• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.631-636
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• 2007

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the, we proposed a two-level condensation scheme(TLCS) for the construction of a reduced system. In first step, the of candidate elements by energy estimation, Rayleigh quotient, through Ritz vector calculation, and next, the primary degrees of freedom is selected by sequential elimination from the degrees of freedom connected the candidate elements in the first step. In the present study, we propose TLCS combined with iterative improved reduced system(IIRS) to increase accuracy of higher modes intermediate range. Also, it possible to control the accuracy of the eigenvalues and eigenmodes of the reduced system. Numerical examples demonstrate performance of proposed method.

• Structural Engineering and Mechanics
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• v.12 no.4
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• pp.363-376
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• 2001

Sandwich plates are widely used in lightweight design due to their high strength and stiffness to weight ratio. Due to the heterogeneous structure of sandwich plates, they can exhibit local instabilities (wrinkling), which lead to a sudden loss of stiffness in the structure. This paper presents an analytical solution to the wrinkling problem of sandwich plates. The solution is based on the Rayleigh-Ritz method, by assuming an appropriate deformation field. In contrast to the other approaches up to now, this model takes arbitrary and different orthotropic face layers, finite core thickness and orthotropic core material into account. This approach is the first to cover the wrinkling of unsymmetric sandwiches and sandwiches composed of orthotropic FRP face layers, which are most common in advanced lightweight design. Despite the generality of the solution, the computational effort is kept within bounds. The results have been verified using other analytical solutions and unit cell 3D FE calculations.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.461-468
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• 2001

The aim of this work is to establish the coefficient that defines the critical buckling load for isotropic annular plates of variable thickness whose outer boundary is simply supported and subjected to uniform pressure. It is assumed that the plate thickness varies in a continuous way, according to an exponential law. The eigenvalues are determined using an optimized Rayleigh-Ritz method with polynomial coordinate functions which identically satisfy the boundary conditions at the outer edge. Good engineering agreement is shown to exist between the obtained results and buckling parameters presented in the technical literature.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.533-534
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• 2013

This paper is concerned with the active vibration control of rectangular plate equipped with MFC actuators. To this end, the dynamic model of the rectangular plate bonded with MFC sensors and actuators was derived by means of the Rayleigh-Ritz method. The MFC actuator and sensor were modeled based on the pin-force assumption. The theoretical model was then validated experimentally. The multiinput and multi-output (MIMO) Positive Position Feedback (PPF) controller was designed based on the natural mode shapes and implemented using dSpace system and Simulink. The proposed control algorithm was applied to the cantilever plate having two MFC wafers having both sensor and actuator. Numerical and experimental investigations were carried out. Both theoretical and experimental result shows that the proposed control algorithm can effectively suppress vibrations of cantilever plate.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.714-714
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• 2005

This paper presents the modeling and impact analysis for a rotating cantilever beam having a concentrated mass. The concentrated mass takes an impact force during the rotating motion and the transient response of the beam induced by the impact is calculated by applying the Rayleigh-Ritz assumed mode method. The stiffness variation effect caused by the rotating motion is considered in this modeling. The effects of the concentrated mass size, impact position and the angular velocity of the beam on the transient responses are investigated through numerical studies.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.372-375
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• 1995

The magnetization pattern of the central cross section deduced from the ac susceptibility measurement is described with an analytical function. The function is based on a charge-free configuration. The thickness of the $^{\circ}$ wall lying in a (100) plane and the wall energy are calculated analytically. Total energy of the domain structure has been minimized with Ritz's method. As the result of the minimization, the energy density of the $^{\circ}$ wall lying in a (100) plane is $0.58\;erg/cm^{2}$ and the one for a (110) plane is $1.18\;erg/cm^{2}$. Thicknesses of these walls are calculated numerically. Also, the calculation indicates there is a small central domain at the cross section without applied current. With the ac susceptibility measurement the existence of the domain without current can be identified.

• Coupled systems mechanics
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• v.8 no.1
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• pp.19-38
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• 2019

The influence of torsional rigidity of hinged flexible appendage on the linear dynamics of flexible spacecrafts with liquid on board was analyzed by considering the spacecraft's main body as a rigid tank, its flexible appendages as two elastically supported elastic beams, and the onboard liquid as an ideal liquid. The meniscus of the liquid free surface due to surface tension was considered. Using the Lagrangian of the spacecraft's main body (rigid tank), onboard liquid, and two beams (flexible appendages) in addition to assuming the system moved symmetrically, the coupled system frequency equations were obtained by applying the Rayleigh-Ritz method. The influence of the torsional rigidity of the flexible appendages on the spacecraft's coupled vibration characteristics was primary focus of investigation. It was found that coupled vibration modes especially that of appendage considerably changed with torsion spring parameter ${\kappa}_t$ of the flexible appendage. In addition, variation of the main body displacement with system parameters was investigated.

• Geomechanics and Engineering
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• v.28 no.5
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• pp.455-461
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• 2022

Numerical assessment of the dynamic stability behavior of nonlocal beams rested on elastic foundation has been provided in the present research. The beam is made of fucntional graded (FG) porous material and is exposed to thermal and humid environments. It is also consiered that the beam is subjected to axial periodic mechanical load which especific exitation frequency leading to its instability behavior. Beam modeling has been performed via a two-variable theory developed for thick beams. Then, nonlocal elasticity has been used to establish the governing equation which are solved via Chebyshev-Ritz-Bolotin method. Temperature and moisture variation showed notable effects on stability boundaries of the beam. Also, the stability boundaries are affected by the amount of porosities inside the material.

• Steel and Composite Structures
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• v.46 no.2
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• pp.195-202
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• 2023

Dynamic deflection analysis of sandwich beams with cellular core under thermal and pulse loads has been performed in the present article. The cellular core sandwich beam has two layers fortified by graphene oxide powder (GOP) which are micromechanically modeled by Halpin-Tsai formulation. The pulse load has blast type and is applied on the top side of sandwich beam. The system of equations has been developed based on higher-order beam theory and Ritz method. Then, they are solved in Laplace domain to derive the dynamic deflections. The dependency of beam deflection on temperature variation, GOP content, pulse load duration/location and core relative density has been studied in detail.