Kseniia Riabova

Bio: Kseniia Riabova is an academic researcher from University of Parma. The author has contributed to research in topics: Boundary value problem & Masonry. The author has an hindex of 6, co-authored 13 publications receiving 182 citations.

Stability of Non-Linear Vibrations of Doubly Curved Shallow Shells

Abstract: Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular boundary, simply supported at the four edges and subjected to harmonicexcitation normal to the surface in the spectral neighbourhood 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 different 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 geometricimperfections are taken into account. The solution is obtained by Lagrangian approach. The non-linear equations of motion are studied by using (i) a code based on arclengthcontinuation 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.

Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum

Abstract: This study deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to reduce oscillations. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. From the analytical/numerical simulations, we derive some important conclusions, providing us with the tools suitable for the design of absorbers in practical cases.

Vibration Analysis for Monitoring of Ancient Tie-Rods

Abstract: This paper presents an application of vibration analysis to the monitoring of tie-rods. An algorithm for the axial load estimation based on experimentally measured natural frequencies is introduced and its application to a case study is reported. The proposed model of a tie-rod incorporates elastic bed-type boundary conditions that represent the contact between stonework and the tie-rod. The weighed differences between experimentally and numerically determined frequencies are minimized with respect to the parameters of the model, the main being the axial load and the stiffness at the tie-rod/wall interface. Thus, the multidimensional optimization problem is solved. Results are analysed in comparison to a model with simple fixed-end boundary conditions. In addition, the analytical formulation of the problem is delivered.

Dynamical Assessment of the Work Conditions of Reinforcement Tie-Rods in Historical Masonry Structures

Abstract: Tie-rods are essential structural elements, which have been employed for centuries in masonry historical buildings, either during the construction or in successive strengthening interventions, with the aim of containing dangerous horizontal actions. The actual work conditions of these tie-rods, which are strongly influenced by their load history, are difficult to be quantified theoretically, and an effective method for their measure is of great importance in order to ensure the efficiency of these elements during the time and the stability of the entire building. Common measurements are often carried out adopting models based upon significant simplifications, like, for example, hinges at the extremities. These assumptions, rarely represent the real work conditions for anchorages. In this work, a non-destructive testing method is presented, based upon sophisticated dynamical models that can take into consideration many of the circumstances neglected by the simplified models. Four case studies are e...

Nonlinear Vibrations and Stability of Shells and Plates

Abstract: Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

Closure of "Rocking of Rigid Blocks Due to Harmonic Shaking"

Abstract: The dynamic behavior of rigid-block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no-toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady-state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid-block structure under a given amplitude-frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.

Non-linear vibrations of shells: A literature review from 2003 to 2013

Abstract: The present literature review focuses on geometrically non-linear free and forced vibrations of shells made of traditional and advanced materials. Flat and imperfect plates and membranes are excluded. Closed shells and curved panels made of isotropic, laminated composite, piezoelectric, functionally graded and hyperelastic materials are reviewed and great attention is given to non-linear vibrations of shells subjected to normal and in-plane excitations. Theoretical, numerical and experimental studies dealing with particular dynamical problems involving parametric vibrations, stability, dynamic buckling, non-stationary vibrations and chaotic vibrations are also addressed. Moreover, several original aspects of non-linear vibrations of shells and panels, including (i) fluid–structure interactions, (ii) geometric imperfections, (iii) effect of geometry and boundary conditions, (iv) thermal loads, (v) electrical loads and (vi) reduced-order models and their accuracy including perturbation techniques, proper orthogonal decomposition, non-linear normal modes and meshless methods are reviewed in depth.

Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials

Abstract: This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.