Fatieieva Y. Nonlinear dynamics of thin-walled structures made of functionally graded materials with variable in time parameters

This thesis is devoted to obtaining the approximate analytical solutions of nonlinear analysis of dynamic processes in functionally graded shallow shells (FGM) on the base of combination of perturbation, phase integrals and hybrid methods for nonlinear dynamics of imperfect FGM shell structures with variable in time parameters and influence of external dynamic and temperature loads. For some proposed solutions it is shown that discussed problems an approximate analytical approach on the basis of computer algebra gives a good enough correlation to analytical and numerical solutions. Comparison between direct numerical integration of governing equation with approximate analytical solution for nonhomogeneous linear and nonlinear problems are given. It is shown that analytical approach on the basis of hybrid asymptotic methods can be effective for solution of nonlinear differential equations with variable coefficients and different degree of nonlinearity. Solutions of nonlinear dynamic shallow shell with time dependent thickness and periodically external load are presented. An approximate analytical solution of nonlinear oscillations shallow spherical shell made of functionally graded materials with time depending thickness under external temperature and mechanical loading is discussed. The material properties of the shell are changing in thickness direction according to a power law distribution. The governing nonlinear differential equations with variable in time coefficients which describes the effect of temperature on the dynamic behavior of the shell is solved by hybrid asymptotic approach based on perturbation and phase integrals method (WKB). Comparison between results of numerical integration of the governing equation with the proposed approximate analytical solution are given.