Is it correct to account generalized forces in determining natural frequencies of different rigid bodies of railway vehicle coach in Lagrangian formulation? or the generalized forces are not to be accounted in determining natural frequencies?
You have to keep in mind that the natural frequencies are evaluated with the following equation ma+cv+kx=0. In a simplified way ma+kx=0. Therefore, the external forces are not considered.
You have to keep in mind that the natural frequencies are evaluated with the following equation ma+cv+kx=0. In a simplified way ma+kx=0. Therefore, the external forces are not considered.
Hi,
Dr. Gomez is completely right. The natural frequencies are the solution to an eigenvalue problem and the eigenvalue problem is based on the homogeneous partial differential equation ma + cv + kx = 0. Here, m denotes the mass matrix, k the stiffness matrix and c the damping matirx. a is the accelleration, v the velocity and x the displacement. The circular frequency omega is related to the frequency f by
omega = 2*pi*f
In the following the damping will be neglected. The solution is obtained by assuming that the displacements follow an harmonic motion
x = Amp*sin(omega*t),
v = -Amp*omega^2*sin(omega*t).
Now you can substitute this into the partial differential equation
Amp*(k-omega^2*m)*sin(omega*t) = 0.
This equation only holds when:
det(k-omega^2*m) = 0.
The solutions omega^2 are called eigenvalues and the natural frequencies are computed by
f = sqrt(omega^2)/(2*pi).
Best regards,
Sascha
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