Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Numerical and experimental study of tensile strength of single and double-strap repairs

Adhesive bonding as a joining or repair method has a wide application in many industries. Repairs with bonded patches are often carried out to re-establish the stiffness at critical regions or spots of corrosion and/or fatigue cracks. Single and double-strap repairs (SS and DS, respectively) are a viable option for repairing. For the SS repairs, a patch is adhesively-bonded on one of the structure faces. SS repairs are easy to execute, but the load eccentricity leads to peel peak stresses at the overlap edges. DS repairs involve the use of two patches, one on each face of the structure. These are more efficient than SS repairs, due to the doubling of the bonding area and suppression of the transverse deflection of the adherends. Shear stresses also become more uniform as a result of smaller differential straining. The experimental and Finite Element (FE) study presented here for strength prediction and design optimization of bonded repairs includes SS and DS solutions with different values of overlap length (LO). The examined values of LO include 10, 20 and 30 mm. The failure strengths of the SS and DS repairs were compared with FE results by using the Abaqus® FE software. A Cohesive Zone Model (CZM) with a triangular shape in pure tensile and shear modes, including the mixed-mode possibility for crack growth, was used to simulate fracture of the adhesive layer. A good agreement was found between the experiments and the FE simulations on the failure modes, elastic stiffness and strength of the repairs, showing the effectiveness and applicability of the proposed FE technique in predicting strength of bonded repairs. Furthermore, some optimization principles were proposed to repair structures with adhesively-bonded patches that will allow repair designers to effectively design bonded repairs.

Numerical prediction of delamination onset in carbon/epoxy composites drilling

Despite the fact that their physical properties make them an attractive family of materials, composites machining can cause several damage modes such as delamination, fibre pull-out, thermal degradation, and others. Minimization of axial thrust force during drilling reduces the probability of delamination onset, as it has been demonstrated by analytical models based on linear elastic fracture mechanics (LEFM). A finite element model considering solid elements of the ABAQUS® software library and interface elements including a cohesive damage model was developed in order to simulate thrust forces and delamination onset during drilling. Thrust force results for delamination onset are compared with existing analytical models.

A simple approach to numerical modelling of propane combustion in fluidized beds

A mathematical model is proposed for the evolution of temperature, chemical composition, and energy release in bubbles, clouds, and emulsion phase during combustion of gaseous premixtures of air and propane in a bubbling fluidized bed. The analysis begins as the bubbles are formed at the orifices of the distributor, until they explode inside the bed or emerge at the free surface of the bed. The model also considers the freeboard region of the fluidized bed until the propane is thoroughly burned. It is essentially built upon the quasi-global mechanism of Hautman et al. (1981) and the mass and heat transfer equations from the two-phase model of Davidson and Harrison (1963). The focus is not on a new modeling approach, but on combining the classical models of the kinetics and other diffusional aspects to obtain a better insight into the events occurring inside a fluidized bed reactor. Experimental data are obtained to validate the model by testing the combustion of commercial propane, in a laboratory-scale fluidized bed, using four sand particle sizes: 400–500, 315–400, 250–315, and 200–250 µm. The mole fractions of CO2, CO, and O2 in the flue gases and the temperature of the fluidized bed are measured and compared with the numerical results.

Experimental and numerical evaluation of composite repairs on wood beams damaged by cross-graining

An experimental and Finite Element study was performed on the bending behaviour of wood beams of the Pinus Pinaster species repaired with adhesively-bonded carbon–epoxy patches, after sustaining damage by cross-grain failure. This damage is characterized by crack growth at a small angle to the beams longitudinal axis, due to misalignment between the wood fibres and the beam axis. Cross-grain failure can occur in large-scale in a wood member when trees that have grown spirally or with a pronounced taper are cut for lumber. Three patch lengths were tested. The simulations include the possibility of cohesive fracture of the adhesive layer, failure within the wood beam in two propagation planes and patch interlaminar failure, by the use of cohesive zone modelling. The respective cohesive properties were estimated either by an inverse method or from the literature. The comparison with the tests allowed the validation of the proposed methodology, opening a good perspective for the reduction of costs in the design stages of these repairs due to extensive experimentation.

Numerical evaluation of three-dimensional scarf repairs in carbon-epoxy structures

The widespread employment of carbon-epoxy laminates in high responsibility and severely loaded applications introduces an issue regarding their handling after damage. Repair of these structures should be evaluated, instead of their disposal, for cost saving and ecological purposes. Under this perspective, the availability of efficient repair methods is essential to restore the strength of the structure. The development and validation of accurate predictive tools for the repairs behaviour are also extremely important, allowing the reduction of costs and time associated to extensive test programmes. Comparing with strap repairs, scarf repairs have the advantages of a higher efficiency and the absence of aerodynamic disturbance. This work reports on a numerical study of the tensile behaviour of three-dimensional scarf repairs in carbon-epoxy structures, using a ductile adhesive (Araldite® 2015). The finite elements analysis was performed in ABAQUS® and Cohesive Zone Modelling was used for the simulation of damage onset and growth in the adhesive layer. Trapezoidal cohesive laws in each pure mode were used to account for the ductility of the specific adhesive mentioned. A parametric study was performed on the repair width and scarf angle. The use of over-laminating plies covering the repaired region at the outer or both repair surfaces was also tested as an attempt to increase the repairs efficiency. The obtained results allowed the proposal of design principles for repairing composite structures.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Numerical 3D modeling of heat transfer in human tissues for microwave radiometry monitoring of Brown fat metabolismo

Background: Brown adipose tissue (BAT) plays an important role in whole body metabolism and could potentially mediate weight gain and insulin sensitivity. Although some imaging techniques allow BAT detection, there are currently no viable methods for continuous acquisition of BAT energy expenditure. We present a non-invasive technique for long term monitoring of BAT metabolism using microwave radiometry. Methods: A multilayer 3D computational model was created in HFSS™ with 1.5 mm skin, 3-10 mm subcutaneous fat, 200 mm muscle and a BAT region (2-6 cm3) located between fat and muscle. Based on this model, a log-spiral antenna was designed and optimized to maximize reception of thermal emissions from the target (BAT). The power absorption patterns calculated in HFSS™ were combined with simulated thermal distributions computed in COMSOL® to predict radiometric signal measured from an ultra-low-noise microwave radiometer. The power received by the antenna was characterized as a function of different levels of BAT metabolism under cold and noradrenergic stimulation. Results: The optimized frequency band was 1.5-2.2 GHz, with averaged antenna efficiency of 19%. The simulated power received by the radiometric antenna increased 2-9 mdBm (noradrenergic stimulus) and 4-15 mdBm (cold stimulus) corresponding to increased 15-fold BAT metabolism. Conclusions: Results demonstrated the ability to detect thermal radiation from small volumes (2-6 cm3) of BAT located up to 12 mm deep and to monitor small changes (0.5°C) in BAT metabolism. As such, the developed miniature radiometric antenna sensor appears suitable for non-invasive long term monitoring of BAT metabolism.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.

Experimental and numerical study on the evaluation of ventilation efficiency

Buildings account for 40% of total energy consumption in the European Union. The reduction of energy consumption in the buildings sector constitute an important measure needed to reduce the Union's energy dependency and greenhouse gas emissions. The Portuguese legislation incorporate this principles in order to regulate the energy performance of buildings. This energy performance should be accompanied by good conditions for the occupants of the buildings. According to EN 15251 (2007) the four factors that affect the occupant comfort in the buildings are: Indoor Air Quality (IAQ), thermal comfort, acoustics and lighting. Ventilation directly affects all except the lighting, so it is crucial to understand the performance of it. The ventilation efficiency concept therefore earn significance, because it is an attempt to quantify a parameter that can easily distinguish the different options for air diffusion in the spaces. The two indicators most internationally accepted are the Air Change Efficiency (ACE) and the Contaminant Removal Effectiveness (CRE). Nowadays with the developed of the Computational Fluid Dynamics (CFD) the behaviour of ventilation can be more easily predicted. Thirteen strategies of air diffusion were measured in a test chamber through the application of the tracer gas method, with the objective to validate the calculation by the MicroFlo module of the IES-VE software for this two indicators. The main conclusions from this work were: that the values of the numerical simulations are in agreement with experimental measurements; the value of the CRE is more dependent of the position of the contamination source, that the strategy used for the air diffusion; the ACE indicator is more appropriate for quantifying the quality of the air diffusion; the solutions to be adopted, to maximize the ventilation efficiency should be, the schemes that operate with low speeds of supply air and small differences between supply air temperature and the room temperature.

Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removal

This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.

Numerical Method to Predict Void Formation during The Liquid Composite Molding Process

Void formation during the injection phase of the liquid composite molding process can be explained as a consequence of the non-uniformity of the flow front progression. This is due to the dual porosity within the fiber perform (spacing between the fiber tows is much larger than between the fibers within in a tow) and therefore the best explanation can be provided by a mesolevel analysis, where the characteristic dimension is given by the fiber tow diameter of the order of millimeters. In mesolevel analysis, liquid impregnation along two different scales; inside fiber tows and within the open spaces between the fiber tows must be considered and the coupling between the flow regimes must be addressed. In such cases, it is extremely important to account correctly for the surface tension effects, which can be modeled as capillary pressure applied at the flow front. Numerical implementation of such boundary conditions leads to illposing of the problem, in terms of the weak classical as well as stabilized formulation. As a consequence, there is an error in mass conservation accumulated especially along the free flow front. A numerical procedure was formulated and is implemented in an existing Free Boundary Program to reduce this error significantly.

Numerical simulation of plasmonic effects in amorphous silicon induced by embedded aluminium nanoparticles

This work reports a theoretical study aimed to identify the plasmonic resonance condition for a system formed by metallic nanoparticles embedded in an a-Si: H matrix. The study is based on a Tauc-Lorentz model for the electrical permittivity of a-Si: H and a Drude model for the metallic nanoparticles. It is calculated the The polarizability of an sphere and ellipsoidal shaped metal nanoparticles with radius of 20 nm. We also performed FDTD simulations of light propagation inside this structure reporting a comparison among the effects caused by a single nanoparticles of Aluminium, Silver and, as a comparison, an ideally perfectly conductor. The simulation results shows that is possible to obtain a plasmonic resonance in the red part of the spectrum (600-700 nm) when 20-30 nm radius Aluminium ellipsoids are embedded into a-Si: H.

Strap repairs using embedded patches: numerical analysis and experimental results

Adhesively bonded repairs offer an attractive option for repair of aluminium structures, compared to more traditional methods such as fastening or welding. The single-strap (SS) and double-strap (DS) repairs are very straightforward to execute but stresses in the adhesive layer peak at the overlap ends. The DS repair requires both sides of the damaged structures to be reachable for repair, which is often not possible. In strap repairs, with the patches bonded at the outer surfaces, some limitations emerge such as the weight, aerodynamics and aesthetics. To minimize these effects, SS and DS repairs with embedded patches were evaluated in this work, such that the patches are flush with the adherends. For this purpose, in this work standard SS and DS repairs, and also with the patches embedded in the adherends, were tested under tension to allow the optimization of some repair variables such as the overlap length (LO) and type of adhesive, thus allowing the maximization of the repair strength. The effect of embedding the patch/patches on the fracture modes and failure loads was compared with finite elements (FE) analysis. The FE analysis was performed in ABAQUS® and cohesive zone modelling was used for the simulation of damage onset and growth in the adhesive layer. The comparison with the test data revealed an accurate prediction for all kinds of joints and provided some principles regarding this technique.