The dynamics of vortex gyration under spin-polarized current in a spin-torque nano-oscillator with axial symmetry violated by shape imperfection has been studied by micromagnetic modeling. We have considered the following kinds of shape: the displacement of the nanodisks centers, the pyramidal shape and the shape with several small cutouts. The corresponding frequency spectra of the vortex oscillations are presented. We found that shape imperfection can influence not only fundamental frequency but also can genarate second and higher harmonics. The impact of different types of shape on the vortex dynamics has been analyzed qualitatively. New ideas of microwave signal arising by artificial nonidealities of structure were proposed.