Papers by Keyword: Integral Transformation

Abstract: For the first time in this article, a mathematical model has been developed for calculating the temperature fields in arbitrary areas in electron-beam welding; this model was created in the form of a boundary value problem of mathematical physics for a parabolic equation of heat conductivity with Dirichlet boundary conditions. A new integral transformation was constructed for a two-dimensional finite space, with the use of which, as well as the finite element method and Galerkin's method, a temperature field has been determined in the form of a convergent series.

Abstract: Storm surge is an abnormal rise of water generated by a storm, over and above the predicted astronomical tides. The solitary wave theory can be considered good representations of tsunami, storm surge and nonlinear shallow water waves. Based on the same theoretical formulation mentioned in the Part I, we derive the analytical solutions for dynamic responses of an estuary bed to solitary wave excitation are studied by state-space method. State-space method together with Laplace-Fourier transform techniques are used to solve the governing equations. The solitary wave-induced response of estuary bed can be calculated by using the matrix theory, boundary conditions and inverting integral transform. Compared with the special solution in preceding literatures, it’s shown that the proposed method has the advantage of high calculation efficiency and accuracy.

Abstract: The evaluation of the extreme hydrodynamic forces-induced dynamic response in bed is particularly important for coastal geotechnical engineers involved in the design of the foundations of marine structures at estuarine area. As the two main sorts of extreme hydrodynamic forces in Qiantang estuary, tidal bore and storm surge are considered in this work. This paper presents an analytical solution of the tidal bore induced estuary bed response. State-space method together with Laplace-Fourier transform techniques are used to solve the governing equations. The tidal bore-induced response of estuary bed can be calculated by using the matrix theory, boundary conditions and inverting integral transform. Compared with the special solution in preceding literatures, it’s shown that the proposed method has the advantage of high calculation efficiency and accuracy.

Abstract: The surface deflection and displacement is an important performance index to evaluate the bearing capacity of pavement structures. In this work, the dynamical responses of elastic pavement structures subjected to moving vehicles are studied. Based on the elasticity, the strain distribution and the deformation of asphalt pavement structures under coexistence of vertical and horizontal loads are investigated. Integral transform method is used to obtain the deflection response function. The influence of the horizontal braking load on the dynamic response of the pavement structure is analyzed. The results show that the horizontal force plays important roles on the maximum displacement and deflection, distribution of first principal strain of structure.

Abstract: The purpose of the wok is to derive analytical expressions of spectral characteristics at electrical braking of linear induction motor with diverse number of poles as well as to provide results of calculations. The major task in the analysis of braking modes is to determine spectral characteristics of braking current, primary magnetic field and braking force. To this aim Maxwell equations were solved together with Fourier and Laplace integral transformations. The obtained results indicate that in addition to the main component of the magnetic field, when the space frequency is , in the process of braking there appears continuous spectrum of elementary components with the frequencies occupying the infinite sector from - to + . Due to that fact, during the process of energy conversion at the moment of braking, there participate positive – sequence, negative – sequence components and elementary components of the continuous spectrum, motionless in the space.

Abstract: The paper considers some problems of calculating spectral characteristics of magnetic field of the linear induction motor (LIM), operating at the electrical braking modes. In automatic drives with LIM the electric braking modes are usually applied: dynamic, recuperation, single – phase, capacitor type, braking by means of opposite connection, by pulsating current and inverter type (frequency) braking. During the process of braking in the moving part of the LIM and in some cases in an inductor there are initiated complicated interrelated electromagnetic and electromechanical non – stationary processes. The braking processes have been analysed in the motionless right – sided Descartes system of coordinates x, y, z. There have been presented the expressions of volumetric density of braking current which have been regarded the non – periodic functions of coordinate x. Besides that in cases of single – phase and capacitor braking these expressions are also regarded as the non – periodic functions of time. Therefore when compiling the mathematical model there have been applied Laplace and Fourier integral transformations. After having applied Fourier transformation there have been received the expressions of the spectra amplitudes of primary magnetic field at the dynamic braking under the condition that the number of excited zones in the inductor is even, uneven and fractional. The continuous spectra of amplitudes have been calculated by the software Mathcad 2001 Profesional.