Nonlinear Dynamics : міжнародна конференція

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Nonlinear Vibrations of Rotors in Systems with Magnetic Bearings
(NTU "KhPI", 2016) Martynenko, Gennadii Yu.
A method is suggested for building mathematical models of dynamics of rotors in magnetic bearings of different types (passive and active ones). It is based on Lagrange-Maxwell differential equations in a form identical to that of Routh equations in mechanics. The main distinguishing feature of the model is the possibility to account for the following: the nonlinear dependence of magnetic forces on gaps between movable and stationary parts in PMBs and AMBs, and on currents in the windings of AMB electromagnets; current delay in the windings of AMB electromagnets, i. e. nonlinearity linked to the inductance of the coils; the geometric links between the electromagnets of one AMB and the links between all AMB of one rotor, which results in coupling of processes in orthogonal directions; practically any AMB control law; limitations on the control current caused by physical constraints in the control system controller; dissipation fluxes as well as magnetic resistances of AMB magnetic core sections, making the mathematical model insensitive as regards origination of "nonzero" gaps and currents. Numerical analysis has been performed for one of the possible variants of a complete rotor magnetic suspension realised in the form of the laboratory model. It includes two radial passive magnetic bearings with permanent annular magnets and one axial active magnetic bearing with a stator in the form of a shell core. Modelling validity is confirmed by comparing analytical and experimental data. Analysis of linear and nonlinear rotor dynamics phenomena observed in the laboratory model with magnetic bearings is described. It is known that analysis based on linearised models allows judging only the stability of equilibrium states with small deflections. The negligible nonlinear equation terms in this case, when investigating motion with increasing deflection, allow expanding the information content of the mathematical model about nonlinear effects occurring in the system. Estimated results revealed shortcomings of the linearised models. Based on this conclusion the need of using nonlinear models for adequate description of the dynamics of such systems is proved.
Method of Determination of Natural Frequencies and Forms of Nonlinear Vibrations for Layered Cylindrical Panels
(NTU "KhPI", 2016) Marchuk, M. V.; Goriachko, T. V.; Pakosh, V. S.; Lesyk, O. F.
The technique of finding a finite number of first natural frequencies for geometrically nonlinear vibrations of layered elongated cylindrical panels at discrete consideration of components is proposed and verified. The influence of the radius of curvature on the natural frequencies of three- and five-layered panels is investigated. The dependence between the volume of filler three-layer panels and the lowest natural frequency has been established.
Application of the R-Functions Theory to Problems of Nonlinear Dynamics of Laminated Composite Shallow Shells and Plates: Review
(NTU "KhPI", 2016) Kurpa, Lidiya
A review of studies performed using the R-functions theory to solve problems of nonlinear dynamics of plates and shallow shells is presented. The systematization of results and studies for the problems of free and parametric vibrations and for problems of static and dynamic stability is fulfilled. Expansion of the developed original method of discretization for nonlinear movement equations on new classes of nonlinear problems is shown. These problems include researches of vibrations of antisymmetric laminated cylindrical and spherical panels; laminated composite shallow shells with variable thicknesss of the layers; functionally graded (FG) shallow shells and others. The basic issues that arise when using RFM are described. The future prospects of using the theory of R-functions for solving problems of nonlinear dynamics of plates and shallow shells with complex form are formulated. First of all this is an algorithms development and creation of the associated software to apply multi-modes approximations; improvement of approximation tools for nonlinear problems; investigation of the cracked functionally graded shallow shells; FG panels under thermal environments; parametric vibrations, static and dynamical stability of the multilayered and FG plates and shells.
Nonlinear Effects in Rolling Mills Dynamics
(NTU "KhPI", 2016) Krot, Pavel V.; Korennoy, Vladimir V.
This paper intends to describe nonlinear effects occurring in rolling mills dynamics. That is necessarily for vibrations damping and reliable diagnostics of rolling mills equipment under non-stationary working conditions. Three types of nonlinear effects are investigated taking place in drivelines and stands of different design, namely, transient torsional vibrations in hot rolling mills, chatter vibrations in tandem cold rolling mills and parametrical vibrations in high-speed wire and rod rolling mills. The procedure is proposed for natural frequencies identification when short transient torque signals restrict application of the Fourier transform. Some considerations given on using nonlinear effects for wear diagnostics and vibrations control based on natural frequencies and modes analysis of multi-body systems.
Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells
(NTU "KhPI", 2016) Shmatko, T.; Bhaskar, A.
An original method for investigation of geometrically nonlinear vibrations of functionally graded shallow shells and plates with complex planform is presented. Shells under consideration are made from a composite of ceramics and metal. Power law of volume fraction distribution of materials through thickness is chosen. Mathematical statement is implemented in the framework of the refined geometrically nonlinear theory of the shallow shells of the first order (Timoshenko type). The proposed approach combines the application of the Rfunctions theory (RFM), variational Ritz method, procedure by Bubnov-Galerkin and Runge-Kutta method. Due to use of this combined algorithm it is possible to reduce the initial nonlinear system of motion equations with partial derivatives to a nonlinear system of ordinary differential equations. Investigation task of functionally graded shallow shells with arbitrary planform and different types of boundary conditions is carried out by the proposed method. Test problems and numerical results have been presented for one-mode approximation in time. In future, the developed method may be extended to investigation of geometrically nonlinear forced vibrations of functionally graded shallow shells with complex planform.
Identification of Nonlinear Damping for Large-Amplitude Vibrations of Plates and Curved Panels
(NTU "KhPI", 2016) Amabili, Marco
A nonlinear identification technique is presented to obtain the damping of isotropic and laminated sandwich rectangular plates and curved panels subjected to harmonic excitation as a function of the vibration amplitude. The response of the structures is approximated by (i) reduced-order models with 10 to 100 degrees of freedom and (ii) a single-degree of freedom Duffing oscillator. The method uses experimental frequency-amplitude data and the leastsquares technique to identify parameters and reconstruct frequency-response curves by spanning the excitation frequency in the neighbourhood of the lowest natural frequencies. In order to obtain the experimental data, a sophisticated measuring technique has been used. The results reveal a strongly nonlinear correlation between the damping and the vibration amplitude.