Nonlinear Dynamics : міжнародна конференція

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Modelling and Nonlinear Dynamics of Third-Order Thermomechanically Coupled Laminated Plates
(NTU "KhPI", 2016) Saetta, Eduardo; Rega, Giuseppe
Thermomechanically coupled, geometrically nonlinear, laminated plates are addressed through a unified 2D formulation that integrates mechanical and thermal aspects and consistently accounts for cubic variations along the thickness of both in-plane displacement components and temperature. It allows to address a variety of thermal boundary conditions on the plate upper and lower surfaces. Minimal dimension reduction of the problem is pursued for symmetric cross-ply laminates. A numerical case study provides hints on the potential of the reduced model for the analysis of thermomechanical coupling effects on the system nonlinear dynamics.
Nonlinear dynamics of SWNTs. Energy beating and localization
(NTU "KhPI", 2016) Strozzi, Matteo; Manevitch, Leonid I.; Smirnov, Valeri V.; Pellicano, Francesco
In this paper, the nonlinear vibrations and energy exchange of single-walled carbon nanotubes (SWNTs) are investigated. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported boundary conditions are considered. The circumferential flexural modes (CFMs), radial breathing modes (RBMs) and beam-like modes (BLMs) are studied. A numerical model of the SWNT dynamics is proposed. The three displacement fields are expanded in the nonlinear field by using approximate linear eigenfunctions. An energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved using the implicit Runge-Kutta numerical method. The nonlinear energy exchange along the SWNT axis is analysed for different initial excitation amplitudes. The internal resonances between CFMs, RBMs and BLMs are investigated. The transition from energy beating to energy localization in the nonlinear field is studied.
Nonlinear Dynamics of Composite Plates and Shells
(NTU "KhPI", 2016) Kushnir, R. M.; Marchuk, M. V.
The equations of refined geometrically nonlinear theory of dynamic deformation of flexible with respect to transversal shear and compression ofplates and shells are proposed. The solutions for problems of transversal nonlinear vibrations of hinge fixedplate-strip are obtained. Numerical results are compared with the known in literature.
Semi-Inverse Method in the Nonlinear Dynamics
(NTU "KhPI", 2016) Manevitch, Leonid I.; Smirnov, Valeri V.
The semi-inverse method based on using an internal small parameter of the nonlinear problems is discussed on the examples of the chain of coupled pendula and of the forced pendulum. The efficiency of such approach is highly appeared when the non-stationary dynamical problems are considered. In the framework of this method we demonstrate that both the spectrum of nonlinear normal modes and the interaction of them can be analysed successfully.
Dynamics of Multielement Agricultural Aggregates, Taking Into Account Nonholonomic Constraints and Spatial Motion
(NTU "KhPI", 2016) Andreev, Yuri; Antoshchenkov, Roman
The paper studies a discrete system of multielement agricultural aggregate composed of a tractor, hopper and seeder. Mechanical model includes these elements, which are considered as rigid bodies and perform spatial motion subject to of the wheels considering elasticity. As the geometric constrains taking into account the flat surface of the earth and the hinges connecting the units. The aggregate is controlled by angle of the steering wheel or the angle between the tractor half-frames. A feature o f the model is the account of non-holonomic constraints caused by the rolling o f the wheels. This significantly reduces the number o f degrees o f freedom and also complicates the process of forming the equations o f motion. Differential equations are automatically generated by a special system of computer algebra KiDyM based on a general dynamics equation. The gravity force, the driving force and the resistance force applied to the elements o f the aggregate defined as force interactions. The studied linear motion, maneuvers with constant and harmonic law change o f control angle.