Efficient Semi-analytical Approach Research Articles

Numerical Solution of External Boundary Conditions Inverse Multilayer Diffusion Problems

The present study is concerned with the numerical solution of external boundary conditions in inverse problems for one-dimensional multilayer diffusion, using the difference method. First, we formulate multispecies parabolic problems with three types of Dirichlet–Neumann–Robin internal boundary conditions that apply at the interfaces between adjacent layers. Then, using the symmetry of the diffusion operator, we prove the well-posedness of the direct (forward) problem in which the coefficients, the right-hand side, and the initial and boundary conditions are given. In inverse problems, instead of external boundary conditions of the first and the last layers, point observations of the solution within the entire domain are posed. Rothe’s semi-discretization of differential problems combined with a symmetric exponential finite difference solution for elliptic problems on each time layer is proposed to develop an efficient semi-analytical approach. Next, using special solution decomposition techniques, we numerically solve the inverse problems for the identification of external boundary conditions. Numerical test examples are discussed.

Thermal evaluation of MHD Jeffrey fluid flow in the presence of a heat source and chemical reaction

In this paper, the flow of an incompressible fluid is thermally studied. Investigations into the heat transfer process have been conducted in non-Newtonian fluid flows with chemical reactions and heat sources present. The application of this work is the fluid flow around the stretching sheet; fluid flow on a stretching sheet can be applied to polymer extrusion, drawing or plastic films, hot rolling, casting and other engineering problems. The novelty of this paper is that the governing equations have been solved by a new and efficient semi-analytical approach, the Akbari–Ganji method (AGM). In order to investigate the issue, the finite element method (FEM) has also been applied. Comparing the results of problem-solving with the applied methods with the results of the previous research shows a perfect agreement. The results show that the parameters of Hartmann number and interaction improve the velocity profiles. Additionally, for greater Hartmann number values, raising the parameter of interaction decreases the temperature value, but a smaller value has the reverse effect. As the Hartmann number increases, the fluid velocity decreases and it shows that with the increase of electromagnetic force, the velocity of fluid flow decreases.

Double-panel metastructure lined with porous material for broadband low-frequency sound insulation

Insulating low-frequency sound using lightweight structures is very difficult according to the classical mass law. To challenge this problem, we present a comprehensive theoretical analysis and experimental verification of the sound transmission loss (STL) of double-panel metastructures (DPMSs) composed of two layers of metamaterial plates lined with a porous material (PM) layer. To facilitate the analysis, an efficient semi-analytical approach based on the transfer matrix method is proposed to predict the normal, oblique and diffuse field STL of the DPMS with PM. The effects of various structural and material parameters on the STL of the DPMS are analyzed. Some parameters that have significant influences are revealed. Based on semi-analytical predictions and experimental measurements, we demonstrate that an appropriately designed large-scale DPMS lined with PM can achieve a diffuse field STL being much higher than the mass law over a broadband low-frequency range below 500 Hz. More interestingly, compared with the conventional double layer homogeneous plates lined with PM (with the same total mass and thickness), the DPMS lined with PM also has a significantly improved diffuse field STL at broadband low frequencies below 500 Hz.

Incremental harmonic balance method for multi-harmonic solution of high-dimensional delay differential equations: Application to crossflow-induced nonlinear vibration of steam generator tubes

Diverse science and engineering problems are governed by delay differential equations (DDE). Seeking periodic solutions of DDEs is crucial for many nonlinear dynamic systems. The incremental harmonic balance (IHB) method is an efficient semi-analytical approach for periodic solutions of DDE. Among various DDE systems, flow-induced vibration (FIV) of tube bundles with loose support is unique, in the sense that the added damping cancels out structural damping in the vicinity of critical velocity, making it extremely slow to retain a convergent solution if numerical integration (NI) is utilized. Despite the efforts of developing IHB for various mechanical vibration problems with time-delay, no attempt has been made to employ IHB to nonlinear FIV problems. Here we fill this blank by separately combining two spatial discretization strategies, i.e., discretization via linear vibration modes or via finite element method (FEM), with IHB to capture limit cycle solutions after the onset of instability. Within the range of gap velocity of interest, the IHB demonstrates excellent convergence by increasing harmonic terms, and good agreement is obtained between IHB results and the results by NI method. An 18 degree-of-freedom (DOF) nonlinear DDE system was readily dealt by integrating FEM and IHB, each DOF being approximated by three harmonics. This is the first attempt to employ IHB for multi-harmonic solution of high-dimensional FIV problems, which opens a door for solutions of other DDEs. All the codes used in this paper could be downloaded via: https://github.com/XJTU-Zhou-group/IHB.

Efficient assimilation of sparse data into RANS-based turbulent flow simulations using a discrete adjoint method

Turbulent flow simulations based on the Reynolds-averaged Navier–Stokes (RANS) equations continue to be the workhorse approach for industrial flow problems. However, due to the inherent averaging and the closure models required for the Reynolds stresses, their accuracy is limited. Experimental data, on the other hand, represents the true flow features but is potentially only available in limited locations or at low resolution. Data assimilation (DA) can be used to combine closure models with such experimental data to obtain accurate simulation results. In this scenario, the result of the DA process can be interpreted as a physics-based interpolation and serve as a basis for further studies of the flow. Moreover, such tuned models may be used in machine learning approaches aiming at a priori closure model enhancement. The main objective of this work is to recover a spatially varying eddy viscosity correction factor from sparsely distributed reference data.We use an efficient in-house data assimilation implementation based on the discrete adjoint method for RANS simulations in OpenFOAM to recover an optimal eddy viscosity field. A gradient optimization procedure is used to minimize a velocity-based cost function with a regularization term. All the partial derivatives in the gradient computation are evaluated with an efficient semi-analytical approach at the cost of approximately one forward solution step.The effectiveness of the proposed approach is demonstrated for a periodic hill test case at Re=10595 with different spatial distributions of the reference data. The results show improvements in the agreement between simulation and reference for a range of reference data configurations and highlight the performance of linear eddy viscosity models.

Experimental and semianalytical investigation of X850 ± IM190 CFRP bolted joints

Considering the fact that the foundation data for a new X850 ± IM190 carbon/epoxy material system adopted in commercial aircraft industry are extremely scarce in the literature, an in-plane, static tensile experiment was carried out to investigate the bearing performance of double-lap, single-bolt joints in X850 ± IM190 carbon fiber-reinforced polymer (CFRP) composites. The effects of ply ratio, 0° layers’ combination percentage, bolt diameter, and curing method were considered. Then, special attention was paid to determine the design parameters of X850 ± IM190 CFRP bolted joints, such as tensile strength of un-notched laminate and stress concentration relief factor. Based on these design parameters, an efficient semianalytical approach was established to obtain the ultimate bearing strength of the joints. The failure prediction exhibited excellent agreement with the experimental data. These results will play an important role in design and strength evaluation of X850 ± IM190 CFRP bolted joints.

Multiscale process simulation of residual stress fields of laser beam welded precipitation hardened AA6082

In this study, a multiscale modelling approach for the determination of residual stresses for the laser beam welded, precipitation hardened aluminium alloy AA6082-T6 is presented and applied. The material behaviour is described by an elasto-visco-plastic material model, specially suited for fusion welding processes. The microstructure evolution during the welding process has a direct influence on the macroscopic mechanical properties. The modelling approach accounts for the change in the microstructure via a Kampmann–Wagner Numerical model which takes into account the kinetics of the precipitates. The macroscopic mechanical properties are determined via classic dislocation theory, which accounts for the interaction between dislocations and precipitates. The temperature field of the welding process is described by a highly efficient semi-analytical approach. The solution of the temperature field in connection with a three dimensional moving heat source is achieved by using the method of Green’s functions. By employing the method of Green’s functions, it is possible to reduce the numerical effort significantly. The results of this modelling approach are compared to temperature, hardness as well as residual stress measurements, obtained from synchrotron X-ray diffraction, for welded sheets to clarify the accuracy of the applied model.

Effects of ultrashort laser pulses on angular distributions of photoionization spectra

We study the photoelectron spectra by intense laser pulses with arbitrary time dependence and phase within the Keldysh framework. An efficient semianalytical approach using analytical transition matrix elements for hydrogenic atoms in any initial state enables efficient and accurate computation of the photoionization probability at any observation point without saddle point approximation, providing comprehensive three dimensional photoelectron angular distribution for linear and elliptical polarizations, that reveal the intricate features and provide insights on the photoionization characteristics such as angular dispersions, shift and splitting of photoelectron peaks from the tunneling or above threshold ionization(ATI) regime to non-adiabatic(intermediate) and multiphoton ionization(MPI) regimes. This facilitates the study of the effects of various laser pulse parameters on the photoelectron spectra and their angular distributions. The photoelectron peaks occur at multiples of 2ħω for linear polarization while odd-ordered peaks are suppressed in the direction perpendicular to the electric field. Short pulses create splitting and angular dispersion where the peaks are strongly correlated to the angles. For MPI and elliptical polarization with shorter pulses the peaks split into doublets and the first peak vanishes. The carrier envelope phase(CEP) significantly affects the ATI spectra while the Stark effect shifts the spectra of intermediate regime to higher energies due to interference.

A simplified moment-curvature based approach for large deflection analysis of micro-beams using the consistent couple stress theory

Abstract Micro-scale structures are observed to be mechanically stiffer than the predictions obtained from the conventional elastic theories. This led to the development of models which include the effect of couple stresses to capture the size-dependent behavior. This paper develops a large elastic deflection version of the micro-beam analysis within the consistent couple stress theory framework. A material length parameter naturally appears in the moment-curvature relationship to account for the length scale effect. The method proposed here shows that starting with a moment-curvature relation unlike stress-strain relationship leads to a non-linear governing differential equation in terms of slope of the deformed beam. The differential equation is integrated to obtain the expressions for co-ordinates of the deformed beam which are in the form of improper integrals. An efficient semi-analytical approach involving removal of singularity is introduced. The proposed method is easy to implement as compared to the elliptic integral approach and is faster than direct numerical integration. Upon inclusion of couple stress effects, the static bending results show a stiffer response than the classical elasticity theory. It is also shown in this work that a common governing differential equation is obtained for predicting the deflections of micro as well as macro-beams.

A differential transformation approach for solving functional differential equations with multiple delays

In the paper an efficient semi-analytical approach based on the method of steps and the differential transformation is proposed for numerical approximation of solutions of functional differential models of delayed and neutral type on a finite interval of arbitrary length, including models with several constant delays. Algorithms for both commensurate and non-commensurate delays are described, applications are shown in examples. Validity and efficiency of the presented algorithms is compared with the variational iteration method, the Adomian decomposition method and the polynomial least squares method numerically. Matlab package DDE23 is used to produce reference numerical values.

Wave farm modelling of oscillating wave surge converters

A mathematical model is described to analyse the hydrodynamic behaviour of a wave energy farm consisting of oscillating wave surge converters in oblique waves. The method is a highly efficient semi-analytical approach based on the linear potential flow theory. Wave farms with a large number of such devices are studied for various configurations. For an inline configuration with normally incident waves, the occurrence of a near-resonant behaviour, already known for small arrays, is confirmed. A strong wave focusing effect is observed in special configurations comprising a large number of devices. The effects of the arrangement and of the distance of separation between the flaps are also studied extensively. In general, the flaps lying on the front of the wave farm are found to exhibit an enhanced performance behaviour in average, owing to the mutual interactions arising within the array. A random sea analysis shows that a slightly staggered arrangement can be an ideal layout for a wave farm of this device. The hydrodynamics of two flaps that oscillate back to back is also discussed.

Vibrations of Pipes and Their Supporting Beams Caused by Tank Bulging Mode

The vibrations of pipes and their supporting beams caused by the tank bulging mode are analyzed. A computationally efficient semianalytical approach is presented by introducing a local velocity potential for each pipe and developing a reduced order model for the frame structure consisting of the pipes and their supporting beams. To enable the analysis, the system of governing equations and boundary conditions is derived in a variational form. Numerical results show that large bending stress occurs in the supporting beams attached to the lower part of the tank wall. This bending stress can be reduced by decreasing the outer diameter of the supporting beams based on the fact that the dependence of the bulging-mode-induced displacements of the supporting beams on their stiffness is weak. This stress reduction method does not increase but decreases the stiffness of the supporting beams and therefore the cost, unlike many methods for improving structural reliability. A method for reducing the axial compressive stress in the supporting beams is also investigated.

Blocking property of energy vortices in elastic waveguides

Energy vortices in time-averaged energy flows of time-harmonic fields are considered. The purpose of the paper is to verify the supposition that the energy flux along an elastic waveguide with an obstacle is blocked completely at the stop frequencies by the vortices. It is hoped that this work will draw attention to the analogy between energy and fluid flows which is potentially fruitful for understanding various wave phenomena. The normal-mode diffraction by a surface punch on an elastic layer is taken as an example. For tracing energy streamlines in the near field up to the obstacle, a special efficient semianalytical approach has been developed. To illustrate the stated supposition, plots of transmission coefficients versus frequency and figures of the near-field streamline structures are given.

Performance of digital DECT radio links based on semianalytical methods

We report a very efficient semianalytical approach for the performance evaluation of differential detection schemes for GMSK signals of the DECT standard. Precisely, for a given channel, the performance is determined by means of an analytical procedure which includes the saddlepoint approximation. We consider both static channels (with impulse response generated by the simulation program SIRCIM) and two-ray Rayleigh and log-normal fading channels. As a departure from previous works, our receiver includes an all-digital part after the analog differential detection scheme. The digital part includes: (1) a block for the estimation of both the optimum sampling phase and the nonlinear channel coefficients (by making use of the DECT training sequence), (2) a one-tap decision feedback (DF) equalizer, and (3) a block for the evaluation of the approximate optimum bias level (/spl gamma//sub e/) in the threshold detector. Both the DF equalizer coefficient and /spl gamma//sub e/ are based on the nonlinear channel coefficients estimate. For channels with a normalized delay spread up to 0.2, the use of the optimum threshold together with the DF equalizer permits a gain of about 2 dB at BER=10/sup -6/ with respect to a receiver without equalization and a zero-level decision threshold. In addition, we discover that, in indoor environments, the 2-bit GMSK detector performs roughly the same as the 1-bit detector. The threshold optimization is also effective in the presence of channels affected by fading. To support this statement, we report the performance of the 1-bit differential detection scheme combined with antenna selection diversity in the presence of a two-ray log-normal and Rayleigh fading channel.