• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.556-558
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• 1995

This paper presents a new simplified method for finding the multiple load flow solutions and through their solutions the voltage stability can be evaluated. Line flow($P_{ij}$, $Q_{ij}$) may be formulated with the second-order equations for $V_{i}^{2}$ in polar coordinates or two circle equations for $e_{i}$ and $f_{i}$ in rectangular coordinates. Based on this feature, multiple load flow solutions are calculated with simple works, results of multiple load flow solutions are used for sensitivity analysis of voltage stability. Also, in the case that reactive power sources is considered, method of evaluating the voltage stability is introduced. The proposed method was validated to 2-bus and IEEE 6-bus system.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.705-718
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• 2011

The aim of the investigation described in this paper is to study the nonlinear parametric vibrations and stability of a simply-supported viscoelastic beam with an intra-span spring. Taking into account a time-dependent tension inside the beam as the main source of parametric excitations, as well as employing a two-parameter rheological model, the equations of motion are derived using Newton's second law of motion. These equations are then solved via a perturbation technique which yields approximate analytical expressions for the frequency-response curves. Regarding the main parametric resonance case, the local stability of limit cycles is analyzed. Moreover, some numerical examples are provided in the last section.

• Structural Engineering and Mechanics
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• v.43 no.1
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• pp.89-103
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• 2012

In this study, the stability of laminated homogeneous and non-homogeneous orthotropic truncated conical shells with freely supported edges under a uniform hydrostatic pressure is investigated. It is assumed that the composite material is orthotropic and the material properties depend only on the thickness coordinate. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated non-homogeneous orthotropic truncated conical shells. Applying Galerkin method to the foregoing equations, the expression for the critical hydrostatic pressure is obtained. The appropriate formulas for the single-layer and laminated, cylindrical and complete conical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, effects of non-homogeneity, number and ordering of layers and variations of shell characteristics on the critical hydrostatic pressure are investigated.

• Steel and Composite Structures
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• v.13 no.2
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• pp.157-169
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• 2012

Shell structures are very interesting from the design point of view and these are well recognized in the scientific literature. In this paper the analysis of the buckling loads and stability paths of a sandwich conical shell with unsymmetrical faces under combined load based on the assumptions of moderately large deflections (geometrically nonlinear theory) is considered and elastic-plastic properties of the material of the faces are taken into considerations. External load is assumed to be two-parametrical one and it is assumed that the shell deforms into the plastic range before buckling. Constitutive relations in the analysis are those of the Nadai-Hencky deformation theory of plasticity and Prandtl-Reuss plastic flow theory with the H-M-H (Huber-Mises-Hencky) yield condition. The governing stability equations are obtained by strain energy approach and Ritz method is used to solve the equations with the help of analytical-numerical methods using computer.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.8
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• pp.958-964
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• 1999

The distance in load parameter space to the closest saddle node bifurcation (CSNB) point provides the worst case power margin to voltage instability and the left eigenvector at CSNB identifies the most effective direction to steer the system to maximize voltage stability under contingency. This paper presents an improved direct method for computing CSNB: the order of nonlinear systems equations is reduced to about twice of the size of load flow equations in contrast to about three-times in Dobson's direct method; the initial guess for the direct method is computed efficiently and robustly by combined use of continuation power flow, a pair of multiple load flow solution with Lagrange interpolation. It is also shown that voltage stability may be enhanced significantly with shift of generations in the direction of the left eigenvector at CSNB.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.979-985
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• 2002

The paper presents the dynamic stability of a vertical cantilevered pipe conveying fluid and haying translational linear spring supports. Real pipe systems may have some elastic hanger supports or other mechanical attached parts. which can be regarded as attached spring supports. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to the equations of small motion of the pipe. Effects of spring supports on the dynamic stability of a vortical cantilevered pipe conveying fluid are fully investigated for various locations and spring constants of elastic supports.

• Advances in aircraft and spacecraft science
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• v.6 no.4
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• pp.297-314
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• 2019

Dynamic stability of a porous metal foam nano-dimension plate on elastic substrate exposed to bi-axial time-dependent forces has been studied via a novel 3-variable plate theory. Various pore contents based on uniform and non-uniform models have been introduced. The presented plate model contains smaller number of field variables with shear deformation verification. Hamilton's principle will be utilized to deduce the governing equations. Next, the equations have been defined in the context of Mathieu-Hill equation. Correctness of presented methodology has been verified by comparison of derived results with previous data. Impacts of static and dynamical force coefficients, non-local coefficient, foundation coefficients, pore distributions and boundary edges on stability regions of metal foam nanoscale plates will be studied.

• Structural Engineering and Mechanics
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• v.85 no.6
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• pp.809-823
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• 2023

In this work, dynamic stability analysis of the ball after contacting with the earth in the volleyball game is presented. Via spherical shell coordinate, the governing equations and general boundary conditions of the ball after contacting with the earth in the volleyball game is studied. Via Comsol multi-physics simulation, some results are presented and a verification between the outcomes is studied. Harmonic differential quadrature method (HDQM) is utilized to solve the dynamic equations with the aid of boundary nodes of the current spherical shell structure. Finally, the results demonstrated that thickness, mass of the ball and internal pressure of the ball alters the frequency response of the structure. One important results of this study is influence of the internal pressure. Higher internal pressure causes lower frequency and hence reduces the stability of the ball.

• Steel and Composite Structures
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• v.48 no.2
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• pp.145-161
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• 2023

This study investigates the influences of porosity on the stability of the orthotropic laminated plates under uniaxial and biaxial loadings based on the hyperbolic shear deformation theory. Three different porosity distribution are considered with three specific functions through the plate thickness. The stability equations of porous orthotropic laminated plates are derived by the virtual work principle. Applying the Galerkin method to partial differential equations, the critical buckling load relation of porous orthotropic laminated plates is obtained. After validating the accuracy of the proposed formulation in accordance with the available literature, a parametric analysis is performed to observe the sensitivity of the critical buckling load to shear deformation, porosity, orthotropy, loading factor, and different geometric properties.