Dynamics of composite nonlinear systems and materials for engineering applications and energy harvesting – The role of nonlinear dynamics and complexity in new developments

This engineering research focus issue was inspired by the workshop organised by us on March 19th 2012 at the Lublin University of Technology (in the framework of CEMCAST) titled “Dynamics of functionally graded materials and systems with hysteresis” The collection of the present research papers followed our fruitful discussions focussing on “Dynamics of composite nonlinear systems and materials for engineering applications and energy harvesting” which is now the title of the present volume. In the next two sections we briefly discuss the topics included in this focus issue.     

Large amplitude vibrations and damage detection of rectangular plates

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates are used to study the sensitivity of some nonlinear vibration response parameters to the presence of damage. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour. Damage is represented as a stiffness reduction in a small area of the plate. The plate is subjected to harmonic loading with a frequency of excitation close to the first natural frequency leading to large amplitude vibrations. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the plate and the change in the time-history diagrams and the Poincaré maps caused by the damage. Finally, a criterion and a damage index for detecting the presence and the location of the damage is proposed. The criterion is based on analysing the points in the Poincaré sections of the damaged and healthy plate. Numerical results for large amplitude vibrations of damaged and healthy rectangular and square plates are presented and the proposed damage index for the considered cases is calculated. The criterion demonstrates quite good abilities to detect and localize damage.     

A novel embedding method for characterization of low-dimensional nonlinear dynamical systems

Nonlinear Dynamics - Characterization of dynamical systems remains a central challenge in real-world applications because, in most cases, governing equations of the systems cannot be obtained...     

Dynamics of a laminated composite beam with delamination and inclusions

In this work numerical and experimental study of the dynamic behaviour of a composite laminated beam having delamination is presented. The model of delamination takes into account a contact interaction between sublaminates including normal forces, shear forces and additional damping. In order to verify the model special samples of multilayered beams have been manufactured. Small parts of adjacent layers have been cut and replaced by inclusions from different materials modelling delamination. The mechanical properties of the inclusions have been considered during the numerical calculations. The beams were subjected to a short pulse loading and then their response was registered. The results from the numerical simulation were in a good agreement with the experimental results. The significance of the additional damping due to delamination on the response of the beam was confirmed numerically and experimentally.     

Nonlinear dynamics of a reduced multimodal Timoshenko beam subjected to thermal and mechanical loadings

Large amplitude vibrations of a Timoshenko beam under an influence of temperature are analysed in this paper. In the considered model the temperature increases instantly and the heat is uniformly distributed along the beams length and cross-section. The mathematical model, represented by partial differential equations takes into account thermal and mechanical loadings. Next, the problem is reduced by means of the Galerkin method, considering the first three natural vibration modes of a simply supported beam in the both ends. The influence of the temperature on amplitudes and localisation of the resonance zones and stability of the solutions is studied numerically and analytically by the multiple time scale method. The bifurcation points, existence of unstable lobes and transition from regular to chaotic oscillations are shown.