Action of a heat source and influence of initial condition on the plane state of temperature

The work takes an advantage of the temperature component method for some heat conduction problems. Simplifications of the method for 2D problems are considered. Some examples of calculations are quoted

Mechanical systems with two nonlinear springs connected in series.

The aim of the paper is analysis of dynamical regular response of the nonlinear oscillator with two serially connected springs of cubic type nonlinearity. Behaviour of such systems is described by a set of differential-algebraic equations (DAEs). Two examples of systems are solved with the help of the asymptotic multiple scales method in time domain. The classical approach has been appropriately modified to solve the governing DAEs. The analytical approximated solution has been verified by numerical simulations

Double pendulum colliding with a rough obstacle.

The externally excited and damped vibrations of the double pendulum in the vertical plane are considered. The pendulum can collide with a rough obstacle many times during its motion. The pendulum is modeled as a piecewise smooth system. The differential equations govern the motion of the system in the relatively long time between the collisions. When a contact with the obstacle occurs, the pendulum exhibits a discontinuous behaviour. The velocities of both parts of the pendulum and the reaction forces are changing stepwise. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson's hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Furthermore, during the collision the dynamic behaviour may change. Therefore the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space

On Efficiency of Two-Degree-of-Freedom Galloping Energy Harvesters with Two Transducers

This paper examines the energy efficiency of three variations of the two-degree-of-freedom transverse galloping energy harvester. These variants differ in the number and placement of electromechanical transducers. By utilizing the harmonic balance method, the limit cycles of mathematical models of the devices were determined. Analytical expressions derived from the models were then used to formulate the efficiency of the systems. It was demonstrated that efficiency depends on flow speed and can be comprehensively characterized by the following criteria parameters: peak efficiency, denoting the maximum efficiency of the system, and high-efficiency bandwidth, which describes the range of flow speeds within which the efficiency remains at no less than 90% of peak efficiency. The values of these parameters are heavily reliant on two other parameters: the speed at which the system achieves peak efficiency, referred to as the nominal speed, and also the flow speed at which the system undergoes Hopf bifurcation, namely the critical speed. Comparative analysis revealed that only the device equipped with two electromechanical transducers can potentially outperform a simple one-degree-of-freedom system. For selected parameters, this gain reached nearly 10%

Minimization of critical flow velocity of aeroelastic energy harvester via delayed feedback control

The paper describes the procedure of modelling and optimization of the aeroelastic energy harvester from the point of view of their operation at very low flow velocities. Using analytical solutions of models of different device variants, the relationships between their efficiency and flow velocity were presented. By way of analytical considerations, the conditions for high performance operation of the device have been demonstrated, indicating at the same time the difficulty in maintaining it at low operation velocities. As a solution to the problem, the application of external delayed feedback control was proposed and its effectiveness was demonstrated

Special Issue “Application of Non-Linear Dynamics”

Nonlinear phenomena occur in engineering structures, biological systems, social processes, and in economics [...

AI-based method of vortex core tracking as an alternative for Lambda2

The paper presents a new method of vortex core detection developed for use in CFD simulation result analysis. Apart from the conventional approach involving vector algebra, mainly the Lambda2 method, it focuses on the identification of certain features in a graphic representation of the velocity field. It is done by generating a series of slices of the said field in the postprocessing software and training a Convolutional Neural Network (AI) to recognize vortex cores. The neural network can be integrated into a simple python program and used to quickly identify vortex cores on a large number of images and translate their locations to coordinates of a CFD model for visualisation