I think that the natural frequencies are independent from boundary conditions but I found some papers which express that the natural frequencies vary with the boundary conditions.

Yes it is. Refer to Chopra's book for methods of evaluating the natural frequency

Boundary conditions have strong influence on natural frequencies. A beam when free-free, hinged, elastic supports or fixed will have different frequencies even though all other parameters may be same.

Yes, simply supported beam will have different frequencies than a clamped beam. Although the modes maybe same but the frequencies will not be the same with different boundary conditions.

:-) Of course it is! E.g the frequencies of vibration of the cantilever beam and simply supported remain in the ratio as 31/2/481/2=0,25 or the frequencies of vibration of the cantilever beam and on both sides, rigidly fixed remain in the ratio 31/2/1921/2=0,125.

Every dynamic system (beam, plate, shell, solid) has stiffness and mass properties. Mass introduces inertia due to kinetic energy (motion) and stiffness comes from potential energy, which is a function of boundary condition. Different boundary condition introduces different reactions (forces/moments) at the support, accordingly the stiffness of the vibrating system changes, mass being the same. So frequency (potential to kinetic) obviously changes.

yes, of course.

Thanks so much for your answers!!! 

I made a mistake comparing with the discrete vibration; whereas, the natural frequencies just depend on the equivalent mass and stiffness. 

Thank you so much Dear colleagues!! :)

@Samikkannu Raja. I would like to know more about this concept. could you please suggest book/article which explains the concept?

Boundary conditions greatly affect the natural frequency. If the BCs are not properly modeled, it can give totally wrong results compromising the analysis. Boundary conditions change the stiffness in a particular mode and hence the frequency.

One may note that Hamilton's principle not only provide us the governing equation of the system but also the the boundary conditions... So, yes, the BC affect the whole eigenvalue problem and hence the resonance conditions and the mode shapes... Thanks