Superposition Method Research Articles

Flow past a rotating porous sphere in the existence of a toroidal magnetic field

This model consists of a porous spherical body rotating in an incompressible conducting fluid in the existence of a toroidal magnetic field. The toroidal field is generated by an electric dipole along the axis of symmetry. The model is split into two parts—the clear fluid region and the porous sphere. The clear fluid area is driven by the momentum equation and the permeable sphere region is driven by the Brinkman equation. The study is being done for the scenario where the impact of viscous force is much more than inertia force. The expression is found for fluid velocity and stream function by the superposition method. The results depict the impact of rotational parameters and the Darcy number on separation parameter. It is shown that the separation is low for the highly permeable sphere.

Study on the bending behavior of CFRP-confined square concrete-filled steel tubes reinforced with internal latticed steel angles

The bending mechanical properties of FRP-confined square concrete-filled steel tubes (CFST) reinforced with internal latticed steel angles, including the failure modes, characteristic curves and characteristic mechanical parameters of tested specimens, were investigated through experiments in this paper. The bending mechanisms were also analyzed using an established finite element model, including the analysis of the bending moment borne by each component, the distributions of contact pressure between different components at the mid-span section, and the distributions of the neutral axis under the bending capacity. The key influential parameters, including the tensile strength and thickness of the FRP, were also examined. The results indicate that the FRP has almost no influence on bending stiffness, however, it enhances the yield bending moment and bending capacity to a certain extent. It was also found that the enhancement decreases as the width of steel tube increases, and the influence of FRP is more profound before reaching the peak load. The calculation formulas for the bending capacity were developed using the superposition method and numerical fitting method. Analysis of their accuracy shows that the formulation using the superposition method yields relatively accurate and safe prediction results, with the prediction errors of less than 20 %.

New Analytical Solutions for Free Vibration of Cracked Functionally Graded Rectangular Plates

In aerospace engineering, the existence of cracks highly alters the mechanical behaviors of structural components. As a new class of key structural components, functionally graded material (FGM) rectangular plates with an interior/side crack are focused on in this study. New analytical free vibration solutions are put forward for such cracked FGM plates. First, a cracked plate is decomposed into several subplates with the necessary continuity conditions to address the physical discontinuity issue caused by the crack. The challenge then becomes deriving analytical free vibration solutions for each subplate. To accomplish this task, a symplectic superposition method (SSM) is developed to deal with FGM rectangular plates with various boundary conditions, including the complex continuity conditions. The SSM eliminates the need for a predefined solution form, and its solution procedure, including variable separation and eigen expansion, is mathematically rigorous. Afterward, the analytical solutions obtained via the SSM are integrated to serve as the final free vibration solution of the cracked FGM plate. Comprehensive results based on the obtained analytical solutions, including natural frequencies and vibration modes, are presented and validated. The solutions are further used to investigate the effects of some important parameters, such as crack length and crack location.

Modeling the thermo-oxidative aging effects on fatigue life of natural rubber using a continuum damage mechanics approach

Thermo-oxidative aging (TOA) significantly impacts the fatigue life of rubbers by reducing the fatigue strength and modifying the slope of the Wöhler curve, rendering traditional time-temperature superposition methods inadequate. In this work, we aim to develop a model capable of predicting the effect of TOA on the fatigue properties of rubbers. For this purpose, dumbbell specimens of natural rubber (NR) were subjected to aging in an air-vented oven at different temperatures prior to mechanical testing. Tensile tests were conducted to quantify the aging effects on a microscale network parameter known as elastically active chains (EAC) density, along with determining ultimate properties such as the stress and strain at break. By using a time-temperature equivalence and the Arrhenius shift factor, master curves were constructed for both EAC density and ultimate properties. Subsequently, the fracture properties of the aged material were predicted using an energy limiter approach whose evolution follows that of EAC density. Furthermore, a relationship between the parameters of the continuum damage mechanics (CDM) approach (specifically, the power law parameters of the Wöhler curve) and the fracture properties was proposed, resulting in accurate estimates of the fatigue life regardless of the aging conditions. Satisfactory agreement was observed between the model predictions and the data for nine aging conditions encompassing four different temperatures. The CDM approach also allows assessing the evolution of mechanical damage within the material influenced by TOA. The novelty of this approach lies in establishing a direct relationship between fatigue and fracture properties. Moreover, this is the first time to the best of our knowledge that TOA has been explicitly incorporated into a fatigue life prediction model via the evolution of the EAC density.

Exact cosmological solutions for a Chaplygin Gas in anisotropic petrov type D spacetimes in Eddington-inspired-Born-Infeld gravity: Dark Energy model

We consider a Petrov Type D physical metric g, an auxiliary metric q and a Chaplygin Gas of pressure P in Eddington-inspired-Born-Infeld theory. From the Eddington-inspired-Born-Infeld-Chaplygin Gas equations, we first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order linear ordinary differential equations for the non-vanishing components of the pressure P, the physical metric g and the auxiliary metric q. Thanks to the superposition method, we collect an analytical solution for the nonlinear system obtained, which allows to retrieve new exact cosmological solutions for the model considered. By studying the Kretschmann invariant, we see that a singularity exists at the origin of the cosmic time. By the Kruskal-like coordinates, we conclude that this solution is the counterpart of the Friedman-Lemaître-Robertson-Walker spacetime in the Eddington-inspired-Born-Infeld theory. The Hubble and deceleration parameters in both directions of the physical metric g and the auxiliary metric q, as well as their behaviours over time, are also studied. The thermodynamic behaviour of the Chaplygin Gas model is investigated and, as a result, we show that the third-law of thermodynamics is verified. This means that the value of the entropy of the Chaplygin Gas in the perfect crystal state is zero at a temperature of zero Kelvin, which yields a determined value of the entropy and not an additive constant. Finally, we show that the solutions change asymptotically to the isotropic regime of expansion of Dark Energy. With this, we infer that the Chaplygin Gas can show a unified picture of Dark Energy and Dark Matter cooling during the expansion of the Universe.

A unified dynamic stiffness modeling of multi-plate coupled systems with discrete spring connections

This work presents a unified dynamic stiffness modeling for the vibration analysis of multi-plate coupled systems with discrete spring connections (MPCS-DSC). First, based on the governing differential equation of the plate, the dynamic stiffness matrix (DS) of transverse and in-plane vibration for a completely free rectangular plate is separately derived by combining the generalized superposition method and the projection method. Then, according to the continuity of displacements at the connection point between the spring and the plate, the projected DS matrix of the discrete spring is developed. Then, using an element assembly concept similar to that in the finite element method (FEM), global DS matrices of various coupled systems are determined by assembling the spring's DS matrice and the transverse or in-plane DS matrices of the plate. In order to verify the accuracy and applicability of the proposed method, the free and forced vibration analysis of four types of coupling systems is carried out. The reliability and applicability of the proposed method are confirmed by comparing the present results with those from open literature and the finite element solutions. This study not only expands the application range of DS modeling theory but also provides a powerful tool to investigate the vibration characteristics of the MPCS-DSC.

The Vibration Characteristics Analysis of Fiber-Reinforced Thin-Walled Conical–Cylindrical Composite Shells with Artificial Spring Technique

In this paper, the vibration characteristics (free vibration and forced vibration) of fiber-reinforced thin-walled conical–cylindrical composite shells (FTCCS) are analyzed by combining theory and experiment. Based on the classical shell theory and Kirchhoff–Love assumption, the overall structure of the FTCCS is theoretically modeled. The artificial spring technology is used to simulate the arbitrary boundary conditions at the joint, which is divided into a main spring and a secondary spring. At the same time, the displacement functions of the two sub-structure shells of the FTCCS are established by the orthogonal polynomial method, and the energy function of the FTCCS is constructed according to the continuity condition of the bolt joint. Then, the vibration characteristics of the FTCCS are solved using the Rayleigh–Ritz method and the modal superposition method. Finally, the TC300/epoxy resin-based fiber-reinforced thin-walled conical–cylindrical composite shells are selected as the research object, and the rationality of the mathematical model is verified by pulse, frequency sweeping and resonance excitation tests. The experimental results show that the errors between the natural frequency and the resonance displacement calculated by the theory and the experimental results are 1.75–4.76% and 3.79–9.28%, which confirms the rationality of the proposed model. By changing the length of the shell, the lamination angle and the semi-cone angle of the conical shell, the vibration characteristics parameters under different conditions are calculated to evaluate the influence of three physical parameters on the vibration characteristics of the FTCCS.

A broad-beam reflective metasurface enhancing signal coverage for indoor wireless communication

ABSTRACT A broad-beam planar reflective metasurface design for indoor signal coverage is presented in this letter. The proposed metasurface unit is designed as a multi-resonant structure using an additional branch on the double ring, which achieves a reflection phase shift covering 360° and a reflection magnitude remaining above 0.8 by varying the length of the square ring. To simplify the array configuration, the unit incorporates 2-bit phase quantization. In order to broaden the reflection beam of metasurface, the phase distribution of the array is determined by the aperture field superposition method. The angles of the different electromagnetic (EM) waves within the single aperture are adjusted to be moderately distinct. The co-simulation and measurement of the horn antenna and the reflective metasurface are carried out. The results show that the metasurface can generate a broad beam at 4.8 GHz with a 3 dB beamwidth of 21°, achieving a beam gain of 18dBi. The broad beam can maintain a 3 dB beamwidth greater than 19° in the 4.2–5.6 GHz band. The reflective metasurface can be used as a passive repeater to optimize signal quality and enhance wireless communication coverage in indoor non-line-of-sight (NLOS) paths.

Analytical solutions for out-of-plane response of curved beams resting on an elastic foundation under a random moving load

In this study, the vibration behaviour of a horizontally curved beam resting on an elastic foundation and subjected to a random moving force is studied. The governing coupled differential equations for the out-of-plane vibration of curved beams are derived based on the mode superposition method, Duhamel's integral, and the Laplace transformation. Note that the out-of-dynamic responses of curved beams induced by a random moving load are composed of the centred random and mean value. Analytical solutions are proposed for the beam’s vertical and torsional deflections and the bending moment, where the rotary inertia, warping constant, and foundation stiffness are incorporated in these formulations. Because analytical studies on the random vibration of a curved beam resting on an elastic foundation are very limited, the aim of this study is to investigate the effect of relative parameters, namely, high-mode vibrations, the radius of curvature, the moving velocity, and foundation vertical and torsional stiffnesses, on the centred random and mean values of the beam dynamic responses. The results show that high-mode vibrations have a greater impact on the beam responses at higher velocities. To obtain precise results, the first 30 modes are considered in the calculation for the dynamic responses of the beams. The critical velocity is an inherent property of bridges, and it increases as the radius of curvature and foundation stiffness increase. In addition, an increase in the velocity and foundation stiffness results in a reduction in the centred random values for responses.

Logging Identification Methods for Oil-Bearing Formations in the Chang 6 Tight Sandstone Reservoir in the Qingcheng Area, Ordos Basin

The Chang 6 sandstone reservoir of the Upper Triassic Yanchang Formation in the Ordos Basin is one of the tight-oil-rich intervals in the basin. Owing to the strong heterogeneity and complex lithology of the Chang 6 reservoir, lithology and fluid identification have become more challenging, hindering exploration and development. This study focused on the Chang 6 member in the Qingcheng area of the Ordos Basin to systematically analyze the lithology, physical properties, and oil-bearing properties of the Chang 6 reservoir. We adopted the method of normalized superposition of neutron and acoustic time-difference curves, the method of induced conductivity–porosity–density intersection analysis, the method of superposition of difference curves (Δφ), and the induced conductivity curve. Our results indicated that the method of normalized superposition of neutron and acoustic wave time-difference curves could quickly and effectively identify the lithologies of tight fine sandstone, silty mudstone, mudstone, and carbonaceous mudstone. The induced conductivity–porosity–density cross-plot could be used to effectively identify oil and water layers, wherein the conductivity of tight oil layers ranged from 18 to 28.1 mS/m, the density ranged from 2.42 to 2.56 g/cm3, the porosity was more than 9.5%, and the oil saturation was more than 65%. Based on the identification of tight fine sandstone using the dual-curve normalized superposition method, the oil layer thickness within the tight fine sandstone could be effectively identified using the superposition of difference curves (Δφ) and induced conductivity curves. Verified by oil-bearing reservoir data from the field test, the overall recognition accuracy of the plots exceeded 90%, effectively enabling the identification of reservoir lithology and fluid types and the determination of the actual thickness of oil layers. Our results provide a reference for predicting favorable areas in the study area and other tight reservoirs.

Analytic analysis of free vibration problem of the plate with a rectangular cutout using symplectic superposition method combined with domain decomposition technique

Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.

Investigation on dynamic modelling and nonlinear vibration behaviors of composite structures: A case of cable-beam model

This paper conducts a nonlinear analysis of cable-beam model of cable-stayed bridges by using the exact mode superposition method (EMSM) and the cable-beam dragging method (CBDM), respectively, comparing and exploring their theoretical foundations and practical implications. The EMSM is based on the global mode function of the cable-beam structure for nonlinear analysis, yet it requires more computational resources. The CBDM is based on the cable-beam dragging equations for nonlinear analysis, which can quickly obtain the static equilibrium state and dynamic response of the cable-beam system, but it requires some simplifying assumptions on the cable-beam connection conditions. Research results demonstrate qualitative and quantitative differences between these two methods through parametric analysis on dynamic behaviors, which provide a significant methodological study and a reference for the design and dynamics of composite structures.

Solvent-induced phase separation and Hofmeister effect enhanced strong, tough, and adhesive polyion complex hydrogels

Polyion complex (PIC) hydrogels possess excellent strength and toughness due to the dynamic and synergetic energy dissipation mechanism associated with the co-existence of both strong and weak bonds, ionic and hydrogen, in their networks. On the other hand, PIC hydrogels usually exhibit poor wet adhesion properties. Furthermore, the role such dynamic energy dissipation mechanism plays in determining interfacial binding is unknown. To address these challenges, here, we report the fabrication of an adhesive PIC hydrogel, poly(sodium p-styrenesulfonate) (NaSS)/poly(acryloyloxyethyltrimethyl ammonium chloride (DAC)–co-2-vinyl-4,6-diamino-1,3,5-triazine (VDT), i.e. PNaSS/P(DAC-co-VDT), by introducing a multi-hydrogen bonding capacity functional co-monomer, VDT, and solvent-induced gel phase separation into the fabrication process. The resulting hydrogel exhibited as high as 174 kPa adhesion strength, with retained high mechanical properties, typically 1.2 MPa tensile strength, 2.12 MPa Young’s modulus, and 452% strain. The mechanical properties of PNaSS/P(DAC-co-VDT) were tunable by adjusting the content of VDT and of the total monomer concentration in hydrogel precursor solutions (Cm), as well as by taking advantage of the Hofmeister effect. The dynamic modulus spectra of PNaSS/P(DAC-co-VDT) hydrogels at different Cm’s in extended frequency windows with time–temperature superposition method (TTS) were acquired and analyzed to explore the influence of polymer entanglement on the hydrogel network structure. The microscopic structure-macroscopic mechanical property relationship of PNaSS/P(DAC-co-VDT) hydrogels at different Cm’s and immersed in different salt solutions was further studied using the Mooney-Rivlin equation and by fitting the tensile data to Creton’s viscoelastic model. This study may provide new insights into designing and constructing strong and tough PIC hydrogel-based adhesives.

Study on the Length of the Effective Vibration Area of the Catenary in a Pantograph–Catenary Interaction System

The effective vibration area includes most of the catenary vibration caused by pantograph–catenary interactions and is the basis of the real-time catenary model for hardware-in-the-loop simulation. However, while the length of the effective vibration area is one of the most important parameters of the real-time catenary model, it has not been fully studied at present. In this paper, the length of the effective vibration area is first investigated. A pantograph–catenary interaction model is developed based on the modal superposition method. After the validation of the model, the vibration energy distribution of the catenary is used to determine the length of the effective vibration area based on the converged total energy. The influence of vehicle velocity and contact wire tension on the vibration energy distribution and length of the effective vibration area is investigated. The obtained appropriate length of effective vibration area is validated by a real-time catenary model and online measurement data of the contact force. The investigation results show that the energy distribution of the catenary can accurately determine the length of effective vibration area, and it increases with increasing vehicle velocity but decreases with increasing contact wire tension. The appropriate length of effective vibration area should be at least 160 m (approximately three spans) in the pantograph–catenary system.

Symplectic analytical solutions for free vibration of elastically line-hinged orthotropic rectangular plates with rotationally restrained edges

The elastically line-hinged orthotropic rectangular plates with rotationally restrained edges are commonly used in engineering applications such as deployable structures. However, it is intractable to obtain the analytical solutions for the free vibration problems of such structures owing to the challenges in processing the high-order partial differential equations. Here, we make a first attempt to deal with such issues within the Hamilton system-based symplectic space. The problem of a plate is transformed into the symplectic space from the Euclidean space, and the subplates that may be analyzed analytically by the symplectic superposition method are then obtained with the division of the entire plate. The complex boundary and connection forms are achieved by enforcing mechanical quantities with undetermined expansion coefficients on the edges of the subplates. By integrating the solutions of the subplates, the final solution of an elastically line-hinged orthotropic rectangular plate with rotationally restrained edges is accessible. The proposed solution scheme is performed with rational derivations, with no requirement for pre-defined solution forms. Comprehensive results with validations under various boundary and hinge connection cases are presented. Moreover, detailed parametric investigations are conducted, which could facilitate the engineering design of deployable structures.

Degradation of handmade paper: Exploration of water adsorption behavior and estimation of lifespan based on time-temperature-humidity superposition

Traditional handmade papers, as the carriers of paper-based cultural relics, inevitably undergo various deteriorations during long-term preservation. Establishing a reasonable degradation kinetic model of handmade paper under the synergistic action of multiple factors is the crucial to evaluate paper aging and lifespan of paper. This study explores the moisture content and diffusion behavior of water molecules in traditional handmade paper to identify the interaction between fibers and water molecules at the accessible sites by two-dimensional infrared spectroscopy (2D-COS). Additionally, the optimized second-order kinetic models for the degradation of three types of Kaihua handmade papers was presented based on the time-temperature-humidity superposition method. A time-temperature-humidity translation factor is incorporated into the dynamic model to quantitatively analyze the synergistic effect of temperature and humidity on the degradation rate of handmade paper. The degradation rates of handmade paper with different raw materials and handcraft processes demonstrated significant effects of the cooking and bleaching processes on the aging degradation process and the durability of the paper. The improved second-order degradation kinetic model, considering the cooperation process with multi-factors and mechanisms, enables the extrapolation of paper aging properties at arbitrary temperature and humidity effectively, which provides a more reasonable estimation of handmade paper's lifespan.

Numerical study on slamming characteristics of an elastic wedge based on a two-way coupled finite volume and modal superposition method

Numerical study on slamming characteristics of an elastic wedge based on a two-way coupled finite volume and modal superposition method

Projection superimposition for the generation of high-resolution digital grating.

Fringe projection profilometry based on MEMS micro-vibration mirrors is very promising due to its rapid projection, large depth of field, compact size, and low cost. Although high-frequency fringes can achieve accurate reconstruction, the projector must offer sufficient pixel resolution. In this paper, we proposed a high-resolution projection technique called the delay superposition method. During a single exposure time of the camera, the projector projects a group of low-resolution fringe patterns, which are delayed according to the movement characteristics of the vibration mirror. Then, the camera exposure superimposes these low-resolution images to form a high-resolution image. These two steps effectively subdivide the angle intervals, thereby achieving a pixel interpolation. Finally, experimental results show that the proposed method can significantly improve the projector's pixel resolution and reconstruction accuracy. The proposed method allows the MEMS projector's pixel resolution (along one direction) to far exceed that of common DLP projectors. It holds great application potential for high-frequency fringe projection.

Superposition Rate: A Developed Approach for Analyzing Production Data in Tight Gas Reservoirs

The paper examines the application of various methods to analyze production data in which the superposition principle being one of them. This principle is divided into two main methods: Superposition rate and Superposition time. Both are designed to deal with multiple flow rates within production data. The Superposition time converts the production time into constant values and uses the final flow rate value. On the other hand Superposition rate consolidates multiple rates into a single flow rate during production time. This study focuses on analysis of production data using a developed method based on superposition-rate approach. This method converts variables such as flow rate and pressure into constant values, where each flow regime has its own technique by which superposition-rate is utilized. In addition, comparison between conventional and unconventional reservoirs is involved, particularly emphasizing the benefits and drawbacks of tight gas reservoirs.Various types of superposition methods with their functions were discussed. Among them, a workflow part includes a case study of a dominated flow regime used for a hydraulic fractured single well. The workflow part of this study includes a case study of hydraulically fractured well under a dominant flow regime. Results comparing multiple rates method with super position-rate method indicate that the latter has better accuracy with (R) coefficient of (0.96). Case study on fracture reservoir also shows further validated of superposition-rate by accurately estimating drainage volume.

Self-oscillation of cantilevered silicone oil paper sheet system driven by steam

Self-oscillation is to draw energy from a stable external environment to maintain its own continuous motion, making it a highly relevant concept for intelligent materials, soft robots and medical devices. Exploring a simple and durable system driven by steam for self-sustained motion is a tough challenge. In this article, a novel steam-driven self-oscillation cantilevered silicon oil paper is proposed, incorporating a rectangular silicon oil paper sheet, a fixed end and a set of vertically rising steam. Experiments show that the silicone oil paper sheet can engage in continuous periodic self-oscillation in a steady steam. According to the above phenomenon, the dynamic model of the self-oscillation system is established, and the control equation is derived. The semi-analytical form of solution is obtained using the modal superposition method. It shows that the paper sheet has two motion patterns, namely, the static pattern and the self-oscillation pattern. The theoretical predictions are in general agreement with the experimental results. The silicone oil paper sheet maintains the self-oscillation by absorbing thermal energy to offset the damping dissipation. In addition, the critical conditions for self-oscillation and the key system parameters affecting its frequency and amplitude are also examined thoroughly. The oscillation amplitude can be controlled by adjusting the inclined angle, steam temperature factor, damping coefficient and thermal characteristic time, while the frequency mainly depends on the inclined angle and steam temperature factor. The cantilevered silicone oil paper sheet has advantages of simple structure, flexible adjustment, customizable size, and easy assembly. It is expected to have a certain guiding significance in the fields of remote drives, sensors, and micro-robot design.