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This paper proposes a method for studying formal stability of equilibrium points in multiparameter Hamiltonian systems with three degrees of freedom. We detail a technique for the symbolic computation of resonance conditions, employing computer algebra and power geometry to represent the resonant variety as a rational algebraic curve and provide its polynomial parametrization. A non-trivial example of formal stability investigation is considered. An implementation of resonant variety calculations in the computer algebra system Maple is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a methodology to design genuinely two-dimensional (2D) second-order well-balanced path-conservative central-upwind (PCCU) schemes. The scheme studies dam-break with high sediment concentration over abrupt moving topography quickly spatially variable even in the presence of the resonance. This study is possible via a 2D hyperbolic sediment transport model (including arbitrarily sloping sediment beds and associated energy and entropy) in new generalized Shallow Water equations derived with associated energy and entropy in this work. We expose some properties of the model and we establish an existence result of global weak solutions. In addition, we show the convergence of a sequence of solutions of the proposed new model. The second-order accuracy of the PCCU scheme is achieved using a new extension AENO (Averaging Essentially Non-Oscillatory) reconstruction developed in the 2D version of this work. We prove that the derived 2D scheme is well-balanced, positivity-preserving and steady states capturing. Several dam break tests are made to show the ability and the superb performances of the proposed numerical modeling. The proposed method can help to address many engineering problems.

A method for symbolic computation of a condition of existence of a third- and fourth-order resonance for investigations of formal stability of an equilibrium state of a multiparameter Hamiltonian system with three degrees of freedom in the case of general position is proposed. This condition is formulated in the form of zeros of a quasi-homogeneous polynomial of the coefficients of the characteristic polynomial of the linear part of the Hamiltonian system. Computer algebra (Gröbner bases of elimination ideals) and power geometry (power transformations) are used to represent this condition for various resonance vectors in the form of rational algebraic curves. Given a linear approximation of the characteristic polynomial in the space of its coefficients, these curves are used to obtain a description of a partition of the stability domain into parts in which there are no strong resonances. An example of a description of resonance sets for a two-parameter pendulum-type system is given. All computations are carried out in the computer algebra system Maple. [ABSTRACT FROM AUTHOR]

Herein, an approach for the dynamic response of a four-beam system with arbitrary boundary conditions when subjected to successive moving loads is proposed. Based on the proposed method, the resonance condition of high-speed railway simply-support beam bridge with ballastless track-structure under moving train loads has been studied. Sine-Fourier series is an effective method that can play a key role in solving, particularly in transforming the infinite-degree-of-freedom four-beam system into a superimposed four-degrees-of-freedom system. The effect of boundary conditions of the track-structure on the dynamic response of the bridge was analyzed. It is concluded that obtaining the resonant speed of the bridge with ballastless track-structure via single-beam system is not the best route because the track-structure has an impact on the resonance characteristics of the bridges. Compared with previous studies, the four-degrees-of-freedom system obtained by proposed method greatly reduces the difficulty of calculating the natural vibration frequency. Thus, the resonant speed of any HSRSSBB could be quickly obtained, avoiding the dynamic response calculations. The analysis of the resonant speed conversion factor indicates that neglecting the track-structure can drastically overestimate the resonant speed of the bridge. The overestimation is particularly noticeable on the girders of lower mass, which are critical in engineering. [ABSTRACT FROM AUTHOR]

The pantograph-catenary system is used in modern electrified railways to power electric trains. Common sense is that the increase of train speed leads to a deterioration of the interaction performance. But recent studies indicate that a higher speed may result in a better performance in some local speed regions. This paper is the first attempt to provide a theoretical explanation for this phenomenon. A validated pantograph-catenary model is built to reproduce this phenomenon. Referring the definition of critical speed in moving load problems, the catenary's critical speed is defined. The wavelength components can be extracted through the Fourier transformation to the contact wire's vertical mode shape. The speed that satisfies the resonance condition can be regarded as the potential critical speed. The corresponding contact wire amplitude is further evaluated to determine the critical speeds at a given mode. The analysis indicates that a good interaction performance happens when the speed falls in the transition procedure between the critical two speeds. Based on this idea, a simple indicator that describes the overall contribution of all modes subjected to a moving pantograph at a given speed is proposed to facilitate the determination of the local optimal speed. The variation of the proposed indicator with respect to the speed shows good consistency with the trend of the simulation results. The main finding in this paper can be used in the design phase to determine the optimal speed of the pantograph-catenary system in a local speed range. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlocal boundary value problems of fractional systems which involves left and right fractional derivatives at resonance. By using the coincidence degree theory, the solvability results for the problems are obtained under the resonant conditions. As an application of our results, we also deal with the existence result for the solution of fractional differential equation which involves both left and right fractional derivatives and satisfies certain boundary conditions under the resonant conditions. Finally, some examples are presented to illustrate our main results.

The elementary fractional-order models are the extension of first and second order models which have been widely used in various engineering fields. Some important properties of commensurate or a few particular kinds of non-commensurate elementary fractional-order transfer functions have already been discussed in the existing studies. However, most of them are only available for one particular kind elementary fractional-order system. In this paper, the stability and resonance analysis of a general kind non-commensurate elementary fractional-order system is presented. The commensurate-order restriction is fully released. Firstly, based on Nyquist's Theorem, the stability conditions are explored in details under different conditions, namely different combinations of pseudo-damping (ζ) factor values and order parameters. Then, resonance conditions are established in terms of frequency behaviors. At last, an example is given to show the stable and resonant regions of the studied systems. [ABSTRACT FROM AUTHOR]

In this study, we present a novel tri‐section stepped impedance resonator (SIR) with two different lengths (θ1 and θ2). The lengths of the first and the last transmission lines of the proposed tri‐section SIR were intentionally chosen. We compared the properties of the proposed SIR and the existing SIR. In the same impedance ratios (K1 and K2), the second harmonics of the proposed SIR were improved by 1.05‐1.11 times compared to the existing SIR. In addition, the length of the first transmission line, θ1, could be extended by more than twice the length of the existing SIR. That was very advantageous for tight coupling in a coupled line. Finally, a parallel‐coupled line band‐pass filter (PCL BPF) was developed using the proposed SIR, and the design equations were derived. The second harmonic of the PCL BPF was measured with an error of 2.67% compared to the theoretical value. The center frequency was almost identical. A series of processes, including design, simulation, fabrication, and measurement using the proposed structure, was carried out. An analysis of the results of each step proved the validity of our proposal. [ABSTRACT FROM AUTHOR]

The generation and propagation of a second harmonic water wave have been investigated in the frequency range between 7 Hz and 60 Hz where the velocity vs. frequency curve attains its minimum value. A model is proposed by assuming that the second harmonic is locally generated by point sources on the wavefront of the fundamental wave, and that at any point along the propagation direction the second harmonic be given by the cumulative contribution from all the sources up to the considered point. In the frequency range examined the combined effects of gravity and capillarity yield the so called resonance condition where the fundamental and second harmonic waves share the very same phase velocity. In such a case, wave shape matching condition is maintained between the two waves along all the propagation directions, with the amplitude of the second harmonic only limited by the attenuation effect. Evidence is given experimentally of such effect through the wavenumbers mismatching produced by the model vs. frequency and the detection of the maximum distance of second harmonic amplitude from the wave source. Furthermore, it is found that the resonance condition is a threshold effect with respect to water depth. • Experimental proof of 2nd capillarity–gravity harmonic in deep water for 7–60 Hz. • A new model of local harmonic generation matches results at and out of resonance. • A threshold effect with respect to water depth has been found. [ABSTRACT FROM AUTHOR]

Highlights • An appropriate and realistic dynamic modeling of a flexible two-link manipulator with flexible joints incorporating payload has been developed. • The coupled nonlinear dynamic equations of motion and boundary conditions considering the joint dynamics have been solved to compute the vibration eigenfrequency and its spectrums. • Bifurcation states and stability of the solutions have been analyzed under resonance condition. • The identification and progress of the instability regions have been investigated under parametric studies. Abstract The present paper deals with the theoretical studies to determine the modal parameters and investigate the dynamic instability of a harmonically driven planar two-link manipulator with flexible joints. An appropriate dynamic model incorporating both link and joint flexibilities subjected to a harmonic motion has been developed while joint flexibility has been modeled as a combination of torsional spring-inertia elements. Modal parameters for various modes of vibration have been evaluated and graphically demonstrated. Then, method of multiple scales has been employed to further analyze the vibration attributes of steady state responses and their stability under resonance condition. The comparative mode shapes and bifurcation diagrams those describe the vibrating system have been illustrated to demonstrate the dynamics of the flexible manipulator. The effect of geometric and inertial coupling existing between the flexible arms on bifurcation states and stability of the obtained solutions has been thoroughly investigated. Analytically obtained results have been verified numerically and found to be in good agreement. The present theoretical results deliver a useful insight into the attributes of vibration characteristics along with the nonlinear dynamic behavior and operational stability of two-link flexible manipulator under joint motion. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

Abstract Oscillating Water Column (OWC) devices, both the fixed structures and the floating ones, are an important class of Wave Energy Converter (WEC) devices. In this work, we carried out a numerical investigation aiming to give a deep insight into the fluid dynamic interaction between waves and a U-shaped OWC breakwater, focusing on the energy conversion process. The U-OWC breakwater under consideration, represents the full-scale plant installed in the Civitavecchia (near Rome) harbour. The adopted numerical method is based on the solution of the unsteady Reynolds Averaged Navier-Stokes equations (URANS). The water-air interaction is taken into account by means of the Volume Of Fluid (VOF) model. A two-dimensional domain has been adopted to investigate the unsteady flow outside and inside the OWC device. In order to simulate the action of an air turbine of the Wells type, the air chamber has been connected to the atmosphere by means of a porous medium able to reproduce its linear relationship between pressure drop and flow rate of the air turbine. Several simulations have been carried out considering periodic waves of different amplitudes in order to analyze the performance of the plant and, in particular to analyze the resonance with incoming waves, when the U-OWC is expected to absorb more energy. In order to characterize the plant efficiency, we split the energy conversion process into three main steps, 1) the primary conversion from wave energy to hydraulic energy the water discharge flowing inside the U-duct; 2) the secondary conversion from the OWC inlet to the oscillating pneumatic power made available to the turbine and, finally, 3) the turbine mechanical power output. To this purpose, the simulations of three different cases, varying wave period and height, have been carried out to quantify the energy captured by the plant and the fluid dynamic losses both in the water and in the air. [ABSTRACT FROM AUTHOR]

Oscillating water column (OWC) devices, either fixed or floating, are the most common wave energy converter (WEC) devices. In this work, the fluid dynamic interaction between waves and a U-shaped OWC breakwater embedding a Wells turbine has been investigated through unsteady Computational Fluid Dynamic (CFD) simulations. The full-scale plant installed in the harbor of Civitavecchia (Italy) was numerically modeled. A two-dimensional domain was adopted to simulate the unsteady flow, both outside and inside the U-OWC device, including the air chamber and the oscillating flow inside the conduit hosting the Wells turbine. For the numerical simulation of the damping effect induced by the Wells turbine connected to the air chamber, a porous medium was placed in the computational domain, representing the conduit hosting the turbine. Several simulations were carried out considering periodic waves with different periods and amplitudes, getting a deep insight into the energy conversion process from wave to the turbine power output. For this purpose, the three main steps of the overall energy conversion process have been examined. Firstly, from the wave power to the power of the water oscillating flow inside the U-duct. Secondly, from the power of the oscillating water flow to the air pneumatic power. Finally, from the air pneumatic power to the Wells turbine power output. Results show that the U-OWC can capture up to 66% of the incoming wave power, in the case of a wave period close to the eigenperiod of the plant. However, only two-thirds of the captured energy flux is available to the turbine, being partially dissipated due to the losses in the U-duct and the air chamber. Finally, the overall time-average turbine power output is evaluated showing that it is strongly influenced by a suitable choice of the turbine characteristics (mainly geometry and rotational speed).

A methodology is presented to simultaneously modify natural frequencies of an automotive belt drive system via configuration modification to match natural frequencies of the system with its working conditions. In this methodology, the configuration modification is regarded as an inverse eigenvalue problem in which necessary changes of a set of configuration parameters are determined for achieving a desired natural frequency variation relative to the original design value. Natural frequencies and mode shapes of the system are obtained by solving an eigenvalue problem that is directly derived from established governing equations of motion of a typical automotive belt drive system. Explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters are derived by differentiating the eigenvalue equation. Several configuration parameters are selected as design variables and their corresponding modification regions and directions are given based on frequency sensitivity analysis. In the inverse eigenvalue problem, variations of natural frequencies caused by changes of multiple design variables are approximated using the first and second order Taylor series expansions, which are based on explicit expressions of the first and second order derivatives of natural frequencies and eigenvectors with respect to the configuration parameters. By solving the inverse eigenvalue problem, necessary changes of design variables are determined and the desired natural frequencies are achieved so that resonance conditions are successfully avoided. [ABSTRACT FROM AUTHOR]

This study addresses the modelling of a dual band (28 and 38 GHz), circularly polarised slotted‐patch‐antenna for highly demanded millimetre wave multi‐input multi‐output (MIMO)‐systems in fifth generation (5G) networks. A computer‐aided‐design model is derived by means of an artificial neural network (ANN) which allows obtaining the physical dimensions of a single‐fed antenna, satisfying both near‐ and far‐field goals, without resorting to time‐consuming electromagnetic simulation. This mathematical model can be implemented in any CAD‐tool, as demonstrated within the framework of advanced design system. This allows, for the first time, to carry out optimisations of strategic importance for future 5G non‐linear‐radiating‐systems, especially operating at millimetre wave, directly addressing their far‐field behaviour. The model performance is validated by some examples and measurement results. A further important advantage of this approach is that the trained ANN‐model can be further adopted to fast, but accurately, investigate the complex relationships between antenna layout and its near‐field and far‐field performance, such as the resonance conditions and the polarisation behaviour. Indeed arbitrary orthogonal‐polarisations (LHCP/RHCP) have been achieved by the aid of the ANN‐model of the same topology. This result can be adopted to implement a combination of two independent radiation patterns for the antenna pair: this feature is attractive for MIMO applications. This is confirmed by measurements showing antenna‐coupling reduction with the MIMO‐array exploiting polarisation diversity. [ABSTRACT FROM AUTHOR]

In this article, a coplanar-waveguide (CPW)-fed dual-band antenna for applications of the multisystem integration has been demonstrated. The resonance analysis of the stepped-impedance (SI) monopole is presented by using the transmission-line analysis method. The frequency-response characteristics of the SI-monopole, such as the resonance condition and harmonic response, are systematically summarized. Furthermore, utilizing several simple techniques, such as bent feeding topology, asymmetric ground plane, and an L-shaped slot etched in the ground plane, a right-hand circularly polarized (RHCP) radiating wave at 1.57 GHz and a left-hand circularly polarized (LHCP) radiating wave at 2.33 GHz are excited for the applications of the global positioning system (GPS) and the satellite digital audio radio (SDAR) service system. After optimization of the geometrical parameters of the proposed antenna, the measured impedance bandwidths of a reflection coefficient less than −10 dB range from 1.40 to 2.98 GHz and from 4.48 to 6.27 GHz, and thus covers most of the commercial wireless communication systems, such as GPS, digital cellular system (DCS), personal communication system (PCS), international mobile telecommunications (IMT)−2000, wireless local area networks (WLAN), and long-term evolution (LTE) 2300/2600. The measured 3-dB axial ratio (AR) bandwidths are about 80 MHz at 1.57 GHz and 100 MHz at 2.33 GHz. [ABSTRACT FROM AUTHOR]

Different kinds of anomalies in industrial power lines create a number of problems for normal operation of induction motors. One of them is an excessive amount of motor vibration. The industry today widely uses different kinds of nonlinear systems operating in the power lines, for example, adjustable speed drives, which cause voltage distortion in the power lines. Single-phase load in three-phase power systems may cause voltage imbalance. Induction motors operating under voltage distortion or voltage imbalance usually have experienced significant vibration of an electromagnetic nature. Vibration of an electromagnetic nature may also be a result of an internal fault in the motor. Motor vibration data contain substantial analytical information about stator and rotor winding and core condition, air gap eccentricity, current/voltage imbalance, and voltage distortions in the power line, etc. Condition monitoring and fault diagnosis of induction motors based on the vibration analysis technique are widely used in the modern industry. Accuracy of the machinery diagnosis made using vibration analysis depends on the ability to correctly analyze vibration data. The aim of this paper is to clarify the origin of the motor vibration of an electromagnetic nature at line frequency, twice line frequency, harmonics of line frequency, and at twice slip frequency. This opinion is based on the author's many years of experience in the field of vibration diagnostics on electrical machines from different industries. [ABSTRACT FROM PUBLISHER]

We propose a scheme to observe the Majorana-zero-mode-induced crossed Andreev reflection by measuring tunneling current directly. In this scheme a metallic ring structure is utilized to separate electron and hole signals. Since tunneling electrons and holes have different propagating wave vectors, the conditions for them to be constructively coherent in the ring differ. We find that when the magnetic flux threading the ring varies, it is possible to observe adjacent positive and negative tunneling current peaks of about equal amplitudes.

The purpose of this paper is to develop a detailed 3D maglev vehicle and guideway model and investigate the dynamic response characteristics of the coupled system. For this, the maglev vehicle is modeled as one cabin and four bogies having eight electromagnetics, four sensors, and four secondary suspensions based on the Urban Transit Maglev (UTM) system in Korea. The 3D dynamic equilibrium equations of the cabin and bogies are derived by considering the actively controlled electromagnetic forces. Also, the equations of motion for the guideway are derived using the modal superposition method for vertical, lateral, and torsional modes. The resulting coupled equations of motion are then solved using a predictor-corrector iterative algorithm. Finally, through the numerical simulation of the developed system, the responses using the 3D maglev vehicle model are compared with those obtained by the corresponding 2D model. The effects of surface irregularity on the dynamic interaction behaviors are then evaluated for increasing vehicle speeds. Particularly, the 3D resonance conditions of the guideway girder and the maglev vehicle are presented considering the resonance conditions due to equidistant moving loads. In addition, some resonance phenomena are rigorously explored, including the lateral resonance by a series of vehicles running on a girder. [ABSTRACT FROM AUTHOR]

The lateral vibration of railway bridges induced by moving trains has traditionally been solved through numerical integration. Although it provides practical prediction, the numerical approach does not explicitly reveal the underlying driving mechanism of the train- bridge interaction. In this paper, a closed-form solution is derived for the lateral vibration of a simply supported bridge subjected to hunting forces from running wheel sets. Through complex Fourier expansion, this solution leads to the formulation of three influential factors with explicit physical meanings, namely, the effective unit moving load on the bridge, the arrangement of all moving wheel sets, and the frequency response function of the bridge. On the basis of these factors, a simplified formula to estimate the maximum vibration of the bridge is proposed. The closed-form solution and the simplified formula are validated through comparison with results from numerical integration. The resonance conditions of the bridge due to moving hunting forces are derived using the simplified estimation. [ABSTRACT FROM AUTHOR]

• A modified resonance condition for the stepped resonators. • Numerical calculation of sound field in the stepped resonators. • Distribution of pressure amplitude along the axis of the stepped resonators. Investigation of finite amplitude standing waves generated by boundary driving in the stepped acoustic resonator has been carried out both theoretically and experimentally to derive an appropriate tool to design resonators that have characteristics suitable for specific applications such as a microphone calibration system with a higher-pressure level. Initially, a modified resonance condition is proposed, which is deduced from the transfer matrix method and the characteristics of the standing wave resonator. The predictions of the resonance frequencies in a cylindrical resonator are in excellent agreement with those obtained by analytic formula in previous studies. Then, the modified resonance condition is applied to calculate the resonance frequencies of a stepped resonator. The boundary driving is provided by a piston at the open end. The resonant response in the cylindrical and stepped resonator, including the pressure amplitudes, the pressure waveform and the distribution of pressure amplitude along the axis, is calculated numerically by the finite volume method, which is a preliminary prediction of finite amplitude standing waves in the resonators. The calculated results of the stepped resonator are verified in the experiment, in which a stepped acoustic resonator is connected to a loudspeaker functioning as the piston. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear dynamic modelling, free vibration and nonlinear analysis of three-dimensional viscoelastic Euler-Bernoulli beam undergoing hub motion incorporating substantial tip mass is accomplished. The kinetic, and potential energy of the system are derived in terms of velocities of general point on the link and center of gravity of the tip mass expressed in multi-floating co-ordinate systems. Hamilton's principle is used to obtain the governing equations of motion and linearly coupled boundary conditions. The material of the beam is considered as viscoelastic constituted of Kelvin-Voigt rheological model. The mass attached at the terminal end of the beam is assumed to have eccentricity in axial, lateral, as well as transverse directions. Free vibration analysis is performed on the linearized system model to obtain the transcendental eigenfrequency equation. Further, the dynamic equations of motion of beam are discretized using the obtained mode shapes and the response of system under rotary motion of hub is investigated. The steady state solutions and frequency response curves exhibiting bi-stable and tri-stable regions are obtained using method of multiple scales. The bifurcation diagrams of the system are studied for resonance conditions when the frequency of the rotary motion becomes equal or nearly equal to the normalized beam frequencies. The saddle node and pitchfork bifurcations exhibiting multiple solutions and jump phenomena are observed and investigated to avoid catastrophic failure of the system. The numerical simulations of modal parameters of the system, nonlinear characteristics, and their parametric dependency is discussed thoroughly. • Dynamic modeling and free vibration of three-dimensional rotating viscoelastic beam with generic tip mass and rotating hub. • Analytical solution of coupled dynamics equations of motion and boundary conditions to obtain modal parameters. • Nonlinear behaviors and stability of steady state solutions due to harmonic hub rotation have been discussed. • Parametric influence on modal and bifurcation characteristics have been illustrated graphically and tabularly. [ABSTRACT FROM AUTHOR]

A numerical scheme based on Symplectic Integration Algorithm (SIA) has been used to develop an orbit following code to calculate fast ion trajectories in tokamak magnetic configuration. For the purpose of demonstrating the expediency of symplectic schemes, the algorithm has been applied to the H´enon-Heiles system and compared with non- symplectic Runge-Kutta Algorithm (RKA) for numerically integrating the Hamiltonian equations. In contrast to RKA, the long-time stability of SIA has been highlighted. Furthermore, the SIA has been used to find the exact trajectories of, trapped and passing, fast ions in tokamak. In particular, the effect of an intrinsic magnetic field perturbation has been investigated, i.e. toroidal field ripples. This perturbation is toroidal field ripple (TFR) which are there due the discrete number to toroidal coils around the torus. The numerical scheme used shows excellent conservation of particle energy as well as of angular momentum (in axi-symmetric case). The effect of TFR on these trajectories has been simulated and it is shown that the resonance between toroidal precession of bananas and the field ripples results in spread of the trajectories for banana particles, whereas the passing fast ions are unaffected. [ABSTRACT FROM AUTHOR]

Based on the fundamental wave conservation laws of energy, momentum and action, together with the law of symmetry deciding interactions and the Hamilton structure, 2 main categories of resonance conditions for an infinite number of wave interactions and the corresponding 2 major Zakharov-type equations for an infinite number of wave resonances were derived by means of the complex Hamiltonian canonical equation for ocean surface waves, the canonical transformation and the Poisson bracket conditions. The presented Zakharov-type equations, in connection with the classical conditions for the 3-, 4- and 5-wave resonances, therefore build an indispensable, advanced and complete theoretical framework for the most fundamental and universal ocean wave turbulence. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic stability analysis of a simply supported beam excited by a sequence of moving masses is investigated. All components of the mass acceleration including the centripetal, the Coriolis and the vertical one are considered. The periodical traverse of masses across the beam results to a linear time-periodic problem. The Floquet theory and the Incremental Harmonic Balance (IHB) method are implemented to obtain the boundary between stable and unstable regions in the parameters plane. A new approach for identifying the conditions of resonance is investigated by presenting an intuitive definition of resonance for time-varying systems. This approach enables the IHB method to determine inherent curves of resonance conditions besides its ability to find the boundary curve separating the stable and unstable regions. Numerical simulations confirm the correctness of resulted curves. [ABSTRACT FROM AUTHOR]