Search results for: CLOSED FORM ANALYTICAL SOLUTION
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Structural properties of foil bearings: a closed-form solution validated with finite element analysis
PublicationFluid film thickness in a compliant foil bearing is greatly influenced by the deflection of the bearing structure. Therefore, in order to properly model performance of a foil bearing, it is mandatory that the deflection of the compliant bearing structure due to the generated hydrodynamic pressure is determined accurately. This article proposes an easy-to-use two-dimensional model, which takes into account detailed geometry of the...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublicationIn this study a tin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equatio is derived with aid of the principle of stationary potential energy. The critical load for simply supported bar is found in an analytical form and it is copared with the FEM solution. Sufficient accuracy of the...
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Distortional buckling of thin-walled columns of closed quadratic cross-section
PublicationThe elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with...
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A method for preliminary estimation of the length of midship body block to be inserted during ship’s conversion
PublicationThe paper presents a method for preliminary estimation of the length of the midship body block, which inserted in the original hull, increases the deadweight of the ship in line with a required quantity. The method may be useful for establishing the scope of conversion to better adjust the ship for transportation tasks. The problem is formulated by using a mathematical model so selected that its solution, under set of assumptions,...
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On local buckling of cold-formed channel members
PublicationThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...
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Parametric method for evaluating optimal ship deadweight
PublicationThe paper presents a method of choosing the optimal value of the cargo ships deadweight. The method may be useful at the stage of establishing the main owners requirements concerning the ship design parameters as well as for choosing a proper ship for a given transportation task. The deadweight is determined on the basis of a selected economic measure of the transport effectiveness of ship – the Required Freight Rate (RFR). The...
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Selected local stability problems of channel section flanges made of aluminium alloys
PublicationThe paper addresses the issue of local buckling of compressed flanges of cold-formed thin-walled channel columns and beams with nonstandard flanges composed of aluminium alloys. The material behaviour follows the Ramberg–Osgood law. It should be noted that the proposed solution may be also applied for other materials, for example: stainless steel, carbon steel. The paper is motivated by an increasing interest in nonstandard cold-formed...
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Parametrical Method for Determining Optimal Ship Carrying Capacity and Performance of Handling Equipment
PublicationThe paper presents a method of evaluating the optimal value of the cargo ships deadweight and the coupled optimal value of cargo handling capacity. The method may be useful at the stage of establishing the main owners requirements concerning the ship design parameters as well as for choosing a proper second hand ship for a given transportation task. The deadweight and the capacity are determined on the basis of a selected economic...
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Propagation of Acoustic Disturbances in Shallow Sea
PublicationPropagation of acoustic waves in shallow sea differs fundamentally from the same phenomenon occurring in deep sea in view of non-negligible distance from the sea bottom in the first case, where presence of two regions limiting the water layer results in the acoustic pressure distribution induced by a harmonic source has an interferential nature as a result of multi-path propagation of the acoustic signal. These interferential properties...
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Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublicationWe present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublicationIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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Second-order Stark effect and polarizability of a relativistic two-dimensional hydrogenlike atom in the ground state
PublicationThe second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green's function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves the generalized hypergeometric function ${}_{3}F_{2}$...
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Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closed-form expression for the magnetizability of an arbitrary discrete state of the relativistic one-electron atom with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...
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An Analysis of Scattering from Ferrite Post of Arbitrary Convex Cross Section with the Use of Field Matching Method
PublicationA problem of electromagnetic wave scattering from ferrite post is presented. The post is assumed to be located in closed areas as waveguide junction, or in open area illuminated by a plane wave. The object is of arbitrary convex cross section and the method of analysis is semi-analytical, based on the direct field matching technique.
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Closed Form Constraint Equations Used to Express Frictionless Slip of Multibody Systems Attached to Finite Elements—Application to a Contact between a Double Pendulum and a Beam
PublicationThis paper focuses on the numerical modeling of the dynamics of mechanical systems. Robots that can inspect high-voltage lines inspired this research. Their control systems must anticipate potential grab positions appropriately. We intend to formulate equations dedicated to the numerical description of the robot/cable contact. The investigated problem is not straightforward, since parts of the modeled systems are numerically inhomogeneous....
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Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory
PublicationThis article is intended to analyze forced vibrations of a piezoelectric-piezomagnetic ceramic nanoplate by a new refined shear deformation plate theory in conjunction with higher-order nonlocal strain gradient theory. As both stress nonlocality and strain gradient size-dependent effects are taken into account using the higher-order nonlocal strain gradient theory, the governing equations of the composite nanoplate are formulated....
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.
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On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam
PublicationThe fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the...
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Study of Slip Effects in Reverse Roll Coating Process Using Non-Isothermal Couple Stress Fluid
PublicationThe non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient...