Vasilyev A.V., Maffei L. «International experience of advanced education in built environment acoustics» Защита от повышенного шума и вибрации: Сборник докладов III всероссийской научно-практической конференции с международным участием, 22–24 марта 2011 г., СПб, с. 678-686 (2011)

Rafat A., Rahman M.M., Alam M.S., Mamun A.A. «Effects of nonextensivity on the electron-acoustic solitary structures in a magnetized electron-positron-ion plasma» Физика плазмы, 42, № 8, с. 768-774 (2016)

DOI: 10.7868/S0367292116080096

Mukharlyamov R.G., Amabili M., Garziera R., Riabova K. «Stability of non-linear vibrations of doubly curved shallow shells» Вестник Российского университета дружбы народов (РУДН). Серии Математика. Информатика. Физика, № 2, с. 53-63 (2016)

Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular boundary, simply supported at the four edges and subjected to harmonic excitation normal to the surface in the spectral neighborhood of the fundamental mode are subject of investigation in this paper. The first part of the study was presented by the authors in [M. Amabili et al. Nonlinear Vibrations of Doubly Curved Shallow Shells. Herald of Kazan Technological University, 2015, 18(6), 158-163, in Russian]. Two di?erent non-linear strain-displacement relationships, from the Donnell’s and Novozhilov’s shell theories, are used to calculate the elastic strain energy. In-plane inertia and geometric imperfections are taken into account. The solution is obtained by Lagrange approach. The non-linear equations of motion are studied by using (i) a code based on arc length continuation method that allows bifurcation analysis and (ii) direct time integration. Numerical results are compared to those available in the literature and convergence of the solution is shown. Interaction of modes having integer ratio between their natural frequencies, giving rise to internal resonances, is discussed. Shell stability under dynamic load is also investigated by using continuation method, bifurcation diagram from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension. Interesting phenomena such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations and (iv) chaotic behavior have been observed.