calculate the vertical natural frequency and the horizontal natural frequency of a beam. In order to do this I have been given two values of the vertical and horizontal natural frequency which I need to approximate as closey as possible. Now in order to do this I have to use the moment of inertia in the y and z direction and the surface area. So the values that I need to calculate in this instance are the width(B), the height(H) and the thickness(t_h and t_v). For this I have used two solvers. The first one computes the values for B and H and the second one computes the values for t_h and t_v. Now the first solver works just fine and gives me numerical values. However, the second one somehow does not and only gives me []. Below I have put the code in that I have used. I cannot seem to understand what I am doing wrong in this code and I'm hoping that somebody can help me with his, because I have been at it for a couple of days and cannot seem to figure it out.

import numpy as np
from sympy import symbols, Eq, solve

w_2_vb_g=4.341
w_2_hb_g=2.601
E=210E9
rho=7700
L=100
kL_2=7.85
kL_3=11.00

B,H,t_h,t_v=symbols('B H t_h t_v', real=True, positive=True)
w_2_vb_rec=Eq(((((kL_2)**2)/(L**2))*(((E*((1/12)*H*B**3))/(rho*(B*H)))**(1/2))), w_2_vb_g)
w_2_hb_rec=Eq(((((kL_2)**2)/(L**2))*(((E*((1/12)*B*H**3))/(rho*(H*B)))**(1/2))), w_2_hb_g)
Solution=solve((w_2_hb_rec,w_2_vb_rec), (B,H))
print(Solution)

print("Solutions:")
for var, val in Solution.items():
print(f"{var}: {val}")

list_from_dict = list(Solution.items())
print("List from dict:", list_from_dict)

B=round(float(list_from_dict[1][1]*1.03),3)
H=round(float(list_from_dict[0][1]*1.03),3)

B_list=np.array([t_h, (H-2*t_h), B, t_v])
H_list=np.array([B, t_v, t_h, (H-2*t_h)])
D0_list=np.array([0, (0.5*B-0.5*t_v), (0.5*H-0.5*t_h),0])

w_2_vb=Eq(((((kL_2)**2)/(L**2))*(((E*(2*(((1/12)*B_list[0]*H_list[0]**3)+B_list[0]*H_list[0]*D0_list[0]**2)+2*(((1/12)*B_list[1]*H_list[1]**3)+B_list[1]*H_list[1]*D0_list[1]**2))/(rho*(((2*(B_list[0]*H_list[0])))+(2*(B_list[1]*H_list[1]))))**(1/2))))), w_2_vb_g)
w_2_hb=Eq(((((kL_2)**2)/(L**2))*(((E*(2*(((1/12)*B_list[2]*H_list[2]**3)+B_list[2]*H_list[2]*D0_list[2]**2)+2*(((1/12)*B_list[3]*H_list[3]**3)+B_list[3]*H_list[3]*D0_list[3]**2))/(rho*(((2*(H_list[2]*B_list[2])))+(2*(H_list[3]*H_list[3]))))**(1/2))))), w_2_hb_g)
Solution_beam=solve((w_2_hb,w_2_vb), (t_h,t_v))
print(Solution_beam)


Below You can see the output that my console gives:

{H: 0.279980237079456, B: 0.467279588297547}
Solutions:
H: 0.279980237079456
B: 0.467279588297547
List from dict: [(H, 0.279980237079456), (B, 0.467279588297547)]
[]


I have already tried different solver such as linsolve() or solve_undetermined_coeffs but neither has worked. This could be attributed to my code and that it doesn't work in this case but as far as I can see it should. I have also considered by splitting the equations in multiple parts so as to make it more comprehensive for the solver. However, this is not possible because I have not been given a starting value for the moment of inertia or the surface area which are the only two options in which it could've worked. Hopefully somebody can help, many thanks in advance!

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