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Taking the steam turbine cracked rotor system coupling multi-fault as an example, this paper reports systematic numerical experiments exploring two-parameter periodic complexification cascades. Specifically, we report high-resolution phase diagrams predicting and describing how the periodic sequences unfold over a quite extended range of parameter planes. Surprisingly, such diagrams reveal that the distribution of periodic sequences either agrees well with the characteristics of “eye” of chaos, or is characterized by the derived Farey sum tree and the bidirectional symmetrical Stern–Brocot sum tree. These cascades show that the frequent occurrence of transient multi-period motion is a generic feature for the large rotating machinery system with multi-fault. And the paper obtains a cluster of sequences of the Farey sum tree and the Stern–Brocot sum tree specially suitable for the large nonlinear and nonautonomous systems, which can provide a powerful reference for failure prediction and parameter matching.

Abstract: Electric hand dryers are more environmentally friendly than hand towels to eliminate solid waste and reduce maintenance of refilling. Hand dryers can attract microbes from the floor or wall. Likewise, hand towel attracts microbes from the environment. We present a two-stage (ozone and plasma) disinfection electric hand dryer to dry hands through viral free air. Ozone can disinfect dryers’ wet internal surfaces and air but can be dangerous in high concentrations. We use it for two seconds to disable microbes by 90%. In air exhaust, there are a pair of plasma generators deactivating the remaining microbes and ozone at the air outlet. With the combination use of ozone and plasma, 99.9% of microbes were disabled. Plasma accelerates the neutralization of ozone to oxygen at the outlet.

In the present article the nonlinear control method is used for dual phase and dual anti-phase synchronizations among fractional order chaotic systems with uncertainties. The control functions are designed to achieve synchronization with the help of nonlinear control technique. The nonlinear control method is found to be very effective and convenient to achieve dual phase and dual anti-phase synchronization with parametric uncertainties of the non-identical chaotic systems. The fractional order real and complex chaotic systems with parametric uncertainties are taken to illustrate dual phase and dual anti-phase synchronization process. Numerical simulation results show the possibility of dual phase and dual anti-phase synchronizations, which are carried out using Adams–Bashforth–Moulton method and graphical results are presented to display the effectiveness of the method. The striking feature of the article is the graphical demonstration of fast communication through signals between transmitter and receiver for the complex variable systems compared to the real variable systems.

The paper devotes to the synthesis of synchronizability and mode-locking of two scaled quadratic maps via symmetric direct-coupling. Present research shows that, similar to diffusive-coupling, the direct-coupling also admits all synchronized motions. Nevertheless, the synchronized motions are degenerated to the controlled dynamics instead of the pseudo-orbits of the local map. In consideration of chaos synchronization, nonlinear perturbations on the synchronized subspace are employed to perform the synchronization stability analysis. The synchronizability is also surveyed from a different perspective through investigating the synchronization of the coupled chaotic map in the presence of small parameter mismatch. The emergence of mode-locking phenomena in two-dimensional parameter space is secondary but proclaims the existence of incomplete synchronization.

In this article, the stability analysis, chaos control and the function projective synchronization between fractional order identical satellite systems have been studied. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate and incommensurate fractional order systems are discussed. Feedback control method is used to control the chaos in the considered fractional order satellite system. Using the fractional calculus theory and computer simulation, it is found that the chaotic behavior exists in the fractional order satellite system and the lowest order of derivative where the chaos exits is 2.82. Adams-Bashforth-Moulton method is applied during numerical simulations and the results obtain are displayed through graphs.

The paper presents a novel synchronization scheme for uncertain chaotic systems via complete-adaptive-impulsive controls. The controllers are designed in the form of linear-error feedback coupling, but the control gains are completely adaptive. More details on minimizing interaction terms and accelerating synchronization process are revealed. The interaction terms can be selected on the largest invariant set minimally, but would be optimized corroboratively to promote the stabilization. The analytic expressions of parameter update laws for identifying uncertain parameters are derived from a reasonable truncation directly. A representative chaotic system is employed to show that the present scheme is not only a tactful way of synchronizing chaotic systems with uncertainties imposed on nonlinear terms, but a more radical approach on achieving synchronization with relatively moderate control gains than existed methods.

A novel class of nanoplate-based mass sensor with corner point supports for detecting attached nanoparticles is proposed. Exact solutions for vibrations of three types of nanoscale mass sensors are obtained by a symplectic superposition method combining with nonlocal elasticity theory. A comparison between theoretical prediction and FEM simulation is presented and excellent agreement is reported. Influences of design parameters on the frequency shift are investigated. Numerical results show that increasing magnetic field strength and environment temperature can effectively enhance the sensitivity of the mass sensor, and the nanoplate-based sensor point-supported at only one corner is the optimal design.

A finite element discretized symplectic method is introduced to compute directly the intensity factors of cracked piezoelectric materials. After modeling by the conventional finite elements, the cracked body is divided into two regions: near and far fields. The unknowns in the far field are unchanged while the displacements, electric potentials, stresses and electric displacements in the near field are expanded in symplectic eigenfunctions and their coefficients are taken as unknowns. No new finite element is needed. The intensity factors, energy release rates and analytical expressions of the mechanical and electric fields near the crack are obtained simultaneously without any post-processing.

The present paper is based on CFD modelling of gas–solid flow in cyclone separators with different dust outlet geometries (with and without down-comer tubes at the cyclone bottom) to analyse the flow characteristics and the cyclone performance. Numerically obtained cyclone performance parameters, collection efficiency, and pressure drop were compared with experimental results. Changes in the particle trajectories due to the variation of the flow field inside the cyclone separators with the effect of the dust outlet section were also analysed in detail. The simulation results largely agreed with the experimental results, and discrepancies were caused by modelling limitations and inconsistencies of the particle tracking model with the real gas–solid flow. However, comparable to the experiments, the CFD simulations also predicted the increments in collection efficiencies by dust outlet geometries modified with down-comers within acceptable pressure drops.

The paper proposes a novel calculation method on the sensitivity analysis of bifurcation parameters and states in a single-degree-of-freedom (SDoF) impacting system. It presents the causes to (non-) smooth bifurcations in virtue of parameter sensitivity analysis. The derivation of the system’s Poincaré mappings is used to integrate the Floquet matrix. It performs the identifications of the main and the most sensitive bifurcation parameters by disturbing the eigenvalues of Floquet matrix. Moreover, the ones that have appreciable effect on the dynamic characteristics of the system can be effectively identified from entire bifurcation parameters and states. The coexistence of distinct attractors is demonstrated with the parameter sensitivity analysis on the Floquet matrix associated with bifurcation parameters and states. It also considers the cooperating dynamic performance on the two-dimensional parameter space by varying different pairs of bifurcation parameters.

A symplectic approach based on the Hamiltonian system is proposed to analyze the electroelastic singularities and intensity factors of an interface crack in piezoelectric–elastic bimaterials. By introducing a total unknown vector consisting of generalized displacements and stresses, the Lagrangian equations are transformed to the Hamiltonian equations which can be solved by using the method of separation of variables. The total unknown vector can be expanded analytically in symplectic eigensolutions series (zero- and non-zero-eigensolutions). The unknown coefficients of the eigensolutions series are determined from the continuity conditions at the interface (electric conductor/insulation conditions) and outer boundary conditions. The study concludes that electroelastic singularities and intensity factors directly depend on the first few terms of non-zero-eigensolutions. Numerical examples for various conditions are given to show variations of singularity orders and intensity factors. These analyses may provide some guidance for the design of piezoelectric–elastic bimaterial system.

A finite element discretized symplectic method is proposed to compute the stress intensity factors (SIFs) of interface cracks in multi-material composites subjected to anti-plane loading. The whole body is divided into a near field containing a crack to be solved analytically and a far field to be solved by conventional finite elements. In the near field, analytical series solutions are found by the Hamiltonian formulation. The unknown displacements of the densely populated finite elements are transformed to a handful of unknown coefficients of the series. After combining with the far field, the SIFs are actually the first few coefficients.

An adaptive-feedback control scheme for identical synchronizing two linearly coupled chaotic systems and identifying uncertain parameters is proposed. In comparison with the previous methods it inherited, the present scheme is more flexible and accessible. This is because that the prerequisites on the given chaotic systems are much looser, and the adaptive-feedback controllers involved are relatively independent. Moreover, the present scheme is a thoroughly amendatory one by which the uncertain parameters can be identified. Three concrete chaotic systems are employed to show the effectiveness of the presented scheme. In addition, how the coefficient in the adaptive law affects the convergence rate and the final strength is studied numerically.

A new-finite element discretized symplectic method for solving the steady-state heat conduction problem with singularities in composite structures is presented. The model with a singularity is divided into two regions, near and far fields, and meshed using conventional finite elements. In the near field, the temperature and heat flux densities are expanded in exact symplectic eigensolutions. After a matrix transformation, the unknowns in the near field are transformed to coefficients of the symplectic series, while those in the far field are as usual. The exact local solutions for temperature and heat flux densities are obtained simultaneously without any post-processing.

In this paper, an efficient analytical solution method, namely, multi-level residue harmonic balance, is introduced and developed for the nonlinear vibrations of multi-mode flexible beams on an elastic foundation subject to external harmonic excitation. The main advantage of this solution method is that only one set of nonlinear algebraic equations is generated in the zero level solution procedure while the higher level solutions for any desired accuracy can be obtained by solving a set of linear algebraic equations. In other words, the computation effort to find more accurate nonlinear solutions is much less. In this paper, a multi-mode formulation, which represents the nonlinear beam vibration, is derived and set up. Then, the solution procedures are developed for obtaining the nonlinear multi-mode solution. The results from the multi-level residue harmonic balance method agree well with those from a numerical integration method. The effects of various parameters such as vibration amplitude, foundation modulus coefficient, damping factor and excitation level etc., on the nonlinear behaviors are examined. A convergence study is also performed to verify the solutions. The stability analysis is conducted using the virtue of Floquet theory and steady-state solutions are investigated.

This study addresses the research on the noise and vibration correlation of a bridge movement joint. The aim of this research is to assess the noise induced by the vibration of a bridge movement joint without lane closure during the operation period. There are two methods of developing the correlation between the tyre/joint noise and vibration: (i) Direct Sound and Vibration Measurement Method, (ii) Acoustic-Box-in-Vehicle Method. The first one is the measurements of the vibration change at a bridge movement joint and roadside noise change induced when a control vehicle is passing it (this one requires lane closure). The correlation between the vibration change and roadside noise change is plotted according the measurement data. The second one is the measurements of the structure-borne noise change in an acoustic box installed into the control vehicle and roadside noise change induced. Similarly, the correlation between the structure-borne noise change and roadside noise induced is plotted. It is found that the two correlations are linear and similar to each other, even though the roadside noise is nonlinearly increasing against the control vehicle speed.

In this paper, a symplectic method based on the Hamiltonian system is proposed to analyze the interfacial fracture in the piezoelectric bimorph under anti-plane deformation. A set of Hamiltonian governing equations is derived from the Hamiltonian function by introducing dual variables of generalized displacements and stresses which can be expanded in series in terms of the symplectic eigensolutions. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. The stress\electric displacement intensity factors and energy release rates (G) directly relate to the first few terms of the nonzero eigenvalue solutions. The two ideal crack boundary conditions, namely the electrically impermeable and permeable crack assumptions, are considered. Numerical examples including the complex mixed boundary conditions are considered to show fracture behaviors of the interface crack and discuss the influencing factors.

We investigate the steady state response of a simply supported viscoelastic column subject to axial harmonic excitation. The viscoelastic material is modeled in fractional derivative Kelvin sense. The equation of motion is derived and discretized by the Galerkin approximation resulting in a generalized Mathieu–Duffing equation with time delay. Bifurcations in parametric excitation can be eliminated by appropriate feedback gain and time delay. The bifurcating behavior for various fractional orders and material ratios are also investigated. New criteria of stability determination are established. Based on the Runge–Kutta method, numerical results are obtained and compared with analytical solutions for verification.

When rewriting the governing equations in Hamiltonian form, analytical solutions in the form of symplectic series can be obtained by the method of separation of variable satisfying the crack face conditions. In theory, there exists sufficient number of coefficients of the symplectic series to satisfy any outer boundary conditions. In practice, the matrix relating the coefficients to the outer boundary conditions is ill-conditioned unless the boundary is very simple, e.g., circular. In this paper, a new two-level finite element method using the symplectic series as global functions while using the conventional finite element shape functions as local functions is developed. With the available classical finite elements and symplectic series, the main unknowns are no longer the nodal displacements but are the coefficients of the symplectic series. Since the first few coefficients are the stress intensity factors, post-processing is not required. A number of numerical examples as well as convergence studies are given.

The method of symplectic series discretized by finite element is introduced for the stress analysis of structures having cracks at the interface of dissimilar materials. The crack is modeled by the conventional finite elements dividing into two regions: near and far fields. The unknowns in the far field are as usual. In the near field, a Hamiltonian system is established for applying the method of separable variables and the solutions are expanded in exact symplectic eigenfunctions. By performing a transformation from the large amount of finite element unknowns to a small set of coefficients of the symplectic expansion, the stress intensity factors, the displacements and stresses in the singular region are obtained simultaneously without any post-processing. The numerical results are obtained for various cracks lying at the bi-material interface, and are found to be in good agreement with the reference solutions for the interface crack problems. Some practical examples are also given.

This article deals with the anti-synchronization between two identical chaotic fractional-order Qi system, Genesio–Tesi system, and also between two different fractional-order Genesio–Tesi and Qi systems using active control method. The chaotic attractors of the systems are found for fractional-order time derivatives described in Caputo sense. Numerical simulation results which are carried out using Adams–Boshforth–Moulton method show that the method is reliable and effective for anti-synchronization of nonlinear dynamical evolutionary systems.

In this article, the active control method is used to investigate the hybrid phase synchronization between two identical Rikitake and Windmi systems, and also between two nonidentical systems taking Rikitake as the driving system and Windmi system as the response system. Based on the Lyapunov stability theory, the sufficient conditions for achieving the hybrid phase synchronization of two chaotic systems are derived. The active control method is found to be very effective and convenient to achieve hybrid phase chaos synchronization of the identical and nonidentical chaotic systems. Numerical simulation results which are carried out using the Runge–Kutta method show its feasibility and effectiveness for the synchronization of dynamical chaotic systems.

The nonlinear single-mode dynamic behaviour of the viscoelastic arch whose damping is governed by fractional derivatives is considered. A set of ordinary differential equations is derived for the primary resonance and is solved by the residue harmonic homotopy to obtain all the steady state solutions. A parametric study is carried out to determine the influence of the viscoelastic damping characteristics of the material on the responses. Both the fractional order and material modulus ratio are effective in enhancing the stability of the structure. Multiple bifurcation solutions, jump phenomenon, saddle-node are observed analytically without numerical integration and are confirmed by numerical integration.

An analytical method is presented for finding the complex stress intensity factors (SIFs) and T-stress at an edge bi-material interface crack. A Hamiltonian system is first established by introducing dual (conjugate) variables of displacements and stresses whose solutions are expanded in terms of the symplectic series. With the aid of the adjoint symplectic orthogonality, coefficients of the series are determined by the boundary conditions along the crack faces and along the external geometry. Analytical solutions of SIFs and T-stress are obtained simultaneously. Numerical examples including the complex mixed boundary conditions are given. Factors influencing the SIFs are discussed.

We use the residue harmonic balance scheme to study the periodic motions of a class of second-order delay-differential equations with cubic nonlinearities near and after Hopf bifurcation. The multiple solutions are found by homotopy continuation. Then, the approximation to any desired accuracy for a specific solution is captured by solving linear equations iteratively. The second-order solutions give good predictions for the frequency and amplitude, which are verified by the Runge–Kutta numerical solutions. Two typical examples, the temporal dynamics of the delay Liénard oscillator and the delay feedback Duffing system, are studied and compared. The results show how to trace analytically the relevant effect of the stiffness coefficient and the time delay on the dynamics and on the number of periodic solutions, even for large values of the bifurcation parameters.

For the coupled static and dynamic buckling of thin walled beam subjected to various forces, such as axial force, uniform bending moment, and bending moment due to concentrated and distributed lateral forces, the spline finite element method is employed to obtain the dynamic stiffness matrix. Second order effects of the axial force and moment are considered. A doubly symmetric cantilever beam with uniform cross-section is investigated. Extensive static and dynamic interaction diagrams are plotted. The effects of warping rigidity, torsional rigidity, axial tension and compression on moment buckling, moment on axial buckling compression, higher buckling modes are discussed in detail. The spline finite element method is proved to be very efficient for the present problem and many interaction diagrams can be plotted easily. Some new results are presented. The methodology is based on finite element formulation and therefore it can be easily extended to analyze structural frames.

The residue harmonic balance is developed for coupled systems exemplified by the damped Duffing resonator driven by a van der Pol oscillator. This technique combines the features of harmonic balance and parameter bookkeeping to obtain approximate solutions to any desired accuracy. For the two degrees of freedom system, the zeroth-order approximation uses just one Fourier term resulting in a set of two nonlinear algebraic equations that can be solved analytically. The unbalanced residue due to Fourier truncation is improved by solving linear equations that automatically increase the number of terms to balance the previous truncation completely. Highly accurate bifurcation frequencies for various parameters are obtained and are verified by numerical integration results. The effects of the coupling stiffness on the angular frequency and amplitude of steady state response are investigated. The effects of the nonlinear damping are also studied.

The severity of aneurysmal subarachnoid hemorrhage (SAH) is often assessed by the clinical state of the patient on presentation, but radiological evaluation of the extent of hemorrhage has rarely been examined in the literature. Several CT scan based grading systems exist yet only a few studies have investigated interobserver agreement. We evaluated five radiological grading systems and assessed their clinical value for early prognostication.This was a retrospective study of patients diagnosed with aneurysmal SAH with a CT scan performed within 72 hours of symptom onset. Four independent observers, blinded to patient outcome, evaluated each scan using the five grading systems. A separate assessor determined 6 month outcome from clinical records. The primary outcome was interobserver agreement for each grading system using the Fleiss κ statistic. The secondary endpoint was the 6 month modified Rankin Scale score, with poor outcome defined as a score of 4-6.165 patients with a mean age of 59 years were assessed. Interobserver agreement for the Fisher, modified Fisher, Claassen, Barrow Neurological Institute, and Hijdra grading systems were as follows: k=0.53 (moderate), k=0.42 (moderate), k=0.38 (mild), k=0.20 (poor), and k=0.66 (good), respectively. The only independent clinical risk factor for poor outcome was a World Federation of Neurological Surgeons (WFNS) grade of 4 or 5 (adjusted OR 6.55; p0.05). After adjusting for confounders, Fisher grade 4 (adjusted OR 17.84), modified Fisher grade 4 (adjusted OR 5.65), and Hijdra grade 3 (adjusted OR 3.34) were associated with poor outcome. Receiver operator characteristic analysis revealed that the Hijdra grading system (area under the curve=0.76) was more predictive of outcome compared with the Fisher and modified Fisher systems. A Hijdra cut-off score of 22 was associated with poor outcome (adjusted OR 5.92).The Hijdra grading system had the best interobserver agreement and was a better independent early predictor for 6 month clinical outcome than the other systems. A Hijdra score ≥22 was associated with poor outcome.

This study investigates the effect of dietary fat on the testosterone (T) pharmacokinetics in hypogonadal men following administration of a self-emulsifying capsule formulation of oral T undecanoate (TU). In an open-label, 2-center, 5-way crossover study, a single oral dose of TU containing 300-mg equivalents of T (maximum anticipated human dose per administration) was administered to 16 hypogonadal men with a washout period of at least 5 days between doses. All participants were randomized to receive the TU capsules fasting or 30 minutes after an approximately 800-calorie meal containing 10%, 20%, 30%, or 50% fat. Serial blood samples were collected from 2 hours predose to 25 hours postdose to determine serum T and dihydrotestosterone (DHT) by liquid chromatography tandem mass spectrometry. Administering TU with a meal increased serum T concentrations, with the magnitude of the increase being directly dependent on the amount of fat in the meal. Average and peak serum T concentrations and area under the curve increased as the fat content of the meal was increased. Neither the high-fat meal (50% fat) nor the lower-fat meal (20% fat) showed a significant food effect relative to the normal-fat (Western diet) meal (30% fat). However, administering TU while fasting resulted in 50% or less of the cumulative exposure obtained when administered with 20%- to 50%-fat meals (albeit still substantial). A very-low-fat meal (10% fat) showed a significant food effect relative to the normal meal, but still exceeded the fasting condition by approximately 50%. Serum DHT concentrations showed corresponding increases to the serum T. As expected with the maximum anticipated clinical dose of TU (300 mg T), oral administration of this new formulation with food containing 20% to 50% dietary fat produced T levels at or above the upper range of adult men, and T levels trended higher as dietary fat content increased. Only with a very-low-fat diet (10%) or in a fasted state did a clinically significant food effect occur, but even then sufficient TU was absorbed with the self-emulsifying TU formulation to produce average serum T concentration predicted to be in the normal reference range (10 to 35 nmol/L).

Due to the high complexity and difficulty involved, the behavior of plastic hinge of reinforced concrete members has been previously investigated experimentally. This work investigates the plastic hinge analytically, using the finite element method. Lengths in the plastic hinge region involving rebar yielding zone, concrete crushing zone and curvature localization zone are studied systematically, under different parameters. The results show that none of the existing empirical models is adequate for prediction of plastic hinge length. As high non-linearity occurs in plastic hinge zones, the phenomenon of chaos is observed, for the first time, in flexural response of reinforced concrete structures.