Paweł Fritzkowski

Inertially driven or vibration-driven capsule robots have recently attracted attention from various areas of science and engineering. The main advantage of such a mobile system is the lack of any external driving mechanism, which allows for an encapsulated construction and efficient operation in demanding environments. This study focuses on the conception of a mechanical system whose motion on a rough horizontal plane is caused only by the rotation of two internal masses. The mathematical model of the robot is presented in the non-dimensional form. The conditions for motion are formulated, and the working region of the system is specified. The active phase of the robot dynamics may include both forward motion and minor backward motion, or forward motion exclusively. Extensive numerical studies are conducted using two friction models. The numerical solutions to the dynamic problem are analyzed with regard to the total displacement and the average velocity per period of excitation. The interplay between model parameters is studied. The resulting maps on the parameter planes allow for substantial improvement in the robot performance. Moreover, it is demonstrated that the Stribeck effect occurring in the friction characteristics plays a positive role in the efficient motion of the system.

A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. A conception of the stability analysis of the periodic motions suited for this theoretical approach is presented. The frequency–response curves and force–response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response are verified via a series of numerical experiments and computation of Lyapunov exponents. Finally, the limitations and extensibility of the approach are discussed.

A mechanical system composed of two weakly coupled oscillators under harmonic excitation is considered. Its main part is a vibro-impact unit composed of a linear oscillator with an internally colliding small block. This block is coupled with the secondary part being a damped linear oscillator. The mathematical model of the system has been presented in a non-dimensional form. The analytical studies are restricted to the case of a periodic steady-state motion with two symmetric impacts per cycle near 1:1 resonance. The multiple scales method combined with the sawtooth-function-based modelling of the non-smooth dynamics is employed. The approximate analytical solutions allow for stability analysis of the periodic motions. Moreover, the frequency-response curves and force-response curves with stable and unstable branches are determined, and the interplay between various model parameters is investigated. The theoretical predictions related to the motion amplitude and the range of stability of the periodic steady-state response is verified via a series of numerical experiments and computation of Lyapunov exponents.

A computational model for the kinematics of a vertical axis wind turbine (VAWT) is presented. A H-type rotor turbine with a controlled pitch angle is considered. The aim of this solution is to improve the VAWT productivity. The discussed method is related to a narrow computational branch based on the Blade Element Momentum theory (BEM theory). The paper can be regarded as a theoretical basis and an introduction to further studies with the application of BEM. The obtained torque values show the main advantage of using the variable pitch angle.

A 1D chain of coupled oscillators is considered, including the Duffing-type nonlinearity, viscous damping, and kinematic harmonic excitation. The equations of motion are presented in a non-dimensional form. The approximate equations for the vibrational amplitudes and phases are derived by means of the classical averaging method. A simple analysis of the resulting equations allows one to determine the conditions for the two basic synchronous steady-states of the system: the in-phase and anti-phase motions. The relations between the required excitation frequency and the natural frequencies of the abbreviated (linear) system are discussed. The validity of these predictions is examined by a series of numerical experiments. The effect of the model parameters on the rate of synchronization is analyzed. For the purpose of systematic numerical studies, the cross-correlation of time-series is used as a measure of the phase adjustment between particular oscillators. Finally, some essential issues that arise in case of the mechanical system with dry friction are indicated.