• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.361-371
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• 2023

Boundary condition is an important factor affecting the vibration characteristics of structures, under different boundary conditions, structures will exhibit different vibration behaviors. On the basis of the previous work, this paper extends to the nonlinear resonance behavior of axially moving graphene platelets reinforced metal foams (GPLRMF) plates with geometric imperfection under different boundary conditions. Based on nonlinear Kirchhoff plate theory, the motion equations are derived. Considering three boundary conditions, including four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS), the nonlinear ordinary differential equation system is obtained by Galerkin method, and then the equation system is solved to obtain the nonlinear ordinary differential control equation which only including transverse displacement. Subsequently, the resonance response of GPLRMF plates is obtained by perturbation method. Finally, the effects of different boundary conditions, material properties (including the GPLs patterns, foams distribution, porosity coefficient and GPLs weight fraction), geometric imperfection, and axial velocity on the resonance of GPLRMF plates are investigated.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• Steel and Composite Structures
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• v.50 no.2
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• pp.149-158
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• 2024

Considering that different boundary conditions can have an important impact on structural vibration characteristics. In this paper, the nonlinear forced vibration behavior of functionally graded material (FGM) doubly curved shells with initial geometric imperfections under different boundary conditions is studied. Considering initial geometric imperfections and von Karman geometric nonlinearity, the nonlinear governing equations of FGM doubly curved shells are derived using Reissner's first order shear deformation (FOSD) theory. Three different boundary conditions of four edges simply supported (SSSS), four edges clamped (CCCC), clamped-clamped-simply-simply (CCSS) were studied, and a system of nonlinear ordinary differential equations was obtained with the help of Galerkin principle. The nonlinear forced vibration response of the FGM doubly curved shell is obtained by using the modified Lindstedt Poincare (MLP) method. The accuracy of this method was verified by comparing it with published literature. Finally, the effects of curvature ratio, power law index, void coefficient, prestress, and initial geometric imperfections on the resonance of FGM doubly curved shells under different boundary conditions are fully discussed. The relevant research results can provide certain guidance for the design and application of doubly curved shell.

• Advances in nano research
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• v.14 no.3
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• pp.285-294
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• 2023

The dynamic and sensing performances of nanomechanical resonators with their different boundary conditions are studied based on surface elasticity-based modeling and simulation. Specifically, the effect of surface stress is included in Euler-Bernoulli beam model for different boundary conditions. It is shown that the surface effect on the intrinsic elastic property of nanowire is independent of boundary conditions, while these boundary conditions affect the frequency behavior of nanowire resonator. The detection sensitivity of nanowire resonator is remarkably found to depend on the boundary conditions such that double-clamping boundary condition results in the higher mass sensitivity of the resonator in comparison with simple-support or cantilever boundary condition. Furthermore, we show that the frequency shift of nanowire resonator due to mass adsorption is determined by its length, whereas the frequency shift is almost independent of its thickness. This study enables a design principle providing an insight into how the dynamic and sensing performances of nanomechanical resonator is determined and tuned.

• Tribology and Lubricants
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• v.37 no.1
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• pp.14-24
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• 2021

This study shows the effect of the thermal boundary condition around the tilting pad journal bearing on the static and dynamic characteristics of the bearing through a high-precision numerical model. In many cases, it is very difficult to predict or measure the exact thermal boundary conditions around bearings at the operating site of a turbomachine, not even in a laboratory. The purpose of this study is not to predict the thermal boundary conditions around the bearing, but to find out how the performance of the bearing changes under different thermal boundary conditions. Lubricating oil, bearing pads and shafts were modeled in three dimensions using the finite element method, and the heat transfer between these three elements and the resulting thermal deformation were considered. The Generalized Reynolds equation and three-dimensional energy equation that can take into account the viscosity change in the direction of the film thickness are connected and analyzed by the relationship between viscosity and temperature. The numerical model was written in in-house code using MATLAB, and a parallel processing algorithm was used to improve the analysis speed. Constant temperature and convection temperature conditions are used as the thermal boundary conditions. Notably, the conditions around the bearing pad, rather than the temperature boundary conditions around the shaft, have a greater influence on the performance changes of the bearing.

• Journal of Mechanical Science and Technology
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• v.15 no.5
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• pp.671-680
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• 2001

Boundary condition is one of the major factors to influence the numerical stability and solution accuracy in numerical analysis. One of the most important physical boundary conditions in the flowfield analysis is the wall boundary condition imposed on the body surface. To solve a two-dimensional Euler equation, totally four numerical wall boundary conditions should be prescribed. Two of them are supplied by the flow tangency condition. The other two conditions, therefore, should be prepared additionally in a suitable way. In this paper, four different sets of wall boundary conditions are proposed and then applied to solve high-speed flowfields around a quarter circle geometry. A two-dimensional compressible Euler solver is prepared based on the finite volume method. This solver hires three different upwind schemes; Steger-Warmings flux vector splitting, Roes flux difference splitting, and Lious advection upstream splitting method. It is found that the way to specify the additional numerical wall boundary conditions strongly affects the overall stability and accuracy of the upwind schemes in high-speed flow calculation. The optimal wall boundary conditions should be also chosen very carefully depending on the numerical schemes used to solve the problem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.10a
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• pp.160-165
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• 1997

Structural boundary condition is very important as a part of a structural system because it determines the dynamic characteristics of the structure. It is often to experience that experimental measurements of structural dynamic characteristics are somewhat different from the analytical predictions in which idealized boundary conditions are usually assumed. However, real structural boundary conditions are not so ideal; not perfectly clamped, for instance. Thus this paper introduces a new method to determine the non-ideal structural boundary conditions in the frequency domain. In this method, structural boundary conditions are modeled by both extensional (vertical) and torsional elastic springs. The effective springs are then determined from experimental FRFs (frequency response functions) by using the spectral element method (SEM). For a cantilevered beam experiments are conducted to determine the real boundary conditions in terms of effective springs. Dynamic characteristics (analytically predicted) based on identified boundary conditions are found to be much closer to experimental measurements when compared with those based on ideal boundary conditions.

• Steel and Composite Structures
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• v.48 no.2
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• pp.191-206
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• 2023

The present research investigates how micromechanical models affect the behavior of Functionally Graded (FG) plates under different boundary conditions. The study employs diverse micromechanical models to assess the effective material properties of a two-phase particle composite featuring a volume fraction of particles that continuously varies throughout the thickness of the plate. Specifically, the research examines the vibrational response of the plate on a Winkler-Pasternak elastic foundation, considering different boundary conditions. To achieve this, the governing differential equations and boundary conditions are derived using Hamilton's principle, which is based on a four-variable shear deformation refined plate theory. Additionally, the Galerkin method is utilized to compute the plate's natural frequencies. The study explores how the plate's natural frequencies are influenced by various micromechanical models, such as Voigt, Reuss, Hashin-Shtrikman bounds, and Tamura, as well as factors such as boundary conditions, elastic foundation parameters, length-to-thickness ratio, and aspect ratio. The research results can provide valuable insights for future analyses of FG plates with different boundaries, utilizing different micromechanical models.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.267-277
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• 2011

This paper is concerned with eigenvalues of second-order vector equations on time scales with boundary value conditions. Properties of eigenvalues and matrix-valued solutions are studied. Relationships between eigenvalues of different boundary value problems are discussed.

• Steel and Composite Structures
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• v.36 no.6
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• pp.689-702
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• 2020

The current study deals with the size-dependent free vibration analysis of graphene nanoplatelets (GNPs) reinforced polymer nanocomposite plates resting on Pasternak elastic foundation containing different boundary conditions. Based on a four variable refined shear deformation plate theory, which considers shear deformation effect, in conjunction with the Eringen nonlocal elasticity theory, which contains size-dependency inside nanostructures, the equations of motion are established through Hamilton's principle. Moreover, the effective material properties are estimated via the Halpin-Tsai model as well as the rule of mixture. Galerkin's mathematical formulation is utilized to solve the equations of motion for the vibrational problem with different boundary conditions. Parametrical examples demonstrate the influences of nonlocal parameter, total number of layers, weight fraction and geometry of GNPs, elastic foundation parameter, and boundary conditions on the frequency characteristic of the GNPs reinforced nanoplates in detail.