Nonlinear dynamics


Reduction of the large amplitude resonance dynamics of the systems with limited power supply

The systems with limited power supply (or non-ideal systems, or NIS) are characterized by interaction of source of energy and the elastic sub-system. The most interesting phenomenon here is the Sommerfeld effect, when the large amplitude resonance regime of the elastic sub-system is observed, and a big part of the source energy is leaved to the resonance vibrations. A use of vibration absorber permits to reduce the large amplitude vibrations. It is planned to investigate dynamics of the NIS containing nonlinear absorber, such as the pendulum, Mises girder et al. Both n-DOF and distributed NIS can be considered. Modern methods of nonlinear dynamics will be used in this investigation.

Novelty and benefits:

  • Use of nonlinear absorbers to reduce resonance vibrations of NIS is original. Methods of analysis of the NIS nonlinear dynamics are original.
  • It is expected a determination of the system parameter regions where a strong reduction of the vibration amplitudes can be obtained.

Outlook and perspectives. Results of the investigation of resonance dynamics and absorption of large amplitudes resonance dynamics in NIS can be used in engineering practice, in particular, in civil engineering, bridge construction, transport construction, etc.


Investigation of geometrically nonlinear, free and parametric vibration of the laminated and functionally-graded plates and shallow shells by meshless methods, based on R-functions theory

The basic goal of the project is creation of the universal numerically – analytical method for solving geometrically nonlinear static and dynamic problems of the laminated and functionally graded plates and shallow shells theory with complex plan form and different types of the boundary conditions. The proposed method will be based on the application of the R-functions theory and variational method.

Novelty and benefits:

  •  a new mathematical approach which allows to present problem solution in analytical form. Created the software in order to solve geometrically nonlinear bending problems of a finding natural frequencies of vibrations of multilayered and functionally-graded plates and shallow shells of the any form in the plan;
  • developed algorithms of research of geometrically nonlinear vibrations of laminated functionally-graded plates and shallow shells with complex planform;
  • new approach to investigation parametric vibration of the laminated functionally graded plates with various kinds of boundary conditions and different geometric form.

Outlook and perspectives. New theoretical and numerical results will increase scientific knowledge in order to research parametric vibration, buckling problem, bending and finding frequencies of free vibration of composite laminated and sandwich panels and plates of an arbitrary form. These elements are widely applied in different field of industry, particularly, in aero-space, building manufacturers.


Stochastic dynamics of the vibrational isolation systems with nonlinear suspension

At the present-day engineering practice, nonlinear stiffness or damping suspension is widely used for the reduction of the vibrations. A special attention here should be made on the systems with a quasi-zero stiffness because they can provide a vibro-isolation effect together with the efficiency of usage and compact size. This work deals with the theoretical modelling and experimental observations of the vertical dynamics of a cargo platform with the quasi-zero stiffness suspension under the operational random load. A discrete non-linear computational model has been developed and analysed within numerical simulations of the random vibrations. Dynamics of the system is analysed under a kinematic stochastic wide-band stationary load. A good comparative agreement is found between the numerical simulations and experimental data.

Outlook and perspectives:

  • Analysis of the transient behaviour of the nonlinear vibration of such a system
  • Development of the semi-active adaptive nonlinear suspension and the algorithm of its control
  • Development of the genetic algorithms of optimal designing of the parameters of the nonlinear elastic and damping elements of a vibrational isolation suspension


Full combined magnetic suspension of shafts and rotors in passive and active magnetic bearings

Creating a method for constructing complete magnetic suspensions of shafts and rotors of various systems and machines. Development of new types of passive and active magnetic bearings based on a refined mathematical modeling for a calculation of force and stiffness characteristics, taking into account the laws and algorithms of the control. An introduction of passive-active magnetic suspensions for various systems and machines on a basis of carrying out various phenomena of the dynamics of rotors in magnetic bearings, considering a nonlinear interconnection of electrical, magnetic and mechanical processes.

Novelty and benefits:

  • The use of passive magnetic bearings on ring permanent magnets for an organization of a more competitive full passive-active magnetic suspension.
  • Practical testing of new types of passive magnetic bearings based on an application of the technique of an optimal search for parameters of a system.
  • Computer simulation of rotor dynamic with passive and active magnetic.

Outlook and perspectives. Creating the new types of active and passive magnetic bearings with a development of design solutions, laws, algorithms and control systems. A new type of passive magnetic bearings with a short-term variable stiffness to create competitive full passive-active magnetic suspensions.


Forced nonlinear vibrations of turbine blades package with dynamic contact in the shroud

Failures caused by the increased vibrations are widespread possible breakdowns occurring in steam and gas turbines. The blades assemblies are the most dynamically loaded units of the turbines. Inter-blades detachable joints are typically used for long blades stiffness magnification. Dynamic and strength characteristics of these designs essentially depend on the contact interacting peculiarities in such bandage. Vibrations of the blades assembly become nonlinear under dynamic contact in the bandage and can be accompanied by the great number of the various phenomena. The work deals with the investigation of the forced nonlinear vibrations of blades package of turbine, taking into account the contact interaction in the shroud.

Novelty and benefits. Analysis of the nonlinear dynamics phenomena in resonance and nonresponse regimes (a changing of resonance zones, sub and super harmonics, shifting of the system stability zone etc.).

Outlook and perspectives:
1) Analysis of the process of shroud contact surfaces wear and bladed disks vibrational reliability;
2) Analysis of the nonlinear dynamics of the turbine blades taken into account a mistuning phenomenon.


Oleksiy Larin – Director of Institute Of Education and Science In Engineering and PhysicsProfessor, Doctor of Technical Sciences:

Olena Slipchenko – Director of European Educational Scientific Technological Center – Ph.D. in technical sciences, Senior Researcher: