Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The non-classical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam’s preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.     

Nonlinear vibrations and time delay control of an extensible slowly rotating beam

Nonlinear Dynamics - This paper investigates the time-varying formation tracking (TVFT) problem of multiple heterogeneous Euler–Lagrange agents (MHELAs) with predefined-time convergence...     

Analytical Problems with Preparation of Paraspinal Tissues from Patients with Spinal Fusion for Analysis of Titanium

Preparation of paraspinal tissue of patients with implants for elemental analysis is a challenge because it contains titanium in the ionic form, as well as metallic debris. Most literature reports focus on dissolving the tissue, but the impact of digestion conditions on metallic debris of Ti has not been investigated. In our work, various digestion conditions, including systems, compositions of oxidising mixture, and time, were tested aiming (i) to digest the tissue without digestion of metallic titanium to quantify soluble Ti and (ii) to digest metallic titanium debris to asses total Ti content in tissue. The experiments were performed in a closed mode using a microwave-assisted system and a carbon heating block. Our study revealed that total digestion of titanium was impossible in the tested conditions and the maximal level of digested titanium was below 70%. The mineralisation with the use of concentrated nitric acid was optimal to prepare paraspinal samples to analyse the soluble titanium form because metallic titanium passivated and did not migrate to the solution. The elaborated conditions were applied to determine titanium ion in the periimplant tissue of patients with three different titanium-based surgical systems, including traditional growing rod (TGR), guided growth systems (GGS), and vertical expandable prosthesis titanium rib (VEPTR).     

Nonlinear dynamics and synchronisation of pendula attached to a rotating hub

A model of a nonlinear system composed of a hub with attached two pendula rotating in a horizontal plane is studied in the paper. Each single pendulum, treated as a stiff and massless rod with a lumped mass, is connected to the hub by a flapping hinge. Nonlinear stiffness and viscous damping of the hinge is taken into consideration. The system is excited by an external torque generated by a DC motor which is considered as an ideal system with torque given by a harmonic function. For small oscillations the problem is linearised and then solved analytically. An influence of the structural parameters like mass of the hub and pendula length on natural end excited vibrations is presented. Large oscillations are studied by a continuation technique, directly from the original Ordinary Differential Equations of motion (ODE). The complete synchronisation, phase synchronisation, bifurcations and transition through resonances are analysed considering the influence of the mass of the hub. The existence of chaotic oscillations of the system and paths leading to chaos are demonstrated as well.     

A coupled-field model of a rotating composite beam with an integrated nonlinear piezoelectric active element

Nonlinear Dynamics - The dynamics of a system consisting of a rotating rigid hub and a thin-walled composite beam with embedded active element is presented. The beam comprises of a...