Кафедри
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/35393
Переглянути
2 результатів
Результати пошуку
Документ Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory(Elsevier Inc., 2015) Awrejcewicz, Jan; Kurpa, Lidiya; Shmatko, T.A novel numerical/analytical approach to study geometrically nonlinear vibrations of shells with variable thickness of layers is proposed. It enables investigation of shallow shells with complex forms and different boundary conditions. The proposed method combines application of the R-functions theory, variational Ritz’s method, as well as hybrid Bubnov–Galerkin method and the fourth-order Runge–Kutta method. Mainly two approaches, classical and first-order shear deformation theories of shells are used. An original scheme of discretization regarding time reduces the initial problem to the solution of a sequence of linear problems including those related to linear vibrations with a special type of elasticity, as well as problems governed by non-linear system of ordinary differential equations. The proposed method is validated by the investigation of test problems for shallow shells with rectangular planform and applied to new vibration problems for shallow shells with complex planforms and variable thickness of layers.Документ Geometrical analysis of vibrations of functionally graded shell panels using the R-functions theory(London Calling, 2017) Shmatko, T.; Kurpa, Lidiya; Bhaskar, AtulAn approach for investigation of geometrically nonlinear vibrations of functionally graded shallow shells and plates with complex planform is proposed. It combines the application of the R-functions theory (RFM), variational Ritz’s method, the procedure by Bubnov-Galerkin and Runge-Kutta method. The presented method is developed in the framework of the first–order shear deformation shallow shell theory (FSDT). Shell panels under consideration are made from a mixture of ceramics and metal. Power law of volume fraction distribution of materials through thickness is chosen. Investigation of nonlinear vibrations of functionally graded shallow shells and plates with arbitrary planform and different types of boundary conditions is carried out. Test problems and numerical results have been presented for one-mode approximation in time. Effect of volume fraction exponent, geometry of a shape and boundary conditions on the natural frequencies is brought out.