Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory
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Дата
2015
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
Elsevier Inc.
Анотація
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.
Опис
Ключові слова
laminated shallow shells, R-functions theory, Ritz’s method, Bubnov-Galerkin method, frequencies, differential equations
Бібліографічний опис
Awrejcewicz J. Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory / J. Awrejcewicz, L. Kurpa, T. Shmatko // Composite Structures. – 2015. – Vol. 125. – P. 575-585.