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.

Georgiev V.B., Ranavaya R.L., Krylov V.V. «Finite element and experimental modelling of structure-borne vehicle interior noise» Noise Theory and Practice (Электронный ресурс), 1, № 2, с. 10-26 (2015)

The present paper describes the results of the combined finite element and experimental approach to studying structure-borne vehicle interior noise using a simplified reduced-scale model of a car. The numerical investigation included finite element calculations of structural and acoustic modes as well as frequency response functions for interior acoustic pressure. Experimental tests included measurements of frequency response functions at driver’s and passenger’s ear positions, when an electromagnetic shaker exciting structural vibrations was located at different places. The effects of engine mass and of boot load on structure-borne interior noise have been investigated as well. Some of the obtained numerical results have been compared with the experimental ones. The obtained reasonably good agreement between them indicates that structure-borne interior noise in the vehicle model under consideration can be predicted and understood rather well. This implies that the proposed combined numerical and experimental approach to studying vehicle interior noise based on using reduced-scale structural models is simple and reliable, and it can be used successfully by noise and vibration engineers for prediction and mitigation of vehicle interior noise on a design stage.

Georgiev V.B., Krylov V.V. «Structural-acoustic properties of flexible rectangular boxes» Noise Theory and Practice (Электронный ресурс), 2, № 2, с. 2-18 (2016)

Rectangular box-like structures are used widely in a large number of engineering applications, e.g. as elements of railway carriages, heavy goods vehicles, buildings, civil engineering constructions, etc. Although flexible rectangular boxes represent one of the geometrically simple types of engineering structures, their structural-acoustic properties can not be described by closed-form analytical solutions. In the present study, a comprehensive numerical investigation of typical all-flexible rectangular box structures has been carried out to elucidate the physics of structural-acoustic interaction in them and to explore the possibilities of reduction of the associated structure-borne interior noise. Finite element method has been used to compute the resonant frequencies, the mode shapes and the structural-acoustic frequency response functions of different rectangular box models. The obtained results could assist in better understanding of structural-acoustic properties of flexible rectangular boxes as well as of numerous more complex structures using rectangular boxes as their building elements.