Budnikov N. Investigation of forced geometrically nonlinear vibrations of laminated shallow shells and plates using R-functions theory

The thesis is devoted to the development of numerical-analytically method for solving nonlinear vibration problems of laminated shallow shells and plates with complex geometric shapes at their geometrically nonlinear deformation using multimode approximation. Previously a similar approach to study the nonlinear free vibration of laminated shallow shells using the single-mode approximation was proposed. According to the proposed method the initial system of differential equations of motion of the shell which containing the partial derivatives is reduced to a system of ordinary differential equations on time. The expressions for the coefficients of the re-sulting system are obtained in analytical form. Solving the system is carried out by the Runge-Kutta method. So-lutions of auxiliary problems are obtained by variation-structural method. Considering the complex boundary region made using the R-functions theory. Testing of the developed software is completed, new problems of vi-bration of laminated shallow shells with complex shape plan are solved. Amplitude-frequency and resonance curves have been build.