Nonlinear vibration analysis of laminated shallow shells with clamped cutouts by the R-functions method

In present work, an effective method to research geometrically nonlinear free vibrations of elements of thin-walled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is numerical–analytical. It is based on joint use of the R-functions theory, variational methods, Bubnov–Galerkin procedure and Runge–Kutta method. The mathematical formulation of the problem is performed in a framework of the refined first-order shallow shells theory. To implement the developed method, appropriate software was developed. New problems of linear and nonlinear vibrations of laminated shallow shells with clamped cutouts are solved. To confirm reliability of the obtained results, their comparison with the ones known in the literature is provided. Effect of boundary conditions is studied.