Numerical analysis of thin cylindrical shell vibrations with a weak nonlinearity

In this paper, nonlinear vibrations of an infinite thin cylindrical shell as a limiting case nanotube are studied. The main relations Sanders-Koiter’s theory and the Hamilton variation principle applied to obtain mathematical model allow fully accounting for influence effects. Using method multiple scales with specification fast slow times, high-order asymptotic taking into account quadratic cubic nonlinearities found. Based on solution scheme at fourth order application inextensibility condition semi-membrane theory, numerical analysis tangential radial displacements leading relative Fourier coefficients is conducted. impact wave number, polar angle, radius, wall thickness amplitude period arising investigated. Numerical illustrations obtained solutions presented several cases.