Papers by Keyword: Perturbation Method

Abstract: An interface crack between two semi-infinite piezoelectric/piezomagnetic media under out-of-plane mechanical load and in-plane electric and magnetic fields parallel to the crack faces is examined. A portion of the faces is electrically conducting and kept at a uniform magnetic potential, while the remaining portion is electrically and magnetically permeable. The coupled fields are represented by functions analytic in the plane outside the crack. With these representations, the mixed crack-face conditions lead to a combined Dirichlet–Riemann and Hilbert boundary-value problem, which is solved in closed form for arbitrary conductive versus permeable segment lengths. The solution yields explicit expressions for stresses, electric and magnetic fields, and the crack-face sliding (displacement jump). The singular behavior at both crack tips and at the transition between conducting and permeable zones is characterized, and intensity factors are defined accordingly. Parametric results illustrate how applied electric and magnetic fields modulate the fracture driving force; in particular, suitable magnetic loading can markedly reduce the mechanical stress intensity at the permeable tip. The formulas supply benchmark data for verification and enable design guidelines for tailoring electrode coverage and field application to mitigate interface fracture. The approach provides an analytic framework for mixed electromagnetic conditions in magnetoelectroelastic interface fracture.

Abstract: A new approach to evaluate the Newtonian flow between concentric rotating spheres is introduced in this paper. A general analytic solution to the problem is deduced using a perturbation method that takes into account the primary and secondary flows produced between the spheres, as well as an alternative analytical method. In order to exemplify the results of the previous analysis, six particular cases were studied. The results of the perturbation method show that under certain circumstances the secondary flow is no negligible, as is usually considered, but it is comparable to the value of the primary one. While the analytical method allows us to simulate the flow with results very similar to those of other authors.

Abstract: The paper considers the dynamic deformation features of constructional materials with nonlinear stress-strain dependence. For the one-dimensional shock waves with nonzero curvature arising in constructions under dynamic loading the propagation regularities are studied on the basis of the matched asymptotic expansions method. In the nonstationary problem with the longitudinal spherical shock wave the relations for simultaneous consideration of dynamic properties in the outer and inner problem of the perturbation method are obtained. The solution in the front-line area is constructed on the basis of the evolution equation different from ones for a plane longitudinal wave. The need for a solving of an additional ODE system for matching outer and inner expansions is shown. It is obtained that the outer solution asymptotics in the spherically symmetric problem contains waves reflected from the leading front in contrast to the solution behavior behind the front of the plane shock wave.

Abstract: This paper examines the problem of nonlinear heat transfer in a cylindrical solid of combustible materials with two-step exothermic kinetics and radiative heat loss to the ambient surrounding. The reactant diffusion and temperature dependent pre-exponential factors with respect to sensitized, Arrhenius, and bimolecular kinetics are taken into account in the model energy balanced equation. Both regular perturbation method and numerical shooting technique coupled with Runge-Kutta-Fehlberg iteration scheme are employed to tackle the nonlinear model problem. The effects of various thermophysical parameters on the reactive cylindrical solid temperature, Nusselt number and thermal stability are discussed quantitatively with the help of computational illustrations. It is found that radiative heat loss enhances thermal stability of the material while the two-step exothermic kinetics promotes the onset of thermal instability.

Abstract: This design of alcohol detection system uses DSP technology, ADF4350 frequency synthesizer chip developed microwave source controlled by DSP controller, the source excites the microwave resonator cavity, the output signal of the resonator is detected by the detector, then sampled and processed by the DSP processor, and the concentration of alcohol is calculated by perturbation theory and dielectric properties of alcohol. The human-computer interaction of this system is realized by touch screen, so that the display looks easy to operate and very user-friendly. This paper analyzes the feasibility of microwave resonant cavity perturbation method in alcohol materials, and derives the relationship between the concentration of alcohol mixed solution, the dielectric constant and the output frequency of the resonant cavity, and the theoretical basis of this paper is derived. The dielectric properties of different alcohol concentration at different frequencies were studied, and the standard curves of different concentration alcohol dielectric spectra were established by the theoretical model and a large number of experimental data.

Abstract: In order to improve working efficiency of photovoltaic (PV) system and decrease outputs fluctuation. A method of maximum power point tracking (MPPT) based on self-tuning fuzzy PID control is proposed. Based on analysis of typical PV cell characteristics, a combination of PID control and fuzzy control is proposed according to the shortage of perturbation and observation (P&O) method. The model of PV grid-connected system was established and simulated in Matlab. Results show that the method tracks changes of external solar intensity rapidly and accurately, and it makes PV system work with good dynamic and static performance. Besides, viewpoint that the higher of solar intensity, the more instability in the output parameters of PV cell is proposed.

Abstract: In order to improve the development using FPGA solar panels generating speed, through the study on the solar panel maximum power output perturbation method (MPPT) how to develop and how to improve the development efficiency were studied. This algorithm through MATLAB Simulink simulation is confirmed, then use generator to simulate the algorithm, and the algorithm is downloaded into the FPGA, the hardware co_simulation, design of MPPT circuit will be in accordance with the circuit parameters of the modified. Through the hardware circuit operating results, it is proved that the algorithm design of circuit is correct and meet the design requirements, also demonstrate the utility of using generator hardware co_simulation method for the development of FPGA. The development method can improve the design speed, shorten the reliability of control, the development cycle and reduce development costs, achieve a fully compatible and replace physical circuit.

Abstract: This paper presents the effect of surface roughness on soft elastohydrodynamic lubrication in circular contact with non-Newtonian lubricant. The time independent modified Reynolds equation, elastic equation and lubricant viscosity equation were formulated for compressible fluid. Perturbation method, Newton-Raphson method, finite different method and full adaptive multigrid method were implemented to obtain the film pressure, film thickness profiles and friction coefficient in the contact region at various the amplitude of surface roughness, surface speed of sphere, modulus of elasticity and radius of sphere. The simulation results showed that the film thickness in contact region depended on the profile of surface roughness. The minimum film thickness decreased but maximum film pressure and friction coefficient increase when the amplitude of surface roughness and modulus of elasticity increased. For increasing surface speeds, the minimum film thickness and friction coefficient increase but maximum film pressure decreases. When radius of sphere increases, the minimum film thickness increases but maximum film pressure and friction coefficient decrease.

Abstract: A stochastic analysis of multi-scale problem in honeycomb microstructure was introduced in this paper to determine the variation of macroscopic homogenized properties considering uncertainty of micro-property. By assuming the fluctuation of micro-property, specifically the Young's modulus, is in Gaussian normal distribution, the macroscopic (homogenized) properties was formulated in stochastic manner based on first order perturbation approach. Next, the macroscopic property of honeycomb microstructure considering the geometrical defect that might be occurred in manufacturing process was also predicted. The numerical results showed that even with minor geometrical defect could affect the macroscopic properties. It proved the essential of stochastic homogenization method in predicting the reliable macroscopic property for microstructure design.

Abstract: Using the convex model theory, the reliability-based analysis of frequency of the vibration control problem of structures with Interval parameters is discussed. Based on the theory of perturbation method, reliability analysis, and PNET method, the method of reliability-based analysis of eigenvalues of closed-loop vibration control systems with uncertain parameters is studied. And the distribution function of the random eigenvalues will not be computed other than their means and variances. The standard deviations of eigenvalues of the uncertain closed-loop systems can be used to estimate the reliability of frequency. The numerical results show that the present method is effective.