Daniil Yurchenko

Reliability analysis of rotor blades of tidal stream turbines

Tidal stream turbines are used for converting kinetic energy of tidal currents into electricity. There are a number of uncertainties involved in the design of such devices and their components. To ensure safety of the turbines these uncertainties must be taken into account. The paper shows how this may be achieved for the design of rotor blades of horizontal-axis tidal stream turbines in the context of bending failure due to extreme loading. Initially, basic characteristics of such turbines in general and their blades in particular are briefly described. A probabilistic model of tidal current velocity fluctuations, which are the main source of load uncertainty, is then presented. This is followed by the description of reliability analysis of the blades, which takes into account uncertainties associated with tidal current speed, the blade resistance and the model used to calculate bending moments in the blades. Finally, the paper demonstrates how results of the reliability analysis can be applied to set values of the partial factors for the blade design.

Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy

A mathematical model of leukaemia therapy based on the Gompertzian law of cell growth is investigated. The effect of the medicine on the leukaemia and normal cells is described in terms of therapy functions. A feedback control problem with the purpose of minimizing the number of the leukaemia cells while retaining as much as possible the number of normal cells is considered. This problem is reduced to solving the nonlinear Hamilton–Jacobi–Bellman partial differential equation. The feedback control synthesis is obtained by constructing an exact analytical solution to the corresponding Hamilton–Jacobi–Bellman equation.

Tuned Mass and Parametric Pendulum Dampers Under Seismic Vibrations

In the last hundred years, the height of the tallest buildings (skyscrapers) went up from 283 m (Woolworth Building, New York City, 1913) to 830 m (Burj Khalifa, Dubai, 2013). Building such structures presents various architectural and engineering challenges, including the development of plumbing and air conditioning systems, fast elevators, etc. Nevertheless, the main effort is always directed toward safety and reliability of buildings and occupants. These concerns are not immanent to tall buildings only but important as well for any structures, whether it is a bridge or nuclear plant. Earthquake and wind load are the major reasons for worries when designing structures or buildings, especially tall ones, since these loads are hard to predict. Tuned mass damper (TMD) is a concept (Den Hartog 2013; Hunt 1979), which has appeared in the beginning of the twentieth century. The concept seemed to be so attractive that it was properly developed and one of the first TMDs were installed in CN Tower, Toronto, and John Hancock Building, Boston, in 1976. Since then the number of different types of implemented TMDs has been rapidly increasing, approaching one hundred (Soto and Adeli 2013), including those which are used to mitigate the motion of tall buildings (Kareem et al. 1999), bridges, pumps, structures, etc. The basic idea behind a TMD is that an oscillatory two-degree-of-freedom (TDOF) system may have such a response that one of the masses (primary mass) will be motionless. Thus, if the response of the primary mass itself was high due to resonance, adding a second mass will significantly reduce the primary mass response amplitude. However, the response attenuation does not happen by default, so the properties of the added mass-springdamper system have to be tuned to deliver the best outcome; therefore, the name tuned mass damper is used to reflect this feature. A concern may be related to the fact that adding another degree of freedom to the system will result in two peaks of the response amplitude curve rather than one, characteristic for a single-degree-of-freedom (SDOF) system, but this issue can be handled by proper tuning as well. It has also been shown that the tuning of a stochastic system (a system subjected to a random excitation) is different from that for a deterministic system. There are different types of devices, which serve as passive TMDs: conventional TMD, liquid TMD (TLD) (DiMatteo et al. 2014 and references therein), and parametric pendulum TMD (PPD). An excellent review paper by Ibrahim (Ibrahim 2008) provides a full description of various passive vibration isolators. It has been argued that the passive TMDs are effective means of mitigating buildings’ vibrations due to seismic loading. It became a motivation for the development of a theory of active and hybrid TMDs

NUMERICAL INVESTIGATION OF THE PARAMETRIC PENDULUM UNDER FILTERED RANDOM PHASE EXCITATION

The parametrically excited pendulum is a highly nonlinear system which has been thoroughly studied regarding the responses stability and the fundamental types of motion that could be established. The rotating potential of a pendulum having its suspension point ver- tically excited was numerically identified and the appropriate excitation characteristics were presented. In this paper, the excitation is modeled using the random phase modulation and the rotational motion is sought. The resulting stochastic system is analyzed by using a nu- merical Path Integration (PI) method solving the Chapman-Kolmogorov equation to construct parameter space plots. The Probability Density Function (PDF) is computed and the rotational regions are identified as well as the effect of noise intensity onto them. Previous studies have shown that for small values of noise intensity the stochastic response resembles the deterministic one. However numerical simulations showed that with increasing noise intensity the regions of rotational motion become narrower. In order to improve the systems response a linear single- degree-of-freedom (SDOF) system is intercepted to filter the noisy excitation, forming a base excited SDOF system acting on the pendulum suspension point. The interaction between the moving pendulum mass and the SDOF filter is investigated with the goal being for the former to establish rotational motion.

Implementing a GPU-based numerical algorithm for modelling dynamics of a high-speed train

ABSTRACT This paper discusses the initiative of implementing a GPU-based numerical algorithm for studying various phenomena associated with dynamics of a high-speed railway transport. The proposed numerical algorithm for calculating a critical speed of the bogie is based on the first Lyapunov number. Numerical algorithm is validated by analytical results, derived for a simple model. A dynamic model of a carriage connected to a new dual-wheelset flexible bogie is studied for linear and dry friction damping. Numerical results obtained by CPU, MPU and GPU approaches are compared and appropriateness of these methods is discussed.

Optimal bounded noisy feedback control for damping random vibrations

We consider a stochastic optimal feedback control problem for a single-degree-of-freedom vibrational system, where uncertainty is described by two independent noises. The first of them is induced by the control actions and called internal, whereas the second one acts externally. The drift vector also depends on the control function. The set of pointwise control constraints is assumed to be bounded. The minimization functional is taken as the mean system response energy. The Cauchy problem for the corresponding Hamilton–Jacobi–Bellman (HJB) equation without the control constraints is first investigated. This allows us to find the sought-for feedback control strategy in a specific domain of the space of state and time variables. Then a proper extension to the remaining parts of the space is constructed, and the optimality of the resulting global feedback control strategy is proved. The obtained control law is compared with the dry friction and saturated viscous friction control laws.

Beneficial Effect of Noise in Suppression of Self-Excited Vibrations

We discuss the possibility of full suppressions of self-excited vibrations by noise. Recently, periodic excitations have been intensively studied for this aim. We compare the used periodic and random noise excitations in the case of a two-mass system. It is shown that the random noise excitations can be more efficient under certain conditions. The telegraphic process is used as the source of noise. The mean-square (energetic) asymptotic stability of the system is a tool in study of the suppression. The stability charts are presented for different values of the transition rate of the telegraphic noise.

Dynamics and optimization of a new double-axle flexible bogie for a high speed trains

This paper is focused on the discussion of a new double-axle flexible bogie for high-speed trains. The main feature of the flexible bogie is that it consists of two sub-bogies connected with diagonal links. Moreover, an elastic connection between the carriage and both wheelsets is introduced. These features, which help to increase the flexibility of the bogie while passing tracks with a low radius of curvature, are numerically studied in this paper. The results demonstrate the huge potential of the bogie and its ability to travel without significant oscillations at a speed of 432 km/h. Numerical optimization of the bogie’s parameters is performed in order to maximize ride comfort.

Energy Response Probability Density Function of a Rotating Parametric Pendulum

The rich dynamic response of a parametric pendulum to a harmonic excitation acting on its pivot point has been shown to include among others rotational trajectories. On this foundation, the potential of developing a wave energy converter (WEC) has been suggested exploiting the bobbing motion of waves as the necessary excitation for the pendulum to establish rotary motion. Quite often in the study of dynamical systems, the random nature of environmental inputs cannot be ignored rendering deterministic analyses inadequate. Thereafter, stochastic analysis of these systems has to be employed. Considering a pendulum structure floating on ocean waves, the need for a stochastic frame is raised due to the strong randomness dictating the motion of waves. In this paper, the probability density function of the energy transferred to the pendulum is calculated using a path integration (PI) algorithm. Subsequently, this information is utilized to evaluate the probability of the pendulum to lay in a rotational regime.