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In the present paper, we study the analyticity of the leftmost eigenvalue of the linear elliptic partial differential operator with random coefficient and analyze the convergence rate of the quasi-Monte Carlo method for approximation of the expectation of this quantity. The random coefficient is assumed to be represented by an affine expansion $a_0(\boldsymbol{x})+\sum_{j\in \mathbb{N}}y_ja_j(\boldsymbol{x})$, where elements of the parameter vector $\boldsymbol{y}=(y_j)_{j\in \mathbb{N}}\in U^\infty$ are independent and identically uniformly distributed on $U:=[-\frac{1}{2},\frac{1}{2}]$. Under the assumption $ \|\sum_{j\in \mathbb{N}}\rho_j|a_j|\|_{L_\infty(D)}, Comment: 18 pages

Given integers k ��� 2 and a_1,���,a_k ��� 1, let a: = (a_1,���,a_k) and n: = a_1+���+a_k. An a-multiset permutation is a string of length n that contains exactly a_i symbols i for each i = 1,���,k. In this work we consider the problem of exhaustively generating all a-multiset permutations by star transpositions, i.e., in each step, the first entry of the string is transposed with any other entry distinct from the first one. This is a far-ranging generalization of several known results. For example, it is known that permutations (a_1 = ��� = a_k = 1) can be generated by star transpositions, while combinations (k = 2) can be generated by these operations if and only if they are balanced (a_1 = a_2), with the positive case following from the middle levels theorem. To understand the problem in general, we introduce a parameter ��(a): = n-2max{a_1,���,a_k} that allows us to distinguish three different regimes for this problem. We show that if ��(a) < 0, then a star transposition Gray code for a-multiset permutations does not exist. We also construct such Gray codes for the case ��(a) > 0, assuming that they exist for the case ��(a) = 0. For the case ��(a) = 0 we present some partial positive results. Our proofs establish Hamilton-connectedness or Hamilton-laceability of the underlying flip graphs, and they answer several cases of a recent conjecture of Shen and Williams. In particular, we prove that the middle levels graph is Hamilton-laceable., LIPIcs, Vol. 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022), pages 34:1-34:14

We formulate a large-strain model of single-slip crystal elastoplasticity in the framework of energetic solutions. Numerical performance of the model is compared with lab experiments on the compression of a stack of note papers.

There are numerous non-smooth factors in railway vehicle systems, such as flange impact, dry friction, creep force, and so on. Such non-smooth factors heavily affect the dynamical behavior of the railway systems. In this paper, we investigate and mathematically analyze the double grazing bifurcations of the railway wheelset systems with flange contact. Two types of models of flange impact are considered, one is a rigid impact model and the other is a soft impact model. First, we derive Poincaré maps near the grazing trajectory by the Poincaré-section discontinuity mapping (PDM) approach for the two impact models. Then, we analyze and compare the near grazing dynamics of the two models. It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into a chaotic motion after the gazing bifurcation, while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through a period doubling bifurcation. Our results also extend the applicability of the PDM of one constraint surface to that of two constraint surfaces for autonomous systems.

In this paper, the validity of two extended transmission line approaches proposed for calculating the ground-return impedance and admittance of an underground insulated cable is evaluated taking as reference a full-wave approach based on the 3-D finite-difference time-domain (FDTD) method. The transient responses of an underground cable with realistic radius are calculated for a wide range of soil resistivities and cable lengths. It is shown that the extended transmission line approaches lead to transient waveforms in good agreement with the FDTD method even for relatively short cables and high soil resistivity. The limitations of a traditional formulation that neglects the influence of the ground-return admittance on the calculation of the cable parameters are also demonstrated. Overall, the results confirm the accuracy of the newly-proposed expressions for the calculation of underground cable parameters.

Soft Magnetic Composites (SMC) are an alternative to laminated steels for the design of smaller and lighter electromagnetic devices.Such electromagnetic devices might be subjected to significant mechanical stresses that can alter their electromagnetic properties. This paper presents a homogenization model which provides estimates for both the nonlinear magnetic response and the Eddy Current Losses of SMC subjected to a stress state.

An increasing interest for permanent magnet synchronous machines with low torque ripple and low vibration is observed. The purpose of this paper is to investigate the topology of non-uniformly distributed teeth and its influence of on cogging torque, tooth ripple harmonics and torque ripple of permanent magnet synchronous machines. The topologies with different number of non-uniformly distributed teeth are investigated. Analytical procedure is developed to illustrate the impacts of non-uniformly distributed teeth on cogging torque and unbalanced magnetic pull (UMP), and then identify the appropriate non-uniformly distributed teeth. A commercial 10kW 8-pole 48-slot V-shaped IPM machine is taken as the reference base machine. The machines with 2- and 6 non-uniformly distributed teeth are chosen to make an overall comparison to that with the well-known skewing slots. The machine with 2 non-uniformly distributed teeth is finally chosen to be fabricated. Intensive experiments including cogging torque, back-EMF, load current, efficiency and instantaneous torque are done.

With the development of compressors towards high speed and multiple columns, the torsional vibration phenomenon has become a major factor affecting the service life and reliability of the shaft system. Therefore, this paper considers the influence of friction between piston and cylinder on the instantaneous inertia of the crank connecting rod mechanism, establishes a nonlinear torsional vibration mechanics model of shale gas compressor shaft system, solves the natural frequency of the shaft system under undamped and damped conditions using the eigenvector method, and investigates the influence of the friction coefficient between piston and cylinder and the operating speed on the torsional vibration response of the shaft system under the self-excitation of the shaft system and the action of and excitation moment by the Runge-Kutta methods. The results show that after considering the friction between the piston and the cylinder, the 2nd order natural frequency of the shaft system shows a "high-low-high" fluctuation pattern; As the friction coefficient increases, the amplitude of the shaft system and the peak vibration speed show a rising trend; Meanwhile, when the speed increases, the vibration of the shaft system changes from chaotic \ period to the proposed periodic state, but the amplitude shows a decreasing trend. The research in this paper aims to improve the theory of nonlinear dynamics of compressor shaft systems, and the determined nonlinear parameters can be used to guide the operation and maintenance of compressors in engineering.

In order to study the effects of a steel spring floating slab track (SSFST) on the vibration and noise of rail transit overhead box-girders, a train–track system coupling model in the frequency domain was established. Two numerical models – a finite-element model to analyse the vibration and a boundary-element model for predicting structure-borne noise – were then built. Based on a field test of one 30 m long simply supported box-girder paved with ordinary slab track (OST) in an urban rail transit system, the models were verified to be effective at predicting the vibration and noise of the box-girder. Meanwhile, both the vibration- and noise-reduction effects of SSFST were assessed in comparison with OST. After substituting SSFST for OST, the maximum reductions of the overall vibration acceleration level and overall sound pressure level of the box-girder were 34·7 dB and 25 dB, respectively. Finally, the effects of the SSFST's parameters on the noise of the box-girder were investigated. The results showed that the isolator stiffness is the primary factor that affects the noise characteristics of the box-girder, followed by the floating slab thickness. However, the floating slab length and fastener stiffness were found to have little influence on the noise radiation.

We consider a mathematical model for the gas flow through a one-way valve and focus on two issues. First, we propose a way to eliminate the chattering (the fast switch on and off of the valve) by slightly modifying the design of the valve. This mathematically amounts to the construction of a coupling Riemann solver with a suitable stability property, namely, coherence. We provide a numerical comparison of the behavior of the two valves. Second, we analyze, both analytically and numerically, for several significative situations, the maximization of the flow through the modified valve according to a control parameter of the valve and time.

The helical planetary transmission system (HPTS) is widely used in wind power, hydropower, and shield machine, which operating conditions are extremely complicated, and the existence of component installation errors will result in response deviations to the theoretical design. A dynamic model for slice type bending-torsional-pendulum of the HPTS is established in the lumped parameter method considering the installation error of shaft (IEOS) for the 1st planet gear, helical meshing characteristics, and bearing support characteristics. The vibration response characteristics of the HPTS under the IEOS for the 1st planet gear are studied. The results have shown that the FFT amplitudes for the horizontal vibration acceleration of the sun gear increased by 8.3%, and the axial vibration acceleration of the ring gear increased by 11.5%, respectively. The maximum magnitude increase of FFT amplitude for the vibration acceleration under a positive 0.13 mm IEOS for the 1st planet gear is the axial direction of the ring gear. The results indicate that the IEOS needs to be thoroughly introduced into the HPTS to simulate the actual operating conditions of the system.

We study defining inequalities of string cones via a potential function on a reduced double Bruhat cell. We give a necessary criterion for the potential function to provide a minimal set of inequalities via tropicalization and conjecture an equivalence.

For Maxwell operators $(E,H) \to (i \epsilon^{-1} \nabla\times H, -i \mu^{-1} \nabla \times E)$ in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance and Leontovich boundary conditions including the cases of singular, degenerate, and randomized impedance coefficients. To this end we construct Riesz bases in the trace spaces associated with the curl-operator and introduce a modified version of boundary triple adapted for the specifics of Maxwell equations, namely, to the mixed-order duality of the related trace spaces. This provides a translation of the problem to operator-theoretic settings of abstract Maxwell operators. In particular, we show that Calkin reduction operators are naturally connected with Leontovich boundary conditions and provide an abstract version of impedance boundary condition applicable to other types of wave equations. Taking Friedrichs and Krein-von Neumann extensions of related boundary operators, it is possible to associate m-dissipative Maxwell operators to arbitrary non-negative measurable impedance coefficients., Comment: 38 pages

Consider two parallel lines $\ell_1$ and $\ell_2$ in $\mathbb{R}^3$. A rail arc is an embedding of an arc in $\mathbb{R}^3$ such that one endpoint is on $\ell_1$, the other is on $\ell_2$, and its interior is disjoint from $\ell_1\cup\ell_2$. Rail arcs are considered up to rail isotopies, ambient isotopies of $\mathbb{R}^3$ with each self-homeomorphism mapping $\ell_1$ and $\ell_2$ onto themselves. When the manifolds and maps are taken in the piecewise linear category, these rail arcs are called stick rail arcs. The stick number of a rail arc class is the minimum number of sticks, line segments in a p.l. arc, needed to create a representative. This paper will calculate the stick numbers of rail arcs classes with a crossing number at most 2 and use a winding number invariant to calculate the stick numbers of infinitely many rail arc classes. Each rail arc class has two canonically associated knot classes, its under and over companions. This paper also introduces the rail stick number of knot classes, the minimum number of sticks needed to create a rail arcs whose under or over companion is the knot class. The rail stick number is calculated for all knot classes with crossing number at most 9. The stick number of multi-component rail arcs classes is considered as well as the lattice stick number of rail arcs., Comment: 19 pages, 22 figures

The deformation property of marine clay under a heat source has received considerable attention in the geotechnical literature. In this paper, a three-parameter fractional order derivative model is introduced into the thermo-hydro-mechanical coupling governing equations with thermal filtration and thermo-osmosis to simulate viscoelastic characteristics of marine clay. The excess pore pressure, temperature increment, and displacement of marine clay are derived by using the Laplace transform method, and the semianalytical solution for the one-dimensional thermal consolidation in the time domain is derived by using a numerical inversion of the inverse Laplace transform. The influence of the order of the fractional derivative, material parameters, and phenomenological coefficient on thermal consolidation is investigated based on the present solutions. It is shown that the influence of the fractional derivative parameter on the excess pore pressure and displacement of marine clay depends on the properties of soil mass, and the temperature increment has an obvious effect on the thermal filtration and thermo-osmosis process.

Let $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let $G=GL(V)$. Regarding $\boldsymbol{\Lambda}$ as a $G$-module via the `change of basis' action of~$G$ on~$V$, we determine the composition factors of various $G$-submodules of~$\boldsymbol{\Lambda}$ which correspond to certain important families of algebras. This is achieved by introducing the notion of linear degeneration which allows us to obtain analogues over $\mathbb{F}$ of certain known results on degenerations of algebras. As a result, the $GL(V)$-structure of~$\boldsymbol{\Lambda}$ is determined., Comment: 26 pages

The published manuscripts in the area of gyroscope theory were presented mainly by the simplified approaches in which mathematical models contain many uncertainties. New research in machine dynamics opened breakthrough directions in gyroscopic effects of rotating objects that give the correct solutions. The pioneering work meets many problems when solving the scientific innovations that are accompanied by successes and omissions. New mathematical models for the gyroscopic inertial torques were derived with incorrect processing of the integral equations that give distorted results. The gyroscopic devices in engineering manifest gyroscopic effects as the action of the inertial torques which computing is crucial for mathematical describing of their motions. The corrected mathematical processing of the equations for the inertial torques acting in a gyroscope is presented in this manuscript.

Electromagnetic railgun is a launcher that relies on electrical energy to do work to propel a projectile to high speed. In the military application of railgun, the acquisition and adjustment of projectile movement characteristics, including acceleration and velocity, are very important. In order to realize the rapid calculation of the projectile movement characteristics and the precise adjustment of the thrust, the force and projectile movement characteristics for a complex structure railgun, augmented quadrupole hyperbolic railgun, were studied by the method of field-circuit coupling. Based on Biot-savart Law and accurate fitting of current distribution, the electromagnetic characteristics and force characteristics of the launcher are analyzed, and the iterative method is used to realize the coupling between the pulse forming network and the calculation of the force on launcher and finally solve the movement of the launcher projectile characteristic. Comparing the calculation and experiment, the error of speed calculating with this method is small in the low speed stage.

In this paper, velocity and attenuation of ultrasonic S-wave in a water-saturated rock are used for calculating shear modulus and matrix permeability of the rock, via a model improved from Biot theory. The model requires two inputs, i.e., the dry velocity of S-wave and the average distance of aperture representing pores, to yield phase velocity and the quality factor as functions of frequency. By fitting the predicted velocity and quality factor against the ultrasonically measured counterparts, the dry velocity of S-wave and the average distance of aperture are ascertained, which in turn yield shear modulus and matrix permeability, respectively. The modeling results on D’Euville limestone from France show that the specimen has shear modulus of 11.35 and 11.55 GPa (under differential pressures of 3 and 5 MPa, respectively) and matrix permeability of 0.0486 Darcy (under both differential pressures). The matrix permeability appears to be approximately one half of Darcy permeability.

One of the main problems of fracture mechanics is to describe the behavior of media with cracks. At the same time, more and more attention is paid to the study of large systems, including periodic structures. For several cracks, the coefficient of influence is considered to be an important parameter. It is the ratio of the stress intensity factor calculated in the problem of a system of cracks to the stress intensity factor for a single crack under the same load. The paper proposes a method that allows to accurately determine the coefficients of influence for large systems of cracks, including the case of periodic structures, in which the number of cracks is infinite. The method is based on a numerical algorithm developed by the authors that uses the method of discontinuous displacements of a high order of accuracy and an asymptotic representation of stress fields at the crack tip (M. Williams). To verify the method, the results of the implemented algorithm are compared with known analytical solutions both for single cracks and for an infinite doubly periodic system of cracks.

A numerical simulation model has been established to obtain the deformation, strain and stress concentration of slab narrow side. The simulated temperature profiles of slab show a agreement with the results of measured temperatures by using infrared thermal camera. Moreover, the deformation, stress and strain of the slab have been investigated systematically, especially at the slab narrow side along the thickness direction. The relationship between the reduction amount and deformation, stress and strain concentration of slab narrow face has been investigated.

The bulge deformation of slab narrow face can cause surface defects of hot rolled steel plate. A three-dimensional bulging model, was proposed to simulate the evolution of deformation behavior of the continuous casting slab during heavy reduction (HR). The model was taken to investigate the non-uniform deformation of slab during HR process. The bulging deformation behavior of the slab was then calculated in one segment included seven pairs of rollers. To improve the edge defect on hot-rolled steel plates, the relationship between the reduction amount and bulge deformation of slab narrow face has been investigated.

A mode-I crack in a one-dimensional (1D) orthorhombic quasicrystal (QC) strip under in-plane phonon and phason stress loading is considered. Fourier transforms are applied to reduce the mixed boundary value problem of the mode-I crack to solving a system of simultaneous singular integral equations. Asymptotic expressions of the phonon and phason stresses and displacement fields near the crack tips have been obtained in an explicit form. The crack-tip singularities of the mode-I crack have been investigated and the intensity factors of the stresses in the phonon and phason fields are derived explicitly. The stress intensity factors (SIFs) and the hoop stress intensity factors (HSIFs) have been determined to investigate the effect of the geometric size and the crack kinking phenomenon. The effect of the thickness ratio of the cracked strip on the SIFs and energy release rates has been investigated. When the thickness of the cracked strip becomes infinite large, the results obtained for the crack problem can be reduced to the analytic solution for a mode-I crack in an infinite 1D orthorhombic QC media.

The Updated Lagrangian method for nonlinear elasticity with contact is presented. First, we describe the Total Lagrangian for a compressible Neo-Hookean material. Next, we introduce the Updated Lagrangian formulation for Neo-Hookean and Ogden compressible materials with contact. An advantage of this approach is that at each iteration only a linear system is solved. The linear problem to be solved is written in the updated domain. Numerical results are presented: compression of a Hertz half ball and of a hyperelastic ring against a flat rigid foundation, and contact of an elastic cube and a ball.

Analytical dependencies were obtained to calculate the lengths of roll contact curves, the lengths of the slip and no-slip zones, and angles that determine the position of the separation points of these zones. It was revealed that the slip zones asymptotically decrease to zero with an increase in the angle of inclination of the material to the line of centers. It was determined that an increase in the radii of the rolls and the projection of external forces on the axis, and a decrease in the projection of external forces on the axis led to an increase in the slip zone and a decrease in the no-slip zone.

As a critical element of time-varying mesh stiffness (TVMS), contact stiffness of a gear drive has been defined based on simplified Hertzian contact stiffness or semi-empirical nonlinear Hertzian contact stiffness in previous works. This study proposes a general contact stiffness model for elastic bodies through piecewise linear interpolation of contact pressure. The TVMS of a spur gear drive is determined through potential energy method and proposed contact stiffness model verified by Hertzian contact theory and finite-element method. Then, the influence of applied load on contact stiffness is studied, and the differences among proposed contact stiffness, simplified Hertzian contact stiffness, and nonlinear Hertzian contact stiffness are analyzed. Results show that contact stiffness increases with the applied load, and the TVMS based on the proposed contact stiffness model is the smallest among the three contact stiffness models. Effects of tooth width and input torque on the TVMS are further discussed. The TVMS becomes bigger with increased tooth width and input torque, but the increase rate decreases as tooth width or input torque increases. These findings indicate that reasonable matching of design parameters is beneficial for increasing load capacity and optimizing the dynamic performance of gear systems.

The base idea of this paper is to control the electromagnetic engine to enhance a smooth rotation by measuring distance of the piston using an IR sensor. This electromagnetic engine consists of an electromagnet, permanent magnet, Infrared Sensor, powerful microcontroller and power supply. The permanent magnet acts as a piston in this electromagnetic engine, it has magnetic field energy for a proper function. The position of permanent magnet has to be noted for electromagnets energisation in order to reduce power consumption by electromagnet. The infrared sensor mounted with electromagnet set and pointed towards permanent magnet, whenever the permanent magnet moves towards electromagnet, sensor reads the change in magnetic piston position. The electromagnet is energized on the reach of permanent magnet near electromagnet. Control of electromagnets power supply is depends on the signal provided by IR sensor, this sensor is mainly makes timing control of power drive circuit through the microcontroller. This makes engine to run continuously and reducing its power consumption by providing a pulse to electromagnet.

Aiming at the influence of radial electromagnetic force on vibration and noise of the switched reluctance motor (SRM), the radial electromagnetic force under airgap eccentricity is represented based on the virtual displacement principle and Maxwell stress tensor. Multi-objective optimization of motor electromagnetic characteristics including magnetostatic torque, radial electromagnetic force fluctuation, and unbalanced radial force amplitude is completed. First, the analytical representation for the radial electromagnetic force is obtained by the virtual displacement principle, and the expression of the unbalanced radial force caused by airgap eccentricity is deduced. Then, the spatial distribution of the radial electromagnetic force is modeled by the Maxwell stress tensor, which makes the radial electromagnetic force characterization more comprehensive. In order to improve the electromagnetic characteristics of the SRM under airgap eccentricity, sensitivity analysis and multi-objective optimization are carried out to obtain the optimal solution set of the motor structure parameters. The simulation results show that the radial electromagnetic force fluctuation and the unbalanced radial force amplitude decreases by 64.09% and 23.05%, respectively, when the magnetostatic torque is sacrificed by 6.36%, which provides a framework for multi-objective optimization of motor structure parameters.

A mathematical model of the cylinder block moment of a dual-drive axial piston motor considering the dynamic pressure in the piston chamber is developed. The influence of the number of plugs, staggering angle, inlet pressure and swashplate inclination on the individual moments applied to the cylinder block was analyzed. The results show: when the number of pistons in the inner and external emissions is the same, the cylinder block is subjected to a periodic pulsation of each moment and odd-numbered pistons have a higher frequency of torque fluctuations than even-numbered pistons. With increasing intersection angle, the pulsation rate of the torque around the x and y axes tends to increase and then decrease but the output torque varies in the opposite direction; The inlet pressure can increase the torque pulsation rate of the cylinder block in equal proportion. When the inclination angle of the inner and external swashplate is not the same, the reasonable selection of different inner and external swashplate inclination angles can make the overturning torque generated by the inner and external emissions offset and increase, so that the overturning torque of the cylinder block is reduced.

Magnetic gears perform the same function as mechanical gears using magnetic fields instead of interlocking teeth. A review of the design processes used in the literature demonstrates that a critical design parameter, pole pair count, is often given inadequate consideration. In addition to reviewing existing prototypes, this paper uses a parametric simulation study to analyze the impacts of pole pair counts on gear performance and illustrate how the optimal pole counts vary with gear ratio and various design parameters. This paper also introduces new ripple factors, which better correlate with torque ripple than the cogging factor used in previous papers, and illustrates why designs with non-integer gear ratios tend to have much smaller torque ripples than designs with integer gear ratios. While selecting the pole counts to minimize symmetry can reduce torque ripple, designs without any symmetry are shown to experience unbalanced magnetic forces on each rotor. Thus, it is recommended to select pole counts that result in an even number of modulators but not an integer gear ratio. This paper also reveals that, for a fixed gear ratio, a nontrivial optimum pole count minimizes the electromagnetic losses.

Virtual synchronous machine (VSM) based high voltage dc systems enhance the inertia of the power system. However, the dynamic interactions between the VSM-based rectifier station, the inverter station, and the grid could induce the system oscillation, which has been investigated in this article. At first, the hybrid ac-dc impedance models of the VSMs considering the coupling between the ac and dc dynamics are established. Then, the relationships between the dc impedance, dq-frame impedance, and the hybrid ac-dc impedance are presented. It is found that the dc impedance of the VSM-based inverter station and the d-d channel impedance of the dq-frame impedance of the rectifier station behave as negative resistors in the low-frequency range. Moreover, a five-dimensional impedance stability criterion based on the hybrid ac-dc impedance and generalized inverse Nyquist criterion is proposed to assess the system stability. The analysis results show that the low-frequency oscillation occurs when the grid short-circuit ratio of the rectifier station is small. Finally, the simulation and experimental results verify the impedance models and the stability criterion.

Time-dependent nonlinear lateral vibrations of plates composed of a hyperelastic matrix and uniformly/nonuniformly distributed hyperelastic reinforcing inclusions are studied. Since the material constants of a hyperelastic must be extracted from the whole slope-varying stress-strain curve rather than a single slope, choosing power/exponential distributions for the material constants or using Voigt’s rule of mixtures is quite wrong. The neo-Hookean and Mooney–Rivlin constitutive models are adopted, and their results are compared. Another hint is incorporating the incompressibility condition. The governing equations of motion are derived by using Hamilton’s principle, a new energy-equivalence-based micromechanical model that can be employed for reinforcing phases with nonlinear constitutive laws, and von Kármán assumptions in the left Cauchy–Green deformation tensor, and solved by incorporation of an updating finite-element and Newmark’s techniques. Not only the displacement but typical stress results are also reported here. Results show that the neo-Hookean model overestimates the rigidity in comparison to the Mooney–Rivlin model, and unlike the elastic plates, the effect of the stiffer phase is more remarkable in the uniform distribution in comparison to the nonuniform distribution of the stiffening materials because the magnitudes of the tensile stresses of the hyperelastic plate are much larger than that of the bending stresses.

This paper presents the dynamic modeling and analysis of an inverted pendulum robot with an adaptable overcoming wheel. Stairways are inevitable in environments where humans and robots operate and interact. The conventional wheel cannot overcome an obstacle that is higher than the radius of the wheel of the inverted pendulum robot. This paper presents a solution for a problematic situation in which a balancing robot climbs steps with a pair of transformable wheels. Dynamic modeling of the varying radius of the wheel was performed using the Lagrangian approach, and a simple gain controller was selected. Simulations were carried out using MATLAB and Simulink to confirm the dynamic model. In future work, the wheel should be tested on a robot model.

The impedance of the human body is strongly voltage-dependent, and exhibits substantial variation among individuals. We introduce a new statistical model that separates body impedance into three terms (internal tissue, skin, and contact impedances in series). Advantages over simpler models include a physically plausible monotonicity with respect to voltage and the ability to simulate the impedance characteristics of individuals.

We generalize the greedy and lazy $\beta$-transformations for a real base $\beta$ to the setting of alternate bases $\boldsymbol{\beta}=(\beta_0,\ldots,\beta_{p-1})$, which were recently introduced by the first and second authors as a particular case of Cantor bases. As in the real base case, these new transformations, denoted $T_\boldsymbol{\beta}$ and $L_\boldsymbol{\beta}$ respectively, can be iterated in order to generate the digits of the greedy and lazy $\boldsymbol{\beta}$-expansions of real numbers. The aim of this paper is to describe the dynamical behaviors of $T_\boldsymbol{\beta}$ and $L_\boldsymbol{\beta}$. We first prove the existence of a unique absolutely continuous (with respect to an extended Lebesgue measure, called the $p$-Lebesgue measure) $T_\boldsymbol{\beta}$-invariant measure. We then show that this unique measure is in fact equivalent to the $p$-Lebesgue measure and that the corresponding dynamical system is ergodic and has entropy $\frac{1}{p}\log(\beta_{p-1}\cdots \beta_0)$. We then express the density of this measure and compute the frequencies of letters in the greedy $\boldsymbol{\beta}$-expansions. We obtain the dynamical properties of $L_\boldsymbol{\beta}$ by showing that the lazy dynamical system is isomorphic to the greedy one. We also provide an isomorphism with a suitable extension of the $\beta$-shift. Finally, we show that the $\boldsymbol{\beta}$-expansions can be seen as $(\beta_{p-1}\cdots \beta_0)$-representations over general digit sets and we compare both frameworks., Comment: 28 pages, 15 figures

All knots are known to be hyperbolic, satellite, or torus knots, and one important family is Lorenz links, or T-links, which arise from dynamics. However, it remains difficult to determine the geometric type of a Lorenz link from a description via dynamics or as a T-link. In this paper, we consider those T-links that are torus links. We show that T-links obtained by full twists along torus links can never be torus links, aside from a family of cases. This addresses a question of Birman and Kofman., Comment: 8 pages, 1 figure. V2 contains minor changes. To appear in Proceedings of the AMS

This dataset contains all data as used for the manuscript 'Non-orientable order and non-Abelian response in frustrated metamaterials'., X.G. acknowledgdes financial support from the China Scholarship Council. D.B. and D.C. acknowledge support from IdeX Tore and ANR WTF grants. C.C. ac-knowledges funding from the European Research Councilvia the Grant ERC-StG-Coulais-852587-Extr3Me.

We study some observational signatures of nonlinearities of the electromagnetic field. First to all we show the vital role played by nonlinearities in triggering a material behavior of the vacuum with $(\varepsilon > 0, μ, 8 pages

A Universal Mathematical Field Theory (UMFT) is established, which states that the combination of the operations of both gradient and divergence of vector fields, such as electric field and velocity field, create the curl of an axial vector field, such as magnetic field. Utilizing UMFT, we mathematically: (1) derive the Extended-Maxwell equations and the Lorentz force from Coulomb’s law and the velocity of the source; (2) establish Maxwell-type gravitational equations and Lorentz-type gravitational force (Gravito-EM) from Newton’s law and velocity of gravitational source; (3) establish Classical-Spin-Electromagnetism (Spin-EM) from the Coulomb’s law and the spin of the spin angular velocity; (4) predicate the Spin related force. For a source moving with non-spatially-varying velocity the Extended-Maxwell equations reduce to Maxwell equations, which justifies UMFT and shows that the experiments-based Maxwell equations have mathematical origin. This derivation mathematically explains how a moving electric charge creates magnetic field, and shows that there is no magnetic monopole charge. UMFT shows that mathematical identities lead to physical dualities including duality between EM and Gravito-EM. The concepts, effects and phenomena of EM may be directly converted to that of gravity. The Gravito-EM are employed to study the accelerating universe, rotation curve and gravitation waves. The Gravito-EM can be quantized, along the line of quantizing EM, and unified with EM force. We derive, for the first time, the Spin-Lorentz-type force and Lagrangian-Lorentz-type force. If experimentally proved, the Spin-related force may be the 5th force. UMFT provides mathematical origins of physical dualities between Extended EM, Gravito-EM and Spin-EM.

There are different dynamic characteristics in each stage of rail transit network development. It can provide guidance for rail transit network planning and phased construction,Evaluating the evolution degree of urban rail transit network and accurately dividing the evolution stages. Starting from the allometric growth relationship between transfer nodes and ordinary nodes in urban rail transit network, this paper defines the evolution level of rail transit network and the growth rate difference between transfer and ordinary nodes, and deduces the logistic dynamic equation of urban rail transit network evolution level with the help of mathematical derivative and logarithmic relationship, This paper reveals the dynamic law of the evolution process of urban rail transit network from the theoretical level, analyzes the evolution dynamic process on this basis, finds the Threshold for phasing the evolution stage, and divides it into four evolution stages. Finally, the theoretical derivation results are verified with the evolution data of Beijing Rail Transit Network (1984-2020) for 45 years. The verification results are highly consistent with the theoretical derivation results, which proves the correctness of the theoretical model and its practical guiding significance for the construction of rail transit network.

In this paper, Galilean orthogonal matrices in G^5 and G_1^5 are obtained with the help of unit quaternions. Moreover, Galilean orthogonal matrices in G^4 and G_1^4 are acquired. These matrices produce Galilelan motions in Galilean spaces. We investigate the invariance of the plane where shear motion is acting in Galilean and pseudo-Galilean spaces. Additionally, related examples of matrices that belong to both spaces are provided. With a similar method, dual Galilean orthogonal matrices are obtained by using unit dual quaternions. Finally, we strengthen our work with examples and draw their figures to explore visual representations.

This paper presents a realistic model for the simulation of a progressive collapse scenario in a typical low-rise building that is constructed from RC flat slabs and supported by columns. The progressive collapse scenario starts after failure of the top slab connections, where the slab is falling downward and impacts with the slab below. This impact event is analyzed, and the dynamic failure of the impacted slab’s connections starts the progressive collapse event. Two different scenarios are identified, depending on the first slab damage condition prior to impact. The first scenario refers to an undamaged impacting slab where an elastic collision occurs with the slab below; in the second scenario, the first slab is damaged, and its collision with the slab below is plastic. In the first scenario, the impacting slab velocity drops to zero while its velocity is fully imparted to the impacted slab. In the second scenario, both slabs continue their motion jointly at a common velocity. In the subsequent impacts, the impacting slabs are a-priori damaged, hence plastic collisions occur. These impact occurrences are analyzed separately, depending on the number of impacting slabs involved, damage characteristics, and impact velocity. Due to the nature of the first impact, the first scenario is characterized by separate motion of the first impacting slab which is falling behind the other slabs. This slab gains speed until it meets the other falling slabs below at a certain altitude, and an intermediate collision occurs, not necessarily at a floor level. In the analyzed five-story building, the intermediate impact occurs after the third impact event, where the slabs are located slightly above the first story level. The intermediate impact elevates the velocity of the impacted slabs such that their impact with the first level slab is more severe and its motion toward hitting the ground level is faster.

In this paper, a self-similar fractal coiled acoustic metamaterial is designed for the low-frequency noise control problem by combining a perforated plate and a coiled back cavity structure. Based on the multiphysics field coupling method and thermoviscous acoustic theory, the effect of structural parameter changes on the sound absorption performance of the metamaterial structure is investigated using finite element analysis. The sound energy dissipation mechanism of the metamaterial structure is studied. Finally, 3D printing technology is used to prepare the metamaterial model structure, and the low-frequency sound absorption performance of the metamaterial structure is tested through structural sound absorption performance experiments, which verify that the metamaterial has subwavelength sound absorption performance.

The gear-bearing system is the most important part of integrally centrifugal compressors. According to statistics, the majority of integrally geared compressor accidents are caused by excessive vibration of the geared rotor. However, its complicated dynamic characteristics and inevitable vibration faults in actual operation present significant challenges throughout the analysis and design stages. In this paper, the coupled self-excited vibration of the gear system characterized by multipoint meshing and oil film bearing supporting is investigated. Firstly, the structure of the gear system in an integrally geared compressor is used as a research object. The modeling approach of meshing excitation, including time-varying mesh stiffness, gear meshing error, and tooth backlash are introduced. However, the variable stiffness and damping coefficient equations of journal bearing and oil film thrust bearing are modeled and utilized to approximate the variable bearing force and simplify the vibration computation under the assumption of Newtonian fluid. Then, a dimensionless modeling method of the gear system considering gyroscopic moment of gear disk, variable meshing force, as well as variable stiffness and damping coefficient is proposed. Based on the dynamic model, the influence of the bearing dynamic coefficients and load on the vibration of the entire gear system is studied. Among which, the vibration displacement and meshing force are examined using frequency-domain and time-domain analysis methods. The results suggest that the flexible support can restrain the system’s nonlinear motion, whilst increasing load on the gear system can improve gear operation stability and reduce load fluctuation.

Maxwell’s equations and the Lorentz force equation form the foundation of classical electromagnetic theory and their discovery led to the development of special relativity. Despite this achievement, their universal compatibility with the conservation of momentum and relativistic energy transformations is still debated. Incorporating effects of hidden momentum with the Lorentz force equation or using the Einstein–Laub formula are two common approaches to address some of these concerns. Which method to use, or if a change to classical electromagnetism is even required, remains controversial. A new theoretical approach is presented in this paper to address this using relativistic electromagnetic energy inertial frame transformations. These transformations identify a situation where an apparent violation of conservation laws could occur and how to consolidate this with electromagnetic theory. An explanation regarding the elementary nature of magnetism and the relationship between inertia and electromagnetic energy is also commented on.

Magnetic gear is a non-contact transmission mechanism, which overcomes the drawback of mechanical gear transmission. Although the series multi-stage magnetic gear can provide a large gear ratio compared to the single-stage magnetic gear, the lower torque density of the series multi-stage magnetic gear limits its use in high-power wind turbines. According to the magnetic gear field modulation mechanism and the differential transmission method, a differential multi-stage coaxial magnetic gear transmission device is proposed, which can achieve transmission with a large gear ratio and large torque density. Based on the differential multi-stage coaxial magnetic gear structure and its working principle, the finite element method is used to simulate the electromagnetic performance of the multi-stage coaxial magnetic gear. Futhermore, the electromagnetic performance of the two stages of the proposed magnetic gear are compared. The results show that there is a significant difference between the the electromagnetic performance of the first stage and that of the second stage. The torque ripple of the first stage is more dramatic than that of the second stage. The torque ripple amplietude of the inner rotor of the first stage is 5.08‰ larger than that of the second stage. The torque ripple amplietude of the outer rotor of the first stage is 4.591‰ larger than that of the second stage.

Surface appearance of involute gear is the basis to research the dynamic performance of gear transmission system. The Delaunay triangulation method of layered local dynamic is proposed to construct the precise tooth surface of the known tooth surface appearances. The concave and convex region of the real tooth surface was extracted by isosurface subdivision. In order to smooth the surface, the energy method and the improved fractal method with minimum included angle are used to smooth the curve. On the basis of the loaded tooth contact analysis of involute gears, the loaded tooth contact analysis model of digital error tooth surface is constructed. The tooth surface appearances of fuzzy tooth surface were predicted by extracting contact patterns under various working parameters on the experimental platform. Through the analysis on actual examples, it is concluded that the method proposed in this manuscript can accurately predict the tooth surface morphology of fuzzy tooth surface and lay the foundation for the dynamic performance optimization of gear system with fuzzy tooth surface.

Accurate knowledge of the input torque in wind turbine gearboxes is key to improving their reliability. Traditionally, rotor torque is measured using strain gauges bonded to the shaft. Transferring the resulting signal from the rotating shaft to a stationary data acquisition system while powering the sensing devices is complex and costly. The magnitude of the torques involved in wind turbine gearboxes and the high stiffness of the input shaft pose additional difficulties. This paper presents a new alternative method to measure the input torque in wind turbine gearboxes based on deformation measurements of the static first-stage ring gear. We have measured deformation using fiber-optic strain sensors based on fiber Bragg gratings because of their advantages compared to conventional electrical strain gauges. The present study was conducted on a Siemens Gamesa Renewable Energy gearbox with a rated power of 6 MW, in which a total of 54 fiber-optic strain sensors were installed on the outer surface of the first-stage ring gear. The gear mesh forces between the planets and the ring gear cause measurable deformations on the outer surface of the stationary ring gear. The measured strains exhibit a dynamic behavior. The strain values change depending on the relative position of the strain sensors to the planet gears, the instantaneous variations of the input torque, and the way load is shared between planets. A satisfactory correlation has been found between the strain signals measured on the static ring gear and torque. Two signal processing strategies are presented in this paper. The first procedure is based on the peak-to-peak strain values computed for the gear mesh events, and therefore torque can only be estimated when a gear mesh event is detected. The second signal processing procedure combines the strain signals from different sensors using a Coleman coordinate transformation and tracks the magnitude of the fifth harmonic component. With this second procedure, it is possible to estimate torque whenever strain data of all sensors are available, leading to an improved frequency resolution up to the sampling frequency used to acquire strain data. The method presented in this paper could make measuring gearbox torque more cost-effective, which would facilitate its adoption in serial wind turbines and enable novel data-driven control strategies, as well as a more accurate assessment of the consumed fatigue life of the gearboxes throughout their operation.

The objective of this paper is to present an approach for the detection of change in rolling element bearings (REB) operating conditions that can lead to premature failure. The developed technique is based on the measurement of the kinematics of the bearing cage. The rotational motion of the cage is driven by the traction forces produced in the contacts of the rolling elements with the races. It is known that the cage angular frequency relative to shaft angular frequency is dependent of the bearing load, the bearing speed and the lubrication condition, as these factors are determinant for the lubricant film thickness and the associated traction forces. As an important part of REB failures are caused by misalignment or lubrication problems, any evidence of these conditions should be interpreted as an incipient fault. In this paper a novel method for the determination of the instantaneous angular speed (IAS) of the cage is developed. The method is evaluated in a deep grove ball bearing test rig equipped with the cage IAS sensor, as well as custom acoustic emission (AE) transducer and a piezoelectric accelerometer. The cage IAS is analyzed under different bearing loads and shaft speed, showing the dependence of the cage angular speed with the calculated lubricant film thickness. Typical bearing faulty operating conditions (mixed lubrication regime, lubricant depletion and misalignment) are recreated and it is shown that the cage IAS is dependent on the lubrication regime and is sensitive to misalignment. The AE signal is used as a lubrication regime evaluator as well. Experimental results show that the proposed technique can be used as a condition monitoring tool to detect abnormal REB conditions that can lead to premature failure.

In this work, solitary wave solutions of particle mechanical metamaterials are studied, in which the mass-in-mass structure with local resonators is considered. The Hertzian contact theory is used to describe adjacent particles in a precompressed granular chain. The governing wave equations are decoupled, and the expressions of bright, dark, and peaked solitary waves are derived, respectively. According to the results, both the wave velocity and prestress can affect the propagation of solitary waves. The amplitudes of bright and peaked solitary waves are smaller when a larger prestress is applied, which are different from the dark solitons. Furthermore, the wave widths become larger as the prestress increases.