Kinematic Theory Research Articles

Semi-analytical solution for static and free vibration of multilayered functionally graded elastic plates with imperfect interfaces

In this paper, the three-dimensional static behavior and the free vibration of simply supported multilayered functionally graded elastic plates with bonding imperfections is derived. The imperfect interfaces between the adjacent layers are modeled by the spring-type layer model. In each layer, a well-adapted semi-analytical solution coupling the state-space approach with the fourth-order Runge-Kutta numerical procedure is elaborated. In consequence, the intricate three-dimensional problem has been reduced to a one-dimensional recursive problemwith which arbitrary functionally graded material’s model and number of layers can be easily handled. The predicted solution in each layer has been propagated from the bottom to the top layers of the plate using the propagator matrix method and taking into account the transfer matrix at the imperfect interfaces. The transfer relationship linking the top and the bottom surfaces of the multilayered functionally graded plate is therefore obtained. The accuracy and reliability of the proposed methodological approach have been clearly demonstrated by several numerical tests. The predicted numerical results have been well compared with the available ones obtained by the pseudo-Stroh formalism, discrete layer approach, finite elements method, Layerwise method, variable kinematic model, sinusoidal and hyperbolic shears deformations theories, respectively. These results showed that the imperfect interfaces have a strong effect on the static behavior and the natural frequencies of multilayered functionally graded plates. In addition, the obtained results showed that when the dimensionless interface parameter increase the natural frequencies decrease quickly.

On the application of variational theory to urban networks

The well-known Lighthill–Whitham–Richards (LWR) theory is the fundamental pillar for most macroscopic traffic models. In the past, many methods were developed to numerically derive solutions for LWR problems. Examples for such numerical solution schemes are the cell transmission model, the link transmission model, and the variational theory (VT) of traffic flow. So far, the eulerian formulation of VT found applications in the fields of traffic modelling, macroscopic fundamental diagram estimation, multi-modal traffic analyses, and data fusion. However, these studies apply VT only at the link or corridor level. To the best of our knowledge, there is no methodology yet to apply VT at the network level. We address this gap by developing a VT-based framework applicable to networks. Our model allows us to account for source terms (e.g. inflows and outflows at intersections) and the propagation of spillbacks between adjacent corridors consistent with kinematic wave theory (KWT). We show that the trajectories extracted from a microscopic simulation fit the predicted traffic states from our model for a simple intersection with both source terms and spillbacks. We also use this simple example to illustrate the accuracy of the proposed model, and the ability to model complex bottlenecks. Additionally, we apply our model to the Sioux Falls network and again compare the results to those from a microscopic KWT simulation. Our results indicate a close fit of traffic states, but with substantially lower computational cost. The developed methodology is useful for extending existing VT applications to the network level, for network-wide traffic state estimations in real-time, or other applications within a model-based optimization framework.

Computer simulation for stability performance of sandwich annular system via adaptive tuned deep learning neural network optimization

In this article with the aid of adaptively tuned deep neural network (DNN), dynamic stability analysis of the sandwich structure has been investigated. Due to finding the design-points features, the numerical solution procedure called two-dimensional generalized differential quadrature technique has been applied to the ordinary differential equations of the current structure system acquired on the foundation of the kinematic theory with refined higher order terms. Also, the involved parameters with the optimum values in the fully-connected neural network mechanism are obtained via momentum-based optimizer. For modeling a moderately thick structure, higher order terms of shear deformation are chosen. For stability analysis of the current structure the design points considering the method of adaptive learning is presented. For analysis of the current structure 'accuracy (used for determining the design-points) is presented through than the published outcomes in the literature. The outcomes of accuracy section of the current research show that the DNN-based model in analysis of the sandwich structure has less error than other models. The results show that the current momentum-based optimizer can be good tool for future researches about stability analysis of the various structure due to its good accuracy.

Observation of parametric X-ray radiation for the asymmetric Laue geometry

Angular distributions of parametric X-ray radiation from 255-MeV electrons in a thin Si crystal have been investigated for asymmetric Laue geometries using an imaging plate as a two-dimensional position-sensitive X-ray detector. The peak intensities of parametric X-ray radiation observed for (111) and (1¯1¯ 1) reflections, normalized by taking into account the effective target thickness and the transmission fraction of X-rays in the crystal, coincided within several percent. A large intensity difference depending on the asymmetry parameter, which is predicted by a dynamical theory dealing with the asymmetric Laue geometry, was not observed under the present experimental conditions. This indicates that the dependence of angular distributions of parametric X-ray radiation on the asymmetry parameter is negligibly weak, i.e., that it can be well explained by the well-established kinematical theory and dynamical theory as well as those for symmetric Laue and Bragg geometries.

Udkm1Dsim – a Python toolbox for simulating 1D ultrafast dynamics in condensed matter

The udkm1Dsim toolbox is a collection of Python classes and routines to simulate the thermal, structural, and magnetic dynamics after laser excitation as well as the corresponding X-ray scattering response in one-dimensional samples, such as multilayers. The toolbox provides the capabilities to define arbitrary layered structures on the atomic level including a rich database of element-specific physical properties. The excitation of dynamics is represented by an N-temperature-model which is commonly applied in ultrafast physics. Structural dynamics due to thermal stresses are calculated by a linear-chain model of masses and springs. The implementation of specific magnetic dynamics can be easily accomplished by the user employing a generalized magnetization interface class. The resulting X-ray diffraction response is computed by kinematical or dynamical X-ray theory which can also include polarization-dependent magnetic scattering. The udkm1Dsim toolbox is highly modular and allows for injecting user-defined inputs at any step within the simulation procedure. New version program summaryProgram Title: udkm1DsimCPC Library link to program files:https://doi.org/10.17632/bnzw823v6y.1Developer's repository link:https://github.com/dschick/udkm1DsimCode Ocean capsule:https://codeocean.com/capsule/8131941Licensing provisions: MITProgramming language: PythonJournal reference of previous version: Comput. Phys. Commun. 185 (2) (February 2014) 651–660Does the new version supersede the previous version?: YesReasons for the new version: The toolbox has been ported from MATLAB (MathWorks Inc.) to Python and is based exclusively on free and open-source components. Moreover, new features have been added that allow for a broader applicability of the toolbox.Summary of revisions: Porting to Python.Introduction of amorphous layers in the sample structures.Add magnetization property to atoms and layers.Multilayer formalism to calculate laser absorption.New magnetization class to allow for user-defined magnetization dynamics.New resonant magnetic X-ray scattering employing dynamical X-ray theory.Calculation of X-ray scattering as function of photon energy and scattering vector.Nature of problem: Simulate the thermal, structural, and magnetic dynamics of 1D layered sample structures due to an ultrafast laser excitation and compute the corresponding transient (magnetic) X-ray scattering response.Solution method: The program provides an object-oriented toolbox for building arbitrary layered 1D crystalline/amorphous sample structures including a rich database of element-specific parameters. The excitation, thermal transport, and lattice dynamics are simulated utilizing SciPy's ODE solver. Magnetization dynamics can be introduced by the user employing a magnetization interface class. The dynamical (magnetic) X-ray scattering is computed by a matrix formalism that can be parallelized.Additional comments including restrictions and unusual features: The program is restricted to 1D layered sample structures. Phonon dynamics only include longitudinal acoustic phonons (sound waves). Magnetization dynamics have to be defined by the user. X-ray scattering only allows for symmetrical and co-planar geometries due to the 1D nature of the toolbox. The program is highly modular and allows the inclusion of user-defined inputs at any time of the simulation procedure.

Modeling and modal analysis of suspension bridge based on continual formula method

A continnum model is developed for the dynamic analysis of a suspension bridge with inclined main cables and hangers, based on incremental Lagrangian formulation and kinematics theories. The static equilibrium equations are derived from a shape-finding method followed by the equations of motion. Comparison of modal analysis results of the proposed model and the finite element method demonstrates the accuracy of the proposed modelling technique.Modal analysis is further conducted with variations of the following system parameters, i.e. inclination angle of main cable, the ratio of flexural stiffness of deck in the vertical and lateral directions, the ratio of vertical flexural stiffness of deck and tensile stiffness of cable, and torsional moment of inertia of cross-section of deck. Results show that the difference of eigenfrequencies within the eigenfrequency cluster is smaller for a suspension bridge with vertical cables than that with inclined cables. Phenomena of crossover and veering of eigenfrequency loci of the bridge system are observed. The mechanism of such phenomena is further studied with the help of a sectional bridge model. The effect of variation of stiffness matrix of bridge system on the eigenfunction is studied. The condition for crossover and veering of the eigenfrequency loci of this bridge model is identified. It is noted that veering can affect the modal property of the system by coupling two involved modes. This effect should be carefully examined during the design of the suspension bridge.

Dynamics of curved dislocation ensembles

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single slip situation. In order to reduce the complexity of the problem a dipole like approximation for the orientation dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the GND densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

ИССЛЕДОВАНИЕ ПЕРЕХОДНОГО ПРОЦЕССАЭКСПЛУАТАЦИИ ПРИ КОНТАКТНОМ ВЗАИМОДЕЙСТВИИ БАРАБАННОЙ ПЕЧИ И ОПОРНЫХ РОЛИКОВ В ANSYSMECHANICAL

At first glance, a rotary kiln is a simple structural object, which is very widespread in the industry of processing and obtaining materials, both for construction and for other purposes. However, behind the external simplicity, there are complex chemical processes, mechanical, subtleties of the control system, the technology of manufacturing large-sized parts that are part of the general assembly and directly issues related to the design and modernization stage. The study of various regularities of mechanical processes associated with the theory of elasticity, kinematics and contact interactions is difficult even separately, especially when the processes run together. Studying the contact interaction of the kiln with roller supports allows to see the anomalous effects that can occur if the design is incorrect. In a specific case, it is necessary to observe how, under the action of external forces, time-varying deformations, displacements, of individual structural elements occur, which are of key functional importance in the operation of the equipment, in conditions of contact interaction of its individual parts, taking into account inertial loads and damping. The study of transition processes with changing force factors in time will allow to obtain the response of the structure to external influences

Kinestatic Analysis of General Parallel Manipulators

Robotic mechanisms in general can be of either serial-chain, parallel-chain, or hybrid (a combination of both parallel and serial chains) geometry. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when it is considered in the general context. In this article, we present a general procedure for systematic formulation and characterization of the instantaneous kinematics for a robotic mechanism with a general parallel-chain geometry. A kinestatic approach based on screw system theory is adopted in this treatment. The resulting equation is a compact Jacobian matrix of the system which includes attributes from not only the active joints but also the passive constraints. An example has been provided to demonstrate the methodology as well as its theoretical feasibility.

Quasi-static kinematics model for motion errors of closed hydrostatic guideways in ultra-precision machining

Aspheric optics has been widely employed in some high-tech industries for its superiority. In order to achieve the ultra-precision machining of these aspheric surfaces, the large optical ultra-precision grinding machine becomes crucial because it determines the efficiency of the whole process. As the key functional unit in ultra-precision machine tool, the hydrostatic guideways are commonly adopted for the excellent performance. However, the motion errors of hydrostatic guideways have a direct influence on the accuracy of the machined workpiece, and some analysis approaches have been reported correspondingly. Although the existed analysis models do work, their imperfections also can be easily captured. Accordingly, a novel analysis model with less imperfection is deserved to be developed. In this paper, the kinematic theory is utilized to establish the quasi-static analysis model for motion errors in closed hydrostatic guideways. Through the large ultra-precision grinding machine designed by our research group, the consistently good agreement between the predicted results and the measured experimental data are obtained. Furthermore, it is found that the motion accuracy is more sensitive to the profile error of the guide rail bearing the external load rather than that of the other guide rail in the closed hydrostatic guideway. The presented research is supposed to be valuable to the peer designers.

Deformation and fracture at floor area and the correlation with main roof breakage in deep longwall mining

Water inrush at floor area is a natural hazard during coal mining. Especially in the northern coalfield of China, more than 55% of coal mines are threatened by water inrush at floor area. The hazard of water inrush is becoming more serious with increasing mining depth. In this paper, the deformation and failure behavior at floor area in deep longwall mining site were analyzed. The correlation between the floor failure and main roof breakage was studied using kinematics theory. Meanwhile, the impact loads of cantilever beam breakage on the floor area at both longwall face and gob area were calculated. Combining with “Pressure arch hypothesis”, the compression and unloading mechanics processes at floor area were analyzed, and the unloading deformation model of floor structure after the breakage of main roof was established as well. In addition, the correlation between unloading deformation at floor area and the main roof breakage, mining depth and unloading stresses were also obtained. Finally, these studies have been verified by using micro-seismic monitoring data in deep longwall mining site. The results show that the impact loads are proportional to the span and loads of cantilever beam. After the breakage of cantilever beam, the impact loads were transferred to the floor area at longwall face side and gob side, and the rock masses at both sides were failed in compression. Consequently, the position of back arch foot of the pressure arch was rapidly transformed into the contact gangue zone at gob area from the last breakage position of main roof. While as the unloading stress of rock masses inside of the floor pressure arch is increasing, the depth of unloading fracture and heave below longwall face are greater than those before cantilever beam breakage. In addition, the unloading deformation at surface floor increases nonlinearly with the increase in mining depth and unloading stresses.

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation (CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135° with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.

Deployable Telescopic Tubular Mechanisms With a Steerable Tongue Depressor Towards Self-Administered Oral Swab.

Swabbing tests have proved to be an effective method of diagnosis for a wide range of diseases. Potential occupational health hazards and reliance on healthcare workers during traditional swabbing procedures can be mitigated by self-administered swabs. Hence, we report possible methods to apply closed kinematic chain theory to develop a self-administered viral swab to collect respiratory specimens. The proposed sensorized swab models utilizing hollow polypropylene tubes possess mechanical compliance, simple construction, and inexpensive components. In detail, the adaptation of the slider-crank mechanism combined with concepts of a deployable telescopic tubular mechanical system is explored through four different oral swab designs. A closed kinematic chain on suitable material to create a developable surface allows the translation of simple two-dimensional motion into more complex multi-dimensional motion. These foldable telescopic straws with multiple kirigami cuts minimize components involved in the system as the characteristics are built directly into the material. Further, it offers a possibility to include soft stretchable sensors for realtime performance monitoring. A variety of features were constructed and tested using the concepts above, including 1) tongue depressor and cough/gag reflex deflector; 2) changing the position and orientation of the oral swab when sample collection is in the process; 3) protective cover for the swabbing bud; 4) a combination of the features mentioned above.

Dynamic analyses of viscoelastic three-dimensional structures with advanced one-dimensional finite elements

This paper presents mechanical responses of viscoelastic structures with complicated geometries. The structures are discretized with finite beam elements, whose kinematic theories are derived according to the Carrera Unified Formulation. The governing equations are solved in the Laplace domain to avoid the computation of the convolution integral, which mathematically simulates the viscoelastic constitutive law. The three-dimensional displacement, strain, and stress fields are transformed in the time domain through a numerical inversion algorithm. The numerical simulations are performed on a beam with a hole at the center of its cross-section and on a thick-walled cylindrical shell subjected to various loading and boundary conditions. The comparisons between the present results, analytical predictions, and three-dimensional finite element solutions demonstrate the accuracy of the formulation.

Sigma-Lognormal Modeling of Speech

Human movement studies and analyses have been fundamental in many scientific domains, ranging from neuroscience to education, pattern recognition to robotics, health care to sports, and beyond. Previous speech motor models were proposed to understand how speech movement is produced and how the resulting speech varies when some parameters are changed. However, the inverse approach, in which the muscular response parameters and the subject’s age are derived from real continuous speech, is not possible with such models. Instead, in the handwriting field, the kinematic theory of rapid human movements and its associated Sigma-lognormal model have been applied successfully to obtain the muscular response parameters. This work presents a speech kinematics-based model that can be used to study, analyze, and reconstruct complex speech kinematics in a simplified manner. A method based on the kinematic theory of rapid human movements and its associated Sigma-lognormal model are applied to describe and to parameterize the asymptotic impulse response of the neuromuscular networks involved in speech as a response to a neuromotor command. The method used to carry out transformations from formants to a movement observation is also presented. Experiments carried out with the (English) VTR-TIMIT database and the (German) Saarbrucken Voice Database, including people of different ages, with and without laryngeal pathologies, corroborate the link between the extracted parameters and aging, on the one hand, and the proportion between the first and second formants required in applying the kinematic theory of rapid human movements, on the other. The results should drive innovative developments in the modeling and understanding of speech kinematics.

Dispersive evaluation of the Lamb shift in muonic deuterium from chiral effective field theory

We merge the dispersive relation approach and the ab initio method to compute nuclear structure corrections to the Lamb shift in muonic deuterium. We calculate the deuteron response functions and corresponding uncertainties up to next-to-next-to-next-to-leading order in chiral effective field theory and compare our results to selected electromagnetic data to test the validity of the theory. We then feed response functions calculated over a wide range of kinematics to the dispersion-theory formalism and show that an improved accuracy is obtained compared to that with the use of available experimental data in the dispersive analysis. This opens up the possibility of applying this hybrid method to other light muonic atoms and supplementing experimental data with ab initio theory for kinematics where data are scarce or difficult to measure with the goal of reducing uncertainties in estimates of nuclear structure effects in atomic spectroscopy.

Adaptive momentum-based optimization to train deep neural network for computer simulation of hygro-thermo-mechanical vibration performance of laminated plates

This article explores the vibration response of the hybrid composite structure with the aid of the adaptively tuned deep neural network (DNN). In order to find the features of the design-points, the semi-numerical technique is applied to the governing differential equations of the system acquired on the foundation of the kinematic theory with refined higher order terms. Considering higher order terms made the accuracy of this analysis suitable for moderately thick plates as well as thin ones. DNN is trained for vibrational characteristics of the design-points by employing adaptive learning rate method as the high-speed optimizer. Accuracy of the semi-numerical method (used for determining the design-points) is evaluated through the comparison with the results reported in the published studies. While, the validity of the DNN-based model in predicting the response of the system at design-points is tested and confirmed by analyzing the trend of mean squared error.

Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment

A mathematical model is developed, though this article, to investigate a vibrational behaviour of functionally graded (FG) cracked microbeam rested on elastic foundation and exposed to thermal and magnetic fields. The model includes a size scale effect and temperature dependent material properties, for the first time. The crack is modelled as a rotating spring, that is connecting the two parts of the microbeam at the crack’s position. The equation of motion of the FG microbeam is obtained by using the Euler-Bernoulli beam theory for kinematic assumption and nonlocal elasticity theory for size-dependency effects. The transverse Lorentz force induced from the magnetic field is derived using Maxwell's equations. By adding the effects of thermal loading and foundation parameters on the cracked micro beam, the motion equation of the entire system is obtained using the Hamilton’s principle and then solved with a Navier type solution method. Eight constraints equations are used to derived the frequency equation, which are boundary conditions at the end points and the displacement, slope, bending moment and transverse force continuity in the section where the crack is located. The resulting system of equations is solved sequentially, and natural frequencies and vibration modes of the cracked microbeam are obtained. The model is verified with previous published work. Numerical results are presented to illustrate influences of temperature, material composition, foundation parameters and magnetic field on the dynamics of the cracked FG microbeam.

Flow feasibility condition analysis and design optimization of contraflow left-turn lanes at signalized intersections based on kinematic wave theory

Dynamic left turning using lanes exiting an intersection in the opposite direction is a new type of left-turn traffic organization. When the left-turn traffic volume at an intersection is large, several exiting lanes adjacent to the original left-turn lanes can be converted into left-turn lanes during a certain period of free time under the control of a presignal. Based on kinematic wave theory, this paper analyzes the spatiotemporal process of the left-turn traffic flow. Three cases are analyzed, and the corresponding flow feasibility constraints are obtained in the form of requirements on the length of the contraflow left-turn lane and the coordination between the main signal and the presignal. Optimization of the lane length and signal coordination to maximize the number of vehicles entering the contraflow left-turn lane while guaranteeing traffic flow safety is discussed, and a practical example is analyzed.

On the Irreversibility in Mechanical Systems Using a New Macroscopic Energy Structure Modeling

This paper presents a macroscopic applied innovate modeling to study the performance effects of the second law of thermodynamics on the mechanical systems. To investigate the irreversibility in mechanical systems, the energy structure of the system can be studied. Some energy components relate to the reversible processes and remaining relate to the irreversible process. Exiting models are based on the studying sub structures and therefore, need a large volume of the calculations. In this paper, at first, using a macroscopic quasi-statistical approach, a new energy structure equation is extracted and by examining it’s variation in the different paths, the irreversible components as well as their structures are studied. Using the kinematic theories of dissipated energy, it can be concluded that the extracted equations have the same base as the different formulations of the second law of thermodynamics. Finally, as a mechanical system example with the possibility of irreversibility in the possible performed processes, the extracted equations are developed for viscoelasticity problems. And also the matching of the results with expected results is shown.