Investigation of Nonlinear Vibrations in Multi-Degree-of-Freedom Mechanical Systems: Regular and Chaotic Behavior Research Group

1. Research Team

Prof. Yuri Mikhlin

Department of Applied Mathematics

Ms. Yulia Surganova

Department of Applied Mathematics

Ms. Yana Lebedenko

Department of Applied Mathematics

2. Research Focus

Exploring nonlinear oscillations and resonances in mechanical and structural systems 

Analyzing bifurcation scenarios that lead to chaotic dynamics in coupled oscillatory systems 

Applying asymptotic and perturbation techniques based on nonlinear normal modes to predict stability and transitions to chaos 

3. Key Projects

The project focuses on developing innovative composite metamaterials for aerospace structures. By integrating fiber-reinforced layers with 3D-printed honeycomb cores, the project aims to propose lightweight materials with superior mechanical and thermal properties for demanding aerospace applications. 

The project focuses on developing theoretical foundations and efficient algorithmic procedures to enhance vibration protection for people and goods exposed to significant dynamic impacts, particularly those arising from emergencies, including military operations. It involves computational and analytical studies to investigate the dynamic behavior of active and passive damping models for dynamically loaded equipment, especially during transportation under cyclic, random, and impulsive external loads. The research aims to identify the regularities of dynamic damping, assess the influence of model parameters on vibration protection effectiveness, and develop control algorithms for active vibration protection components. Additionally, practical recommendations for optimal design solutions will be provided.

The project addressed the analysis of metamaterial panels, including mechanical characterization of the inner layer, auxetic plate bending, and comparison of 3D and 2D orthotropic models. It also examined the eigenvalue problem of three-layer plates and the static bending of honeycomb-filled composites made via additive manufacturing. Additionally, the dynamics of shallow shells were studied using Donnell’s equations and the Galerkin method, highlighting vibration and beating modes. The vibrations of functionally graded porous sigmoid sandwich plates with complex geometries were also analyzed using the Rayleigh-Ritz method to assess natural frequencies and porosity effects. 

4. Contact Information

Principal Investigator Contact: Prof. Yuri Mikhlin

Email: yuriy.mikhlin@khpi.edu.ua