Application Of Laplace Transformation Research Articles

Adaptive consensus control of uncertain nonlinear multi-agent systems with communication delays and relative output information

This paper explores the challenges of distributed adaptive consensus control problems in nonlinear multi-agent systems with unknown parameters and communication delays. To address these issues, a novel backstepping-based adaptive state feedback control protocol is proposed by utilizing a reference dynamic system. Furthermore, an output-feedback consensus control algorithm incorporating a state observer is introduced. Through the application of Laplace transformation, matrix properties, and graph theory, it is demonstrated that the closed-loop multi-agent system ensures the boundedness of all signals and achieves output consensus, even in the presence of nonuniform communication delays. Numerical simulations on a group of inverted pendulums illustrate the effectiveness of these algorithms.

Production Performance Analysis for Deviated Wells in Carbonate Gas Reservoirs With Multiple Heterogeneous layers

Deviated wells are used to improve the performance of carbonate reservoirs with multiple heterogeneous layers and penetrate the “sweet spot” of each layer, which is full of fractures and vugs. It is difficult to consider in-layer and inter-layer heterogeneities simultaneously, and predict the production performance for these wells accurately. Therefore, a semi-analytical model to analyze the production performance of deviated wells in a multilayer heterogeneous stress-sensitive carbonate gas reservoir is proposed. For each layer, the inner region is a fractured-vuggy porous medium, while the outer region is merely a tight formation with matrix and formation properties, and penetrated inclination angles may be distinct. Pseudo-time/pressure factors are introduced to consider fracture stress sensitivity. Through the application of Laplace transformation, Fourier transform and inverse, Duhamel convolution, and Stehfest numerical inversion, the presented model is solved. The validity of this model is verified through comparison with single-layer composite formation with different porous mediums and vertical well in a multilayer carbonate gas reservoir. Moreover, by matching bottom-hole pressure data collected from a slanted well in the Anyue gas field, the applicability of this model is validated. A synthetic case, which has two composite formations, the first (upper) layer is more permeable than the second (lower) layer, is used to study the variations of inner region radius, fracture/matrix permeability, and inclination angles on production behaviors. The results show the properties of the first layer determine well bottom-hole pressure, whereas the rise of permeability, inner region radius and penetrated angle for the second layer can improve the gas recovery of this layer. In practice, to maintain well bottom-hole pressure with a relatively high level and enhance gas recovery of the tight layer, the inclination angle should be larger than 60° for each layer, and be increased to as large as possible. The findings of this study can help for a better understanding of the production behaviors of deviated wells in multilayer heterogenous reservoirs and could provide some guidance for the design of well trajectory.

On the Numerical Approximation of Three-Dimensional Time Fractional Convection-Diffusion Equations

In this paper, we present an efficient method for the numerical investigation of three-dimensional non-integer-order convection-diffusion equation (CDE) based on radial basis functions (RBFs) in localized form and Laplace transform (LT). In our numerical scheme, first we transform the given problem into Laplace space using Laplace transform. Then, the local radial basis function (LRBF) method is employed to approximate the solution of the transformed problem. Finally, we represent the solution as an integral along a smooth curve in the complex left half plane. The integral is then evaluated to high accuracy by a quadrature rule. The Laplace transform is used to avoid the classical time marching procedure. The radial basis functions are important tools for scattered data interpolation and for solving partial differential equations (PDEs) of integer and non-integer order. The LRBF and global radial basis function (GRBF) are used to produce sparse collocation matrices which resolve the issue of the sensitivity of shape parameter and ill conditioning of system matrices and reduce the computational cost. The application of Laplace transformation often leads to the solution in complex plane which cannot be generally inverted. In this work, improved Talbot’s method is utilized which is an efficient method for the numerical inversion of Laplace transform. The stability and convergence of the method are discussed. Two test problems are considered to validate the numerical scheme. The numerical results highlight the efficiency and accuracy of the proposed method.

Free damped vibration analysis of Mindlin plates with hybrid material-foundation viscoelasticity

Suppressed vibration of shear deformable plates with hybrid viscoelastic damping of material and foundation is investigated. Viscoelasticity of foundation is established by adopting Kelvin-Voigt model while viscoelasticity of materials is expressed by Boltzmann superposition integral, which uses dynamic mechanical analysis (DMA) results in terms of Prony series. Application of Laplace transformation and Mindlin plate theory with Hamilton principle led to a system of coupled integro-PDE of motions. Weighted residual method, numerical iterative algorithm and Fourier transform are implemented to achieve complex frequencies and transient responses of plates. Assessment of accuracy is carried out in the both elastic and viscoelastic domains. In the earlier, the frequencies are compared with counterparts obtained by p-version Ritz method and in the latter, dynamic characteristics of Mindlin and classic plates are examined that represent acceptable correlation. The influences of hybrid material-foundation damping, edge conditions, foundation characteristics and geometrical parameters on dynamic characteristics of plates are studied via a set of parametric study.

Analysis of physical processes via imaging vectors

Practically, all modeling processes in one way or another are random. The foremost formulated theoretical foundation embraces Markov processes, being represented in different forms. Markov processes are characterized as a random process that undergoes transitions from one state to another on a state space, whereas the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it. In the Markov processes the proposition (model) of the future by no means changes in the event of the expansion and/or strong information progression relative to preceding time. Basically, modeling physical fields involves process changing in time, i.e. non-stationay processes. In this case, the application of Laplace transformation provides unjustified description complications. Transition to other possibilities results in explicit simplification. The method of imaging vectors renders constructive mathematical models and necessary transition in the modeling process and analysis itself. The flexibility of the model itself using polynomial basis leads to the possible rapid transition of the mathematical model and further analysis acceleration. It should be noted that the mathematical description permits operator representation. Conversely, operator representation of the structures, algorithms and data processing procedures significantly improve the flexibility of the modeling process.

Thermal Prediction for Transient Coupled Thermoelastic Problem of a Two-Layer Composite Material Exposed to Radiation

Thermoelastic problems are widely investigated for a long time, especially for these materials subject to high temperature and cause apparent variation of stress and strain. The general related researches investigated the internal parameters with known boundary conditions, however, seldom cases investigated the predictions both the boundary thermoelastic values with given internal parameters. This study considers the case of a one-dimensional two-layer composite material with length L. In this paper, we present a methodology with Laplace transformation and the control volume method with the chosen hyperbolic shape function to solve radiation condition in transient coupled thermoelastic problems with two relaxation time constants. As long as the boundary conditions at one end of the material is prescribed, if either the thermal stress or thermal strain at any single point within the material is also known, the thermal stress or thermal strain at other locations can be predicted. For different time constants, the present method also yields good predictions of the boundary conditions for the case where the internal part of the material is initially verified with compression stress or tensile stress. The proposed method extends the application of Laplace transformation and show the effectiveness of the analysis scheme. In addition, it provides more precise prediction than the traditional thermoelastic theory.

The symplectic system method in the stress analysis of 2D elasto-viscoelastic fiber reinforced composites

With the aid of the variational method and Laplace transformation, the symplectic system method is employed into two-dimensional elastic–viscoelastic fiber reinforced composites. The fundamental eigenfunctions of the governing equations are generalized to the time domain. Therefore the problem can be discussed directly in the time domain, and the iterative application of Laplace transformation is not needed. Using this method, all the stress components of the inner fiber and outer matrix, and hence the stress transfer in the interface between the fiber and matrix, are expressed analytically. The results obtained by the approach are accurate, because all the boundary conditions prescribed on the surfaces and ends of the composites can be satisfied. Numerical example demonstrate that both the shear stress and the normal stress decrease with time due to the viscoelastic property of the matrix, and that stress concentration occurs near the end.

Saint-Venant problem of three-dimensional linear viscoelasticity in the Hamiltonian system

The traditional Saint-Venant problem of three-dimensional viscoelasticity is discussed under the Hamiltonia system with the use of the Laplace integral transformation, and the original problem is transformed into finding eigenvalues and eigenvectors of the Hamiltonia operator matrix. Since local effect near the boundary is usually neglected, all solutions of Saint-Venant problems can be obtained directly by the combinations of zero eigenvectors. Moreover, the adjoint relationships of the symplectic orthogonality of zero eigenvectors in the Laplace domain are generalized to the time domain. Therefore the problem can be discussed directly in the eigenvector space of the time domain, and the iterative application of Laplace transformation is not needed. Simply by applying the adjoint relationships of the symplectic orthogonality, an effective method for boundary condition is given. Based on this method, some typical examples are discussed, in which the whole character of total creep and relaxation of viscoelasticity is clearly revealed.

Torsional vibration of a solid finite cylinder having transverse isotropy

Stress and displacement components in a solid circular cylinder of transversely isotropic material under the torsional vibration set up by an impulsive twist applied at one and while the other end remains fixed, have been obtained by the application of Laplace transformation.

Application of Laplace-Transformation to Polarography.

Application of Laplace-Transformation to Polarography.