Chemical reaction and variable viscosity effects on flow and mass transfer of a non-Newtonian visco-elastic fluid past a stretching surface embedded in a porous medium

This work deals with the study of the boundary layer flow and mass transfer of a visco-elastic fluid immersed in a porous medium over a stretching surface in the presence of surface slip, chemical reaction and variable viscosity. The partial differential equations governing the flow have been transformed by similarity transformation into a system of coupled nonlinear ordinary differential equations which is solved numerically by means of the fourth order Runge-Kutta integration scheme coupled with the shooting technique. The effects of various involved interesting parameters on the velocity fields and concentration fields are shown graphically and investigated. In addition, tabulated results for the local skin-friction coefficient and the local Sherwood number are presented and discussed.     

Nonlinear dynamics of an inclined beam subjected to a moving load

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the beam are obtained for various load velocity ratios and the outcome results have been illustrated and compared to the results with those obtained from traditional linear solution. The appropriate parametric study considering the effects of the linear viscous damping, the velocity of the traveling load, beam inclination angle under zero or nonzero axial load are carried out to capture the influence of the effect of large deflections caused by stretching effects due to the beam’s immovable ends. It was seen that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also in the case where the object leaves the inclined beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption. Moreover, the stability analysis of steady-state response for the modes equations having quadratic nonlinearity was carried out and it was observed from the frequency response curves that for the considered parameters in the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon can be predicted for the longitudinal excitation.     

Effects of small world connection on the dynamics of a delayed ring network

This paper presents a detailed analysis on the dynamics of a ring network with small world connection. On the basis of Lyapunov stability approach, the asymptotic stability of the trivial equilibrium is first investigated and the delay-dependent criteria ensuring global stability are obtained. The existence of Hopf bifurcation and the stability of periodic solutions bifurcating from the trivial equilibrium are then analyzed. Further studies are paid to the effects of small world connection on the stability interval and the stability of periodic solution. In particular, some complex dynamical phenomena due to short-cut strength are observed numerically, such as: period-doubling bifurcation and torus breaking to chaos, the coexistence of multiple periodic solutions, multiple quasi-periodic solutions, and multiple chaotic attractors. The studies show that small world connection may be used as a simple but efficient “switch” to control the dynamics of a system.     

Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams; a mechanical solution

This paper deals with enhancing the existing Finite Element formulations through employing basic principles of structural mechanics accompanied with mathematical techniques. Introducing the concept of Basic Displacement Functions (BDFs), the free vibration analysis of rotating tapered beams is studied from a mechanical point of view. It is shown that exact shape functions could be derived in terms of BDFs. The new shape functions turn out to be dependent on the rotational speed, circular frequency, the position of element along the beam and variation of cross-sectional dimensions along the element. Dynamic BDFs are obtained by applying Adomian Modified Decomposition Method (AMDM) to the governing differential equation of motion. Carrying out numerical examples, the competency of the method is verified.     

The effects of variable properties on MHD unsteady natural convection heat and mass transfer over a vertical wavy surface

A mathematical model will be analyzed in order to study the effects of variables viscosity and thermal conductivity on unsteady heat and mass transfer over a vertical wavy surface in the presence of magnetic field numerically by using a simple coordinate transformation to transform the complex wavy surface into a flat plate. The fluid viscosity is assumed to vary as a exponential function of temperature and thermal conductivity is assumed to vary linearly with temperature. An implicit marching Chebyshev collocation scheme is employed for the analysis. Numerical solutions are obtained for different values of variable viscosity, variable thermal conductivity and MHD variation parameter. Numerical results show that, variable viscosity, variable thermal conductivity and MHD variation parameter have significant influences on the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number.     

Modelling the effects of heavy alcohol consumption on the transmission dynamics of gonorrhea

Prior studies have indicated that heavy alcohol drinkers are likely to engage in risky sexual behaviours and thus, more likely to get sexually transmitted infections (STIs) than social drinkers. Here, we formulate a deterministic model for evaluating the impact of heavy alcohol drinking on the reemerging gonorrhea epidemic. The model is rigorously analysed, showing the existence of a globally asymptotically stable disease-free equilibrium whenever the reproductive number is less than unity. If the disease threshold number is greater than unity, a unique endemic equilibrium exists and is globally asymptotically stable in the interior of the feasible region and the disease persists at endemic proportions if it is initially present. Both analytical and numerical results are provided to ascertain whether heavy alcohol drinking has an impact on the transmission dynamics of gonorrhea.     

Study of the effect of thermal gradient on free vibration of clamped visco-elastic rectangular plates with linearly thickness variation in both directions

The effect of thermal gradient on the free vibration of clamped visco-elastic rectangular plate with linearly thickness variations in both the directions has been studied here. The governing differential equation has been solved using Rayleigh-Ritz technique. The frequency equation is derived for the clamped boundary condition on all the four edges. The effect of linear temperature variation has been considered. Deflection and time period corresponding to the first two modes of vibrations of a clamped plate have been computed for various values of aspect ratio, thermal constants, and taper constants.     

Nonlinear resonances in an axially excited beam carrying a top mass: simulations and experiments

In this paper, nonlinear resonances in a coupled shaker-beam-top mass system are investigated both numerically and experimentally. The imperfect, vertical beam carries the top mass and is axially excited by the shaker at its base. The weight of the top mass is below the beam’s static buckling load. A semi-analytical model is derived for the coupled system. In this model, Taylor-series approximations are used for the inextensibility constraint and the curvature of the beam. The steady-state behavior of the model is studied using numerical tools. In the model with a single beam mode, parametric and direct resonances are found, which affect the dynamic stability of the structure. The model with two beam modes not only shows an additional second harmonic resonance, but also reveals some extra small resonances in the low-frequency range, some of which can be identified as combination resonances. The experimental steady-state response is obtained by performing a (stepped) frequency sweep-up and sweep-down with respect to the harmonic input voltage of the amplifier-shaker combination. A good correspondence between the numerical and experimental steady-state responses is obtained.     

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

The multiple timescales method is applied to the exact partial differential equations of the planar motion of a hinged–simply supported beam with a linear axial spring of arbitrary stiffness. The forced-damped and free oscillations of the system around frequencies corresponding to nth natural bending mode are examined thoroughly and compared with numerical simulations as well as with already published results obtained by Lindstedt–Poincaré method. A special numerical technique using explicit finite element method to draw the frequency–response curves is appositely developed. The well-known jump phenomena between resonant and non-resonant branches, as well as superharmonic resonances, have been detected numerically.     

Utilizing nonlinear phenomena to locate grazing in the constrained motion of a cantilever beam

Grazing behavior in soft impact dynamics of a harmonically based excited flexible cantilever beam is investigated. Numerical and experimental methods are employed to study the dynamic behavior of macro- and micro-scale cantilever beam–impactor systems. For off-resonance excitation at two and a half times the fundamental frequency, the response of the oscillating cantilever experiences period doubling as the separation distance or clearance between the beam axis and the contact surface is decreased. The nonlinear phenomenon is studied by using phase portraits, Poincaré sections, and spectral analysis. Motivated by atomic force microscopy, this general dynamic behavior is studied as a means to locating the separation distance corresponding to grazing where the contact force is minimized.     

Relaxation oscillations,subharmonic orbits and chaos in the dynamics of a linear lattice with a local essentially nonlinear attachment

We study the dynamic interactions between traveling waves propagating in a linear lattice and a lightweight, essentially nonlinear and damped local attachment. Correct to leading order, we reduce the dynamics to a strongly nonlinear damped oscillator forced by two harmonic terms. One of the excitation frequencies is characteristic of the traveling wave that impedes to the attachment, whereas the other accounts for local lattice dynamics. These two frequencies are energy-independent; a third energy-dependent frequency is present in the problem, characterizing the nonlinear oscillation of the attachment when forced by the traveling wave. We study this three-frequency strongly nonlinear problem through slow-fast partitions of the dynamics and resort to action-angle coordinates and Melnikov analysis. For damping below a critical threshold, we prove the existence of relaxation oscillations of the attachment; these oscillations are associated with enhanced targeted energy transfer from the traveling wave to the attachment. Moreover, in the limit of weak or no damping, we prove the existence of subharmonic oscillations of arbitrarily large periods, and of chaotic motions. The analytical results are supported by numerical simulations of the reduced order model.     

Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation

In this paper an analysis has been made to study heat and mass transfer in two-dimensional stagnation-point flow of an incompressible viscous fluid over a stretching vertical sheet in the presence of buoyancy force and thermal radiation. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations containing Prandtl number, Schmidt number and Sherwood number which are solved numerically with appropriate boundary conditions for various values of the dimensionless parameters. Comparison of the present numerical results are found to be in excellent with the earlier published results under limiting cases. The effects of various physical parameters on the boundary layer velocity, temperature and concentration profiles are discussed in detail for both the cases of assisting and opposing flows. The computed values of the skin friction coefficient, local Nusselt number and Sherwood number are discussed for various values of physical parameters. The tabulated results show that the effect of radiation is to increase skin friction coefficient, local Nusselt number and Sherwood number.     

The cross-correlations of stock markets based on DCCA and time-delay DCCA

In this paper, the Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) are used to investigate the stock markets. The DFA method is a widely-used method for the determination and detection of long-range correlations in stock time series. DCCA is a recently developed method to quantify the cross-correlations of two non-stationary time series. We report the results of correlation and cross-correlation behaviors in US and Chinese stock markets by using the DFA and DCCA methods, respectively. The DCCA shows that there exists some crossovers in the cross-correlation fluctuation function versus time scale of stock absolute returns. The cross-correlations in Chinese stock markets are stronger than those between Chinese and US stock markets. After documenting the equal-time cross-correlations using DCCA method, we study the dynamics of cross-correlations of stock series based on a time-delay. The time-dependence of the underlying cross-correlations is monitored using a time window by step of 1 day. An interesting finding is that the cross-correlation exponents and crossovers demonstrate periodical uncertainty changing with the time-delay.     

Impulsive control induced effects on dynamics of single and coupled ODE systems

The dynamics of differential system can be changed very obviously after inputting impulse signals. Previous studies show that the single chaotic system can be controlled to periodic motions using impulsive control method. It was well known that the dynamics of hyper-chaotic and coupled systems are very important and more complex than those of a single system. In this paper, particular impulsive control of the hyper-chaotic Lü system was proposed, which is with outer impulsive signals. It can be seen that such impulsive strategy can generate chaos from periodic orbit or control chaos to periodic orbit etc. For the first time, impulsive control induced effects on dynamics of coupled systems are considered in this paper, where the impulse effect has outer input signals. Many interesting and useful results are obtained. The coupled system can realize synchronization and its synchronization manifold can be changed with such impulsive control signals. Strict theories are given, and numerical simulations confirm the correctness of theoretical results.     

Control of vibration on a hinged-hinged beam under a non-ideal excitation using RLC circuit with variable capacitance

In this paper, a model using RLC circuits with variable capacitance is used to control the vibration of a hinged-hinged beam supporting unbalanced machine capable of a limited power output. The modelling of the controlled system is based on the variational principle. Using the numerical simulation, the system is found to show saturation phenomenon leading to the effectiveness of the control characterized by the reduction of the amplitudes of vibration of the mechanical structure. The mathematical approach is then used to give some analytical expressions of the results obtained from the numerical simulation.     

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.     

The influence of the axial force on the vibration of the Euler–Bernoulli beam with an arbitrary number of cracks

The exact closed-form solution for the vibration modes and the eigen-value equation of the Euler–Bernoulli beam-column in the presence of an arbitrary number of concentrated open cracks is proposed. The solution is provided explicitly as functions of four integration constants only, to be determined by the standard boundary conditions. The enforcement of the boundary conditions leads the exact evaluation of the vibration frequencies as well as the buckling load of the beam-column and the corresponding eigen-modes. Furthermore, the presented solution allows a comprehensive evaluation of the influence of the axial load on the modal parameters of the beam. The cracks, which are not subjected to the closing phenomenon, are modelled as a sequence of Dirac’s delta generalised functions in the flexural stiffness. The eigen-mode governing equation is formulated over the entire domain of the beam without enforcement of any further continuity condition. The influence of the axial load on the vibration modes of beam-columns with different number and position of cracks, under different boundary conditions, has been analysed by means of the proposed closed-form expressions. The presented parametric analysis highlights some abrupt changes of the eigen-modes and the corresponding frequencies.     

Periodicity detection on the parameter-space of a forced Chua’s circuit

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim to build the Periodicity-parameter-space (P-parameter-space). As results of the P-parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.     

The genic mutation on dynamics of a predator–prey system with impulsive effect

In this work, we consider a genic mutational predator?Cprey system with birth pulse and impulsive cutting on prey population at different moments. All the solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the globally asymptotically stable predator-extinction boundary periodic solution of the investigated system are obtained. The permanent conditions of the investigated system are also obtained. Finally, numerical simulations are inserted to illustrate the results. Our results present that the genic mutational rate plays an important role on the permanence of the investigated system. Our results also provide reliable tactic basis for the practical biological economics management.