Approximate Analytical Model Research Articles

Three-dimensional contact analysis of coupled surfaces by a novel contact transformation method based on localized Lagrange multipliers

Instead of obsessively emphasizing to reduce the number of time increments and reshape the models, a novel surface contact transformation to increase efficiency is presented in this study. Wear on the bearing surfaces was investigated following the coupled regions from the pressure distribution, computed by means of three-dimensional finite element method models; an approximate analytical model and formulation in three-dimensional frictional contact problems based on modified localized Lagrange multiplier method have also been developed and discussed. Understanding wear behavior patterns in mechanical components is a significant task in engineering design. The proposed approach provides a complete and effective solution to the wear problem in a quasi-dynamic manner. However, expensive computing time is needed in the incremental procedures. In this article, an alternative and efficient finite element approach is introduced to reduce the computation costs of wear prediction. Through the successful verification of wear depth and volume loss of the pin-on-plate, block-on-ring, and metal-on-plastic artificial hip joint wear behaviors, the numerical calculations are shown to be both valid and feasible. Furthermore, the results also show that the central processing unit time required by the proposed method is nearly half that of the previous methods without loss of accuracy.

Continuously Operating Laser Range Finder Based on Incoherent Pulse Compression: Noise Analysis and Experiment

A continuously operating laser range-finder setup based on the incoherent compression of periodic binary unipolar sequences is analyzed and demonstrated experimentally. The periodic cross-correlation between the directly detected echoes and a properly chosen reference sequence exhibits perfect zero sidelobes. An approximate analytic model for the peak-to-noise-sidelobe ratio in the presence of additive detector noise is established. Tradeoffs among transmitted power, measurement range, aperture size, and acquisition time are addressed. Performance is compared against that of time-of-flight measurements, and scenarios in which each protocol is advantageous are discussed. Outdoor ranging measurements at a distance of 270-m and with a ranging resolution of 15 cm are reported. The range to a Lambertian reflector target at that distance could be measured using a peak transmission power of only 800 mW, at a low signal-to-noise ratio (SNR) of −25 dB and with an acquisition time of 50 $\mu\text{s}$ .

Heat Transfer of a Straight Flat Fin Surface Subjected to Low Temperature and Immersed in an Aqueous Medium with a Constant Temperature

An approximate analytical model is proposed to determine the thickness of the water ice layer on the surface of a straight flat fin as part of heat exchange equipment. This solution could be of interest for use in engineering calculations, in particular, in the design of water coolers, TNT evaporators, LNG gasifiers, etc.

Modification of Ohnaka back diffusion equation

The first and simplest analytical model for a binary alloy came from Gulliver-Scheil, considering a constant partition coefficient at the interface during solidification without back diffusion in solid. Later, Brody-Flemings proposed an approximate analytical model, taking into account one dimensional diffusion of solute in solid during solidification in plate-like dendrite arms for parabolic growth. However, this model does not work well at high back diffusion values. Ohnaka modified this back diffusion parameter. The Ohnaka model works well at the low and high back diffusion values but it underestimates between them. In this paper, Voller-Ohnaka back diffusion model is modified further to predict concentration profiles more accurately than all others analytical models for the parabolic growth rate.

A new method for designing dual foil electron beam forming systems. I. Introduction, concept of the method

In Part I of this work existing methods and problems in dual foil electron beam forming system design are presented. On this basis, a new method of designing these systems is introduced. The motivation behind this work is to eliminate the shortcomings of the existing design methods and improve overall efficiency of the dual foil design process. The existing methods are based on approximate analytical models applied in an unrealistically simplified geometry. Designing a dual foil system with these methods is a rather labor intensive task as corrections to account for the effects not included in the analytical models have to be calculated separately and accounted for in an iterative procedure.To eliminate these drawbacks, the new design method is based entirely on Monte Carlo modeling in a realistic geometry and using physics models that include all relevant processes. In our approach, an optimal configuration of the dual foil system is found by means of a systematic, automatized scan of the system performance in function of parameters of the foils. The new method, while being computationally intensive, minimizes the involvement of the designer and considerably shortens the overall design time. The results are of high quality as all the relevant physics and geometry details are naturally accounted for. To demonstrate the feasibility of practical implementation of the new method, specialized software tools were developed and applied to solve a real life design problem, as described in Part II of this work.

Matrix Shear-Lag Parameter in a Shape Memory Alloy-Actuator-Reinforced Silicon Elastomer

The excellent qualities possessed by silicon elastomer when used in designing flexible parts of mechanical systems, make it imperative that we analyze its deformations and distributed axial forces in a matrix of shape memory alloy (SMA) fibers designed as possible appendages for gripping robots. The essence of these analyses is to determine the shear-lag parameter which has influence on the axial distributed forces proposed as a gauge for testing the structure in a high yield, high force and high strain mechanical environment. The insertion of SMA fibers in flexible rods cast using silicon elastomer results in the deformation of the host medium once shape recovery of the fiber occurs. This paper aims to analyze the mechanics of the said shape recovery in a modeled silicon elastomer rod with a single off-axis reinforced SMA actuator. The compressive force distribution mechanism and the bending moment caused by phase transformation in the design are determined using an approximate analytical model. The deformations on the structure proposed as an appendage on gripping robots were further analyzed by determining their equations of equilibrium, force factors and their comparative shear-lag models to be able to estimate the force distribution on the structure.

Determination of the height of the “meteoric explosion”

When cosmic bodies of asteroidal and cometary origin, with a size from 20 to approximately 100 m, enter dense atmospheric layers, they are destroyed with a large probability under the action of aerodynamic forces and decelerated with the transfer of their energy to the air at heights from 20–30 to several kilometers. The forming shock wave reaches the Earth’s surface and can cause considerable damage at great distances from the entry path similar to the action of a high-altitude explosion. We have performed a numerical simulation of the disruption (with allowance for evaporation of fragments) and deceleration of meteoroids having the aforesaid dimensions and entering the Earth’s atmosphere at different angles and determined the height of the equivalent explosion point generating the same shock wave as the fall of a cosmic body with the given parameters. It turns out that this height does not depend on the velocity of the body and is approximately equal to the height at which this velocity is reduced by half. The obtained results were successfully approximated by a simple analytical formula allowing one to easily determine the height of an equivalent explosion depending on the dimensions of the body, its density, and angle of entry into the atmosphere. A comparison of the obtained results with well-known approximate analytical (pancake) models is presented and an application of the obtained formula to specific events, in particular, to the fall of the Chelyabinsk meteorite on February 15, 2013, and Tunguska event of 1908, is discussed.

The Steady-State Convection-Diffusion Equation at High Péclet Numbers for a Cluster of Spheres: An Extension of Levich's Theory

This paper describes an approximate analytical model of competitive effects between members of a dense cluster of absorbing objects, which are modeled as spheres. Neighboring absorbing spheres compete for diffusing species and thereby reduce each other's rate of absorption. Levich's well-known asymptotic (high Peźclet number) theory of convection-diffusion considers only the inner region of the concentration boundary layer; it does not describe the wake zone accurately. An extension of the Levich model is constructed for the wake zone. This is used to model intersphere competitive effects. The model demonstrates that for two neighboring spheres aligned along the flow direction, the absorption of the downstream sphere is substantially reduced vis-aź-vis the upstream sphere. The model is verified by comparison to numerical simulation studies. Both single-sphere simulations (reported in this paper) and multisphere simulations (taken from existing literature) are considered. In the single-sphere case, the discrepancy between the analytical model and the numerical results is maximally 10% at Pe = 10 and much lower at higher Peźclet numbers. An appreciable part of the error stems from the original Levich model itself, rather than from our method of extending the Levich model. In the multisphere case, the difference between the analytical model and the numerical studies is generally less than 30% . At small intersphere separations (say, center-to-center distances $<$ 5 sphere radii), the model tends to overestimate the interference effects. This is related to the fact that flow stagnancy in the space between two closely packed spheres is not taken into account in the model.

Analytical Models for the Response of the Double-Bottom Structure to Underwater Explosion Based on the Wave Motion Theory

The aim of this paper is to apply the elastic wave motion theory and the classical one-dimensional cavitation theory to analyze the response of a typical double-bottom structure subjected to underwater blast. The section-varying bar theory and the general acoustic impedance are introduced to get the simplified analytical models. The double-bottom structure is idealized by the basic unit of three substructures which include the simple panel, the panel with stiffener (T-shaped), and the panel associated with girder (I-shaped). According to the simplified models, the analytical models for the corresponding substructures are set up. By taking the cavitation effect into account, the process of fluid-structure interaction can be thoroughly understood, as well as the stress wave propagation. Good agreement between the analytical solution and the finite element prediction is achieved. On the other hand, the Taylor predictions for the panel associated with girder (I-shaped) including the effects of cavitation are invalid, indicating a potential field for the analytical method. The validated analytical models are used to determine the sensitivity of structure response to dimensionless geometric parametersα-k,β-k, andγ-k. Based on the dynamic response of the substructures, we establish the approximate analytical models which are able to predict the response of double-bottom structure to underwater explosion.

Analytical modeling of thermoelastic damping in bilayered microplate resonators

Accurate determination of thermoelastic damping (TED) is very challenging in the design of microresonators with composite structures. This paper investigates TED in the bilayered microplate. The temperature field in the bilayered microplate with a thermally perfect interface subjected to a time-harmonic excitation is presented. The total damping is obtained by computing the energy dissipated in each layer. An analytical model in the form of an infinite series for TED in the bilayered fully clamped rectangular and circular microplates is developed, and the convergence rate of the present model is studied. For TED in the bilayered cantilever and fixed-fixed microplates oscillating at the first natural frequency, an approximate analytical model is also presented based on Rayleigh’s method. TED calculated by the present model agrees well with that obtained by the finite element method (FEM). Present results show that the effects of the thickness and the property of the metallic layer on the peak damping are significantly. The present model can be used to optimize the design of the high-Q bilayered microplate resonators

To the problem of the intraday nutational motions of the earth pole

Based on celestial-mechanics concepts, we provide an amplitude–frequency analysis of the intraday Earth pole oscillations in terms of classical mechanics. An approximate analytical model for real trajectory measurements of the polar motion in a near-day time interval has been identified.

Conversion of an atomic to a molecular argon ion and low pressure argon relaxation**Project supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. ON171025).

The dominant process in relaxation of DC glow discharge between two plane parallel electrodes in argon at pressure 200 Pa is analyzed by measuring the breakdown time delay and by analytical and numerical models. By using the approximate analytical model it is found that the relaxation in a range from 20 to 60 ms in afterglow is dominated by ions, produced by atomic-to-molecular conversion of Ar+ ions in the first several milliseconds after the cessation of the discharge. This conversion is confirmed by the presence of double-Gaussian distribution for the formative time delay, as well as conversion maxima in a set of memory curves measured in different conditions. Finally, the numerical one-dimensional (1D) model for determining the number densities of dominant particles in stationary DC glow discharge and two-dimensional (2D) model for the relaxation are used to confirm the previous assumptions and to determine the corresponding collision and transport coefficients of dominant species and processes.

Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability

Summary Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account. In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs. Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency (RF) micro electro-mechanical system (MEMS) switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.

Stochastic entropy production arising from nonstationary thermal transport.

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the one-dimensional stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behavior of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behavior and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremization, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.

Validation of a heat transfer model for end winding bars of large hydro generators

Purpose The purpose of this paper is to carry out an analytical approximation model (heat transfer model (HTM)) for the calculation of the heat transfer coefficient at the end winding bars of large hydro generators. These coefficients are needed for lumped parameter thermal models in the design process.

Perturbed motion at small eccentricities

In the study of the motion of planets and moons, it is often necessary to have a simple approximate analytical motion model, which takes into account major perturbations and preserves almost the same accuracy at long time intervals. A precessing ellipse model is used for this purpose. In this paper, it is shown that for small eccentricities this model of the perturbed orbit does not correspond to body motion characteristics. There is perturbed circular motion with a constant zero mean anomaly. The corresponding solution satisfies the Lagrange equations with respect to Keplerian orbital elements. There are two families of solutions with libration and circulation changes in the mean anomaly close to this particular solution. The paper shows how the eccentricity and mean anomaly change in these solutions. Simple analytical models of the motion of the four closest moons of Jupiter consistent with available ephemerides are proposed, which in turn are obtained by the numerical integration of motion equations and are refined by observations.

Mono-dimensional formulation of axial-symmetric spherical shells and characterization of the linear static behaviour

In spherical shells, due to the axial-symmetry of the system, all the quantities involved in the elastic problem only depend on the curvilinear abscissa along the meridian lines. Hence, the mathematical domain of the model becomes mono-dimensional. However, in the classical model of axial-symmetric spherical shells, the kinematic problem is not the adjoint of the static problem. With the aim to clarify this aspect, a mono-dimensional linear model of axial-symmetric spherical shells has been proposed. The adopted mono-dimensional approach furnishes a model where the kinematic problem is the adjoint of the static problem. This model, able to describe the linear static behaviour of the shell, can be considered as a curved beam posed on an elastic variable soil. Specifically, the axis of the generic curved beam coincides with a meridian line and the elastic soil is related to the characteristics of the ring beams along the parallel lines. Several internal constraints and simplifying assumptions have been introduced. The comparison among approximate analytical models and a Finite Element one confirm the effectiveness of the proposed mono-dimensional approach. The most approximate model admits a closed-form solution. It appears to be perfectly capable of describing the classical oscillatory-damped behavior of beams on elastic soil. For this reason it has been used to introduce a criterion to classify spherical shells as long or short shells. Graphical abaci, that permit a handy classification, are then proposed, depending only on the geometrical characteristics of the shell.

Optimizing magnetodipolar interactions for synchronizing vortex based spin-torque nano-oscillators

We report on a theoretical study of the magnetodipolar coupling and synchronization between two vortex-based spin-torque nano-oscillators (STVOs). In this work we study the dependence of the coupling efficiency on the relative magnetization parameters of the vortices in the system. This study is performed in order to propose an optimized configuration of the vortices for synchronizing STVOs. For this purpose, we combine micromagnetic simulations, the Thiele equation approach, and the analytical macrodipole approximation model to identify the optimized configuration for achieving phase-locking between neighboring oscillators. Notably, we compare vortices configurations with parallel (P) core polarities and with opposite (AP) core polarities. We demonstrate that the AP core configuration exhibits a coupling strength about three times higher than in the P core configuration.

Investigating the effect of amplitude and phase relaxation on the quality of quantum information technologies

In the formalism of quantum operations, we investigate the effect of the amplitude and phase relaxation on the evolution of quantum states. A model of the polarizing qubit, whose noises depend on the spectral degree of freedom that manifests itself in the process of light propagation in the anisotropic medium with dispersion, is discussed. An approximate analytical model is proposed for evaluating the effect of the phase plate on the polarizing state, taking into account the dispersion of light.