Volume 22, Issue 3-4

A nonlinear static aeroelastic methodology based on the coupled CFD/CSD approach has been developed to study the geometrical nonlinear aeroelastic behaviors of high-aspect-ratio or multi-material flexible aerial vehicles under aerodynamic loads. The Reynolds-averaged Navier–Stokes solver combined with the three-dimensional finite-element nonlinear solver is used to perform the fluid-structure coupling simulation. The interpolation technique for data transfer between the aerodynamic and structural modules employs radial basis function algorithm as well as dynamic mesh deformation. A high-aspect-ratio structure with multi-material is modeled by the finite element method to investigate the effects of geometrical nonlinearity on the aeroelastic behavior. Numerical simulations of the linear and nonlinear static aeroelasticity were conducted at transonic regime with different angles of attack. By comparing the aeroelastic behaviors of linear and nonlinear structure, it shows that geometrical nonlinearity plays an important role for flexible high-aspect-ratio wings undergoing the large static aeroelastic deformation and should be taken into account in aeroelastic analysis for such structures.

The numerical method developed in the current paper is based on the moving least squares (MLS) method. To this end, the MLS approximation method has been used, and a program has been made which can solve the system of Volterra integral equations (VIEs) with any number of equations and unknown functions. And then the proposed method is implemented on the system of linear VIEs with variable coefficients. The numerical examples are given that show the acceptable accuracy and efficiency of the proposed scheme.

The semilocal convergence using recurrence relations of a family of iterations for solving nonlinear equations in Banach spaces is established. It is done under the assumption that the second order Fréchet derivative satisfies the Hölder continuity condition. This condition is more general than the usual Lipschitz continuity condition used for this purpose. Examples can be given for which the Lipschitz continuity condition fails but the Hölder continuity condition works on the second order Fréchet derivative. Recurrence relations based on three parameters are derived. A theorem for existence and uniqueness along with the error bounds for the solution is provided. The R-order of convergence is shown to be equal to 3 + q when θ = ±1; otherwise it is 2 + q , where q ∈ (0, 1]. Numerical examples involving nonlinear integral equations and boundary value problems are solved and improved convergence balls are found for them. Finally, the dynamical study of the family of iterations is also carried out.

In this article, we discuss a dynamical stochastic model that represents the time evolution of income distribution of a population, where the dynamics develops from an interplay of multiple economic exchanges in the presence of multiplicative noise. The model remit stretches beyond the conventional framework of a Langevin-type kinetic equation in that our model dynamics is self-consistently constrained by dynamical conservation laws emerging from population and wealth conservation. This model is numerically solved and analysed to evaluate the inequality of income in correlation to other relevant dynamical parameters like the mobility M and the total income μ . Inequality is quantified by the Gini index G . In particular, correlations between any two of the mobility index M and/or the total income μ with the Gini index G are investigated and compared with the analogous quantities resulting from an additive noise model.

In this paper, a comparison between the experimental values for the kinetics of the fast redox reaction between Cu 2+ and S 2 O 3 2− and some possible variants of analogical modeling and numerical simulation for this pre-equilibrium reaction have been presented. One of them is based on a function with a periodical, strongly under-damped component. For a non-periodical fast damped evolution of reaction between Cu 2+ and S 2 O 3 2− , this paper proposes a variant of numerical modeling and simulation based on two exponential functions. For this complex reaction kinetics, the proposed approach based on application of neural networks is an efficient and accurate tool to solve modeling problems. The method ensures a good approximation of the experimental data, with a remarkable flexibility of analyses and synthesis as elaborated in the paper. The associated numerical simulation operates with an easy and flexible program, which allows the change in large limits of some structure parameters, for the adaptation of the numerical results with the experimental measurements.

This article presents the fuselage/main rotor coupling dynamics under a modal analysis to study the modes of oscillation. The authors provide a rotorcraft simulation model that captures complex dynamics, wherein the validation is done with existing theories. The model has been set up by using VehicleSim, software specialized in modelling mechanical systems composed by rigid bodies. It is presented a helicopter simulation framework, that allows to study the impact of the main rotor varying angular speed on the system. Moreover, the generated heterodyning behaviour and harmonics can be analysed on the fuselage. The detection of this performance is not a simple task, and this helicopter model provides an accurate system for its study using a short-time Fourier transform processing. The coupled dynamics observed between the fuselage and the main rotor indicate that the model can be a suitable tool to detect this type of performance.

In order to detect the gear tooth surface wear fault, this paper presents a new fault diagnosis method based on Symlets wavelet family multi-structure element difference morphological denoising and frequency slice wavelet transform (FSWT). Besides considering the gear backlash, time-varying mesh stiffness, gear error and bearing longitudinal response, and low frequency excitation caused by the torque fluctuation, random disturbance of damping gear ratio, gear backlash, excitation frequency, and meshing stiffness are also considered. Dynamics equations of a three degrees of freedom spur gear transmission system with tooth surface wear fault are established according to Newton’s laws. The 4–5 order variable step Runge–Kutta method has been used for solving the equations to get the vibration signal of the system. Then, the proposed method is applied to extract the wear fault signal, which verifies the feasibility and effectiveness of the proposed method.

In this article, compact finite difference approximations for first and second derivatives on the non-uniform grid are discussed. The construction of diffusion wavelets using compact finite difference approximation is presented. Adaptive grids are obtained for non-smooth functions in one and two dimensions using diffusion wavelets. High-order accurate wavelet-optimized compact finite difference (WOCFD) method is developed to solve convection–diffusion equations in one and two dimensions on an adaptive grid. As an application in option pricing, the solution of Black–Scholes partial differential equation (PDE) for pricing barrier options is obtained using the proposed WOCFD method. Numerical illustrations are presented to explain the nature of adaptive grids for each case.

The slider-crank mechanism is used widely in modern industrial equipment whereby the contact-impact of a revolute clearance joint affects the dynamic behavior of mechanical systems. Combining multibody dynamic theory and nonlinear contact theory, the computational methodology for dynamic analysis of the slider-crank mechanism with a clearance joint is proposed. The differential equations of motion are obtained considering the revolute clearance joint between the connecting rod and slider. In the mechanical system, the contact force is evaluated using the continuous force model proposed by Lankarani and Nikravesh, which can describe the contact-impact phenomenon accurately. Then, the experimental study is performed whereby the numerical results are compared with the test data to validate the proposed model. Moreover, the dynamic response analysis is conducted with various driving velocities and clearance sizes, which also explains that the sensitive dependence of a mechanical system on the revolute clearance joint.

In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

Consensus problem with faster convergence rate of consensus problem has been considered in this paper. Adding more edges such as that connecting each agent and its second-nearest neighbor or changing the consensus protocol such as mixing asymptotic terms and terms of finite-time has been proved to be possible ways in increasing the convergence rate of multi-agent system in this paper. Based on analysis of Laplacian matrix, increasing of the convergence rate has been proved using the second-smallest eigenvalue for the first method. Concerning the second method, advantages of asymptotic consensus protocol and finite-time consensus protocol have been mixed together with the help of homogeneity function and theory of Lyapunov. Simulation results using matlab are also presented to illustrate the newly designed consensus protocols in increasing the convergence rate.

The population balance equation (PBE) is one of the most popular integro-differential equations modeled for several industrial processes. The solution to this equation is usually solved using a numerical approach as the analytical solutions of such equations are not obtained easily. Typically, the available analytical solutions are limited and are based on momentous Laplace transform. In this study, the reduced equations of the PBE are obtained via the group analysis method. Two particulate cases involving aggregation, growth and nucleation are selected, the determining equations are solved and the reduced equations are solved via approximate methods. The approximate method involves the target solution of the nonlinear evolution equation, here the PBE, to be expressed as a polynomial in an elementary function which satisfies a particular ordinary differential equation termed as an auxiliary equation.

The main objects of this paper focus on the complex dynamics and chaos control of an electromagnetic valve train (EMV). A variety of periodic solutions and nonlinear phenomena can be expressed using various numerical techniques such as time responses, phase portraits, Poincaré maps, and frequency spectra. The effects of varying the system parameters can be observed in the bifurcation diagram. It shows that this system can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. Lyapunov exponents and Lyapunov dimensions are employed to confirm chaotic behavior for EMV. A proposed continuous feedback control method based on synchronization characteristics eliminated chaotic oscillations. Numerical simulations are utilized to verify the feasibility and efficiency of the proposed control technique. Finally, some robustness analysis of parametric perturbation on EMV system with synchronization control is confirmed by Lyapunov stability theory and numerical simulations.

The feedback control of Hopf bifurcation of nonlinear aeroelastic systems with asymmetric aerodynamic lift force and nonlinear elastic forces of the airfoil is discussed. For the Hopf bifurcation analysis, the eigenvalue problems of the state matrix and its adjoint matrix are defined. The Puiseux expansion is used to discuss the variations of the non-semi-simple eigenvalues, as the control parameter passes through the critical value to avoid the difficulty for computing the derivatives of the non-semi-simple eigenvalues with respect to the control parameter. The method of multiple scales and center-manifold reduction are used to deal with the feedback control design of a nonlinear system with non-semi-simple eigenvalues at the critical point of the Hopf bifurcation. The first order approximate solutions are developed, which include gain vector and input. The presented methods are based on the Jordan form which is the simplest one. Finally, an example of an airfoil model is given to show the feasibility and for verification of the present method.

In this paper, nonlinear dynamics study of a RLC series circuit modeled by a generalized Van der Pol oscillator is investigated. After establishing a new general class of nonlinear ordinary differential equation, a forced Van der Pol oscillator subjected to an inertial nonlinearity is derived. According to the external excitation strength, harmonic, subharmonic and superharmonic oscillatory states are obtained using the multiple time scales method. Bifurcation diagrams displayed by the model for each system parameter are performed numerically through the fourth-order Runge–Kutta algorithm.