Obrotowo-symetryczne drgania własne powłoki stożkowej z materiału ściśliwego nieliniowo sprężystego

The paper deals with the analysis of rotationally free vibrations of a thin truncated conical shell, simply supported on both edges. The material of the shell is assumed to be homogeneous, isotropic, non-linear elastic and compressible. The problem is limited to the analysis of small vibrations what makes it possible to use the linear geometric relations. As a result, the system of partial differential equations of fourth order is obtained describing the longitudinal and transverse vibrations. By applying the variational Bubnov-Galerkin method, partial equations are reduced to the ordinary differential equations. Assuming weak non-linearity, the equations are then solved by the perturbation method, the solution being limited only to second approximation. The equations obtained describing the influence of elastic non-linearity of the material on the vibrations of the shell have been presented graphically.