Nonlinear Dynamics and Control of an Ideal/Nonideal Load Transportation System With Periodic Coefficients

In this paper, a loads transportation system in platforms or suspended by cables is considered. It is a monorail device and is modeled as an inverted pendulum built on a car driven by a dc motor the governing equations of motion were derived via Lagrange's equations. In the mathematical model we consider the interaction between the dc motor and the dynamical system, that is, we have a so called nonideal periodic problem. The problem is analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, we also analyze the problem quantitatively using the Floquet multipliers technique. Finally, we devise a control for the studied nonideal problem. The method that was used for analysis and control of this nonideal periodic system is based on the Chebyshev polynomial exponsion, the Picard iterative method, and the Lyapunov-Floquet transformation (L-F transformation). We call it Sinha's theory.

Behavioural Analysis of a Nonlinear Mechanical System Using Transient Trajectories

This work aims at a better comprehension of the features of the solution surface of a dynamical system presenting a numerical procedure based on transient trajectories. For a given set of initial conditions an analysis is made, similar to that of a return map, looking for the new configuration of this set in the first Poincaré sections. The mentioned set of I.C. will result in a curve that can be fitted by a polynomial, i.e. an analytical expression that will be called initial function in the undamped case and transient function in the damped situation. Thus, it is possible to identify using analytical methods the main stable regions of the phase portrait without a long computational time, making easier a global comprehension of the nonlinear dynamics and the corresponding stability analysis of its solutions. This strategy allows foreseeing the dynamic behavior of the system close to the region of fundamental resonance, providing a better visualization of the structure of its phase portrait. The application chosen to present this methodology is a mechanical pendulum driven through a crankshaft that moves horizontally its suspension point.

Dynamics of bone healing after osteotomy with piezosurgery or conventional drilling - histomorphometrical, immunohistochemical, and molecular analysis

Background: Piezosurgery is an osteotomy system used in medical and dental surgery. Many studies have proven clinical advantages of piezosurgery in terms of quality of cut, maneuverability, ease of use, and safety. However, few investigations have tested its superiority over the traditional osteotomy systems in terms of dynamics of bone healing. Therefore, the aim of this study was to evaluate the dynamics of bone healing after osteotomies with piezosurgery and to compare them with those associated to traditional bone drilling.Methods: One hundred and ten rats were divided into two groups with 55 animals each. The animals were anesthetized and the tibiae were surgically exposed to create defects 2 mm in diameter by using piezosurgery (Piezo group) and conventional drilling (Drill group). Animals were sacrificed at 3, 7, 14, 30 and 60 days post-surgery. Bone samples were collected and processed for histological, histomorphometrical, immunohistochemical, and molecular analysis. The histological analysis was performed at all time points (n = 8) whereas the histomorphometrical analysis was performed at 7, 14, 30 and 60 days post-surgery (n = 8). The immunolabeling was performed to detect Vascular Endothelial Growth Factor (VEGF), Caspase-3 (CAS-3), Osteoprotegerin (OPG), Receptor Activator of Nuclear Factor kappa-B Ligand (RANKL), and Osteocalcin (OC) at 3, 7, and 14 days (n = 3). For the molecular analysis, animals were sacrificed at 3, 7 and 14 days, total RNA was collected, and quantification of the expression of 21 genes related to BMP signaling, Wnt signaling, inflammation, osteogenenic and apoptotic pathways was performed by qRT-PCR (n = 5).Results: Histologically and histomorphometrically, bone healing was similar in both groups with the exception of a slightly higher amount of newly formed bone observed at 30 days after piezosurgery (p < 0.05). Immunohistochemical and qRT-PCR analyses didn't detect significant differences in expression of all the proteins and most of the genes tested.Conclusions: Based on the results of our study we conclude that in a rat tibial bone defect model the bone healing dynamics after piezosurgery are comparable to those observed with conventional drilling. © 2013 Esteves et al.; licensee BioMed Central Ltd.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 mu m and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems, Our simulations studies three different profiles, linear, hyperbolic. and constant, One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show my oscillation in the CE value (log eta), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C-i for the generated FWM signal at omega(3) was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems. (c) 2005 Elsevier B.V. All rights reserved.

Is the meander growth in the Brazil Current system off Southeast Brazil due to baroclinic instability?

Temporally-growing frontal meandering and occasional eddy-shedding is observed in the Brazil Current (BC) as it flows adjacent to the Brazilian Coast. No study of the dynamics of this phenomenon has been conducted to date in the region between 22 degrees S and 25 degrees S. Within this latitude range, the flow over the intermediate continental slope is marked by a current inversion at a depth that is associated with the Intermediate Western Boundary Current (IWBC). A time series analysis of 10-current-meter mooring data was used to describe a mean vertical profile for the BC-IWBC jet and a typical meander vertical structure. The latter was obtained by an empirical orthogonal function (EOF) analysis that showed a single mode explaining 82% of the total variance. This mode structure decayed sharply with depth, revealing that the meandering is much more vigorous within the BC domain than it is in the IWBC region. As the spectral analysis of the mode amplitude time series revealed no significant periods, we searched for dominant wavelengths. This search was done via a spatial EOF analysis on 51 thermal front patterns derived from digitized AVHRR images. Four modes were statistically significant at the 95% confidence level. Modes 3 and 4, which together explained 18% of the total variance, are associated with 266 and 338-km vorticity waves, respectively. With this new information derived from the data, the [Johns, W.E., 1988. One-dimensional baroclinically unstable waves on the Gulf Stream potential vorticity gradient near Cape Hatteras. Dyn. Atmos. Oceans 11, 323-350] one-dimensional quasi-geostrophic model was applied to the interpolated mean BC-IWBC jet. The results indicated that the BC system is indeed baroclinically unstable and that the wavelengths depicted in the thermal front analysis are associated with the most unstable waves produced by the model. Growth rates were about 0.06 (0.05) days(-1) for the 266-km (338-km) wave. Moreover, phase speeds for these waves were low compared to the surface BC velocity and may account for remarks in the literature about growing standing or stationary meanders off southeast Brazil. The theoretical vertical structure modes associated with these waves resembled very closely to the one obtained for the current-meter mooring EOF analysis. We interpret this agreement as a confirmation that baroclinic instability is an important mechanism in meander growth in the BC system. (C) 2008 Elsevier B.V. All rights reserved.