Arkadiusz Syta

Chaotic vibrations of the duffing system with fractional damping

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.

Experimental analysis of the dynamical response of energy harvesting devices based on bistable laminated plates.

The use of bistable laminates is a potential approach to realize broadband piezoelectric based energy harvesting systems. In this paper the dynamic response of a piezoelectric material attached to a bistable laminate plate is examined based on the experimental generated voltage time series. The system was subjected to harmonic excitations and exhibited single-well and snap-through vibrations of both periodic and chaotic character. To identify the dynamics of the system response we examined the frequency spectrum, bifurcation diagrams, phase portraits, and the 0–1 test.

Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0-1 test

Shape memory oscillators are thermomechanical hysteretic systems that, in a wide range of model parameters, can exhibit complex non-periodic non-linear dynamic responses under the excitation of a periodic force. In this study, the statistical 0–1 test based on the asymptotic properties of a Brownian motion chain is applied to periodic and non-periodic isothermal trajectories to examine the type of motion. The analysis is based on the computation of the control parameter K that approaches asymptotically 0 or 1 for regular and chaotic motions, respectively. The presented approach is independent of the integration procedure, being based on the characteristic sampling distance between the points of the analysed time series. The numerical results show that the test is able to unambiguously distinguish periodic from chaotic trajectories.

Cutting process dynamics by nonlinear time series and wavelet analysis.

We have modeled the dynamics of a cutting process by a two-degree-of-freedom mass-spring system with dry friction. Using nonlinear time series and wavelet analysis, we have investigated the vibrational instabilities of the system for different values of the cutting force. By constructing the phase portraits and calculating the Lyapunov exponents we have delineated the conditions for which a periodic or chaotic motion can occur. The results are verified by means of a time-scale representation of the wavelet power spectrum.

Failure Diagnosis of a Gear Box by Recurrences

The recurrence analysis method is used in the mechanical diagnosis of a gear transmission system using time domain data. The recurrence is a natural behavior of a periodic motion system, which tells the state of the system, after running some time, and will approach a certain past state. In this paper, some statistical parameters of recurrence qualification analysis are extensively evaluated for the use of mechanical diagnosis, based on fairly short acceleration time series; recurrence results are compared with those obtained from Fourier analysis, and the identification procedures for the failure gear transmission by recurrences is also presented. It is found that, using only fairly short time series, some statistical parameters in quantification recurrence analysis can give clear-cut distinction between a healthy and damaged state.

Multiple Solutions and Corresponding Power Output of Nonlinear Piezoelectric Energy Harvester

Energy harvesting is used for an increasing number of small electronic devices and sensors in various applications. Ambient sources of vibration are exploited to provide low levels of power to devices where battery replacement is difficult. One of the simplest concepts for energy harvesting from mechanical vibrations is based on a linear mechanical resonator combined with a piezoelectric transducer. In this case, mechanical energy scavenged from mechanical stress or strain is transferred to electrical voltage. However, such devices work most efficiently in the vicinity of a resonant frequency and it is difficult to tune them in the presence of variable ambient conditions. On the other hand, nonlinear devices seem to be more effective in such conditions due to the broader frequency spectrum of their response. In this paper, we analyse the dynamics of a nonlinear flexible beam with a piezoelectric layer and a magnetic tip mass under the harmonic excitation. The additional magnets define system multistability, including a tristable configuration. The resonant curves and basins of attraction are predicted and can be helpful in choosing the optimal values of the system parameters.

Dynamics of Composite Milling: Application of Recurrence Plots to Huang Experimental Modes

We study the dynamics of a milling process of a composite material basing on the experimental time series of cutting force components measured in the feeding direction. By using the recurrence plots we observe the differences in the response of the system depending on the feeding direction with respect to composite fibers orientation. This effect has been found after decomposition on the Huang experimental modes. Showing the results of recurrences in particular experimental modes we advocate to use this quantity to analyze the stability of the cutting of composites. The difference between different cases was also noticed using Fourier transform and statistical parameters such as RMS and kurtosis, but for these methods the necessary time interval of the examined time series has to be much longer, while recurrence approach is designed for shorter time series.

Modelling of Energy Harvesting System from Vertically Excited Magnetostrictive Beam

Recently, one can observe increasing number of small devices or sensors in many applicationsthat have to be powered by an energy which can be extracted from surroundings. Simple energyharvesting concept from mechanical vibrations of magnetostrictive materials is based on linear beamwith external excitation. In this case, the beam under load vibrates, and experiences stress or strain.This changes the beam shape which causes direction of sample magnetization (Villari effect) thatcan be captured by external coil and transferred to electrical power. In general, the higher amplitudeof beam vibrations, the higher energy can be extracted from the system. This can be achieve in thevicinity of a resonant frequency. In this paper, we propose energy harvesting model based on linearmagnetostrictive (MsM) beam with external coil. We analyse different shapes of the beam withrespect to different resonant frequencies.

Vibration Analysis in Cutting Materials

The orthogonal cutting process is a highly nonlinear phenomenon, where dry friction is combined with possible contact loss and time delay effects. Unwanted and harmful vibrations may appear during cutting; the vibrations may have a regular or chaotic nature depending on the system vibrations. These vibrations disturb the process and affect the final surface quality of the workpiece. We investigate the dynamics of the cutting process by modeling it as a two-degrees of freedom nonlinear system. Using nonlinear analysis methods, such as nonlinear time series embedding approach, recurrence plots (RP) and recurrence quantification analysis (RQA), we try to identify the system variables and cutting forces that lead to chaotic motion.