Forced and Damped Rotary-Symmetric Vibrations of a Conoidal Shell Made of Nonlinearly Elastic Compressible Material.

Analysis of the forced and damped rotary-symmetric vibrations of conoidal shell having cut apex boeing, freely supported on the both wedges and made of homogeneous, isotropic nonlinearly elastic and compressible material is presented. Assuming small vibrations it is possible to apply linear geometrical vibrations. The obtained system of two nonlinear partial differential equations of the fourth order is reduced by means of the Bubnov-Galerkin method to the ordinary differential equations which by turn are solved by the small parameter method with an accuracy of the second approximation. The solutions obtained illustrating the influence of the elastic nonlinearity on the vibrations of shell are presented in a form of diagrams.