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Superposition Method (superposition + method)
Selected AbstractsAnalysis of Steady Ground Water Flow Toward Wells in a Confined-Unconfined AquiferGROUND WATER, Issue 4 2006Chen Chong-Xi A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells. [source] Hydroelastic vibrations of flexible rectangular tanks partially filled with liquidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Ding Zhou Abstract In this paper, the three-dimensional vibratory characteristics of flexible rectangular tanks partially filled with liquid are studied. The surface waves of the liquid are taken into account in the analysis. Both the bulging modes of the tank-wall vibration and the sloshing modes of the liquid oscillation are investigated. The vibrating modes of the liquid,tank system are divided into four distinct categories: double symmetric modes (SS); antisymmetric,symmetric modes (AS); symmetric,antisymmetric modes (SA) and double antisymmetric modes (AA). Each of these categories is separately investigated. The velocity potential of the liquid is analytically deduced by using a combination of the superposition method and the method of separation of variables. According to the liquid,tank interface conditions and the orthogonality of trigonometric functions, the coefficients in the solution of liquid velocity potential are expressed in the integral forms including the tank,wall dynamic deflection. A set of reasonable static beam functions is constructed as the admissible functions of the tank-wall vibration. The eigenfrequency equation of the liquid,tank system is derived by using a combination of the Rayleigh,Ritz method and the Galerkin method. Convergence study demonstrates the high accuracy and small computational cost of the proposed approach. Finally, some numerical results are presented for the first time. Copyright © 2006 John Wiley & Sons, Ltd. [source] Use of equivalent mass method for free vibration analyses of a beam carrying multiple two-dof spring,mass systems with inertia effect of the helical springs consideredINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Jia-Jang Wu Abstract This paper investigates the free vibration characteristics of a beam carrying multiple two-degree-of-freedom (two-dof) spring,mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring,mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two-dof spring,mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two-dof spring,mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two-dof spring,mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two-dof spring,mass systems attached to the beam. Furthermore, if the total number of two-dof spring,mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter. Copyright © 2005 John Wiley & Sons, Ltd. [source] The revenge of the Patterson methods.JOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5 2007In the present paper, the third and last of a series (the first two papers were dedicated to the crystal structure solution of proteins), the Patterson superposition method, based on the use of the symmetry minimum function, has been applied to powder diffraction patterns. The method has been modified to take into account the special challenges of this kind of data and to optimize the performance of the approach. The new algorithms have been implemented in a computer program and applied also to single-crystal data of small and medium-size crystal structures. The experimental results have been compared with those obtained via direct methods, so enabling the role and the perspectives of these two approaches in the global phasing problem to be established, no matter what the experimental technique (powder or single-crystal diffraction) or the size of the structures (small, medium or macro-molecules). [source] Positron annihilation at grain boundaries in metalsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 10 2007J. Kuriplach Abstract Positron annihilation at selected tilt and twist grain boundaries in iron and nickel is examined theoretically. First the atomic structure of studied perfect and imperfect grain boundaries is obtained using molecular dynamics simulations. Characteristics of positrons trapped at such GBs are then calculated employing the atomic superposition method and are related to free volumes found at GBs. It is observed that in some cases vacancies introduced into ideal grain boundaries do not result in an increase of the positron lifetime. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||