[FlexPDE] Not sure if displacement equations are right

[unscientific]

Hi guys, I'm recently using FlexPDE to find the resonant frequencies of a torsional oscillator, but it does not match the analytic solution. It uses a Finite Element Method to find solutions.

Is there something wrong with the equations I'm using?

C11 = G*(1-nu)
C12 = G*nu
C13 = G*nu
C22 = G*(1-nu)
C23 = G*nu
C33 = G*(1-nu)
C44 = G*(1-2*nu)/2

Strains

ex = dx(U)
ey = dy(V)
ez = dz(W)
gxy = dy(U) + dx(V)
gyz = dz(V) + dy(W)
gzx = dx(W) + dz(U)

VARIABLES

U { X displacement }
V { Y displacement }
W { Z displacement }



Stresses

Sx = C11*ex + C12*ey + C13*ez
Sy = C12*ex + C22*ey + C23*ez
Sz = C13*ex + C23*ey + C33*ez
Txy = C44*gxy
Tyz = C44*gyz
Tzx = C44*gzx

EQUATIONS

U: dx(Sx) + dy(Txy) + dz(Tzx) + lambda*rho*U = 0 { the U-displacement equation }
V: dx(Txy) + dy(Sy) + dz(Tyz) + lambda*rho*V = 0 { the V-displacement equation }
W: dx(Tzx) + dy(Tyz) + dz(Sz) + lambda*rho*W = 0 { the W-displacement equation }

 

[NateD]

It is difficult to determine what might be wrong without seeing the entire model and the equations you are using. It may help to check that you are using the correct boundary conditions and initial conditions, as well as making sure that the values you are using for the material parameters are correct. Additionally, it could be useful to ensure that the mesh you are using is sufficiently refined to properly capture the resonant frequencies.