Zigzag, armchair, and different types of chiral single-walled carbon nanotubes (SWCNTs) have distinct structures, due to different wrapping vectors of the underlying graphene sheets. The electronic properties depend on their structure, but this is less clear with regard to their mechanical properties. We modeled the first four flexural thermal vibrational modes of all three types with clamped ends, as a function of length. We applied a carefully equilibrated molecular dynamics procedure that was previously validated by comparison with the Timoshenko beam model in suitable limits. This analytic model allows for both rotary inertia and shearing deformation, but it cannot differentiate among the three atomistic structures. Comparison between the vibrational behavior of the three types of nanotubes clearly shows that the SWCNT structure does not affect the vibrational frequencies under clamped conditions.