• Coupled systems mechanics
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• v.2 no.4
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• pp.303-327
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• 2013

The coupled free vibration of flexible structures and on-board liquid in zero gravity space was analyzed, considering the spacecraft main body as a rigid mass, the flexible appendages as two elastic beams, and the on-board liquid as a "spring-mass" system. Using the Lagrangians of a rigid mass (spacecraft main body), "spring-mass" (liquid), and two beams (flexible appendages), as well as assuming symmetric motion of the system, we obtained the frequency equations of the coupled system by applying Rayleigh-Ritz method. Solving these frequency equations, which are governed by three system parameters, as an eigenvalue problem, we obtained the coupled natural frequencies and vibration modes. We define the parameter for evaluating the magnitudes of coupled motions of the added mass (liquid) and beam (appendages). It was found that when varying one system parameter, the frequency curves veer, vibration modes exchange, and the significant coupling occurs not in the region closest to the two frequency curves but in the two regions separate from that region.

• Advances in nano research
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• v.6 no.3
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• pp.257-278
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• 2018

Vibration of axially functionally graded nano-rods and beams is investigated. It is assumed that the material properties change along the rod and beam length. The Ritz method with algebraic polynomials is used in the formulation of the problems. Stress gradient elasticity theory is utilized in order to include the nonlocal effects. Frequencies are obtained for different boundary conditions, geometrical and material properties. Nonlocal parameter is assumed as changing linearly or quadratically along the length of the nanostructure. Frequencies are compared to constant nonlocal parameter cases and considerable differences are observed between constant and variable nonlocal parameter cases. Mode shapes in various cases are depicted in order to explain the effects of axial grading.

• Steel and Composite Structures
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• v.19 no.4
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• pp.897-916
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• 2015

A procedure for critical buckling moment of a tapered beam is proposed with the application of potential energy calculations using Ritz method. Respective solution allows to obtain critical moments initiating lateral buckling of the simply supported, modestly tapered steel I-beams. In particular, lateral-torsional buckling of beams with simultaneously tapered flanges and the web are considered. Detailed, numerical, parametric analyses are carried out. Typical engineering, uniformly distributed design loads are considered for three cases of the load, applied to the top flange, shear centre, as well as to the bottom flange. In addition simply supported beam under gradient moments is investigated. The parametric analysis of simultaneously tapered beam flanges and the web, demonstrates that tapering of flanges influences much more the critical moments than tapering of the web.

• Structural Monitoring and Maintenance
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• v.7 no.1
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• pp.27-42
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• 2020

Dynamic stability of graded nonlocal nano-dimension plates on elastic substrate due to in-plane periodic loads has been researched via a novel 3- unknown plate theory based on exact position of neutral surface. Proposed theory confirms the shear deformation effects and contains lower field components in comparison to first order and refined 4- unknown plate theories. A modified power-law function has been utilized in order to express the porosity-dependent material coefficients. The equations of nanoplate have been represented in the context of Mathieu-Hill equations and Chebyshev-Ritz-Bolotin's approach has been performed to derive the stability boundaries. Detailed impacts of static/dynamic loading parameters, nonlocal constant, foundation parameters, material index and porosities on instability boundaries of graded nanoscale plates are researched.

• Steel and Composite Structures
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• v.2 no.5
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• pp.315-330
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• 2002

This paper proposes a model for analysing the non-linear behaviour of steel concrete composite beams prestressed by external slipping cables, taking into account the deformability of the interface shear connection. By assuming a suitable admissible displacement field for the composite beam, the balance condition is obtained by the virtual work principle. The solution is numerically achieved by approximating the unknown displacement functions as series of shape functions according to the Ritz method. The model is applied to real cases by showing the consequences of different connection levels between the concrete slab and the steel beam. Particular attention is focused on the limited ductility of the shear connection that may be the cause of premature failure of the composite girder.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.49-59
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• 2009

Vibrations of the tower structures of 750kW and 6kW wind turbines(WT) are investigated by measurement and analysis. Acceleration responses of the WT towers under various operation condition are monitored in real time by the remote monitoring system using LabVIEW. Using the monitoring system, resonance condition of the tower structures is diagnosed with the wind speed data within the operating speed range. To predict the tower resonance frequency, 750 kW tower is modeled as an equivalent beam with a lumped mass and Rayleigh energy method is applied. For 6 kW WT, Rayleigh-Ritz analysis is carried out on the tower-cable coupled system. Calculated tower bending frequency is in good agreement with the measured value. Using the analysis model, parametric study is available in order to prevent the severe resonance.

• Journal of the Korea Institute of Military Science and Technology
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• v.3 no.1
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• pp.146-154
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• 2000

Buckling behavior was studied for the square plate with bead and hole under shear load. Plates were made to examine the effect of bead and hole to the material, aluminum and composite, the effect of flange angle, bead height and bead radius of curvature. There was little difference between buckling loads obtained by the experiment and Rayleigh-Ritz method to the plate. Buckling load could be increased highly when stress concentration to the hole was dispersed effectively using flange. A well-designed plate using bead and flange showed 3 times as much as stiffness to the plate without bead and flange.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.787-794
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• 2016

In this study, the exact rigidity and the free vibration of trapezoidal corrugated plate are analyzed by being based on the Kirchhoff's plate theory and the Ritz method. The previous rigidity of corrugated plate analyzed by considering just a geometric characteristic, a basic assumption and an equivalent idea can cause large errors in practical behaviors. Accordingly, the exact rigidity supplemented by correction factors of the theoretical rigidity is needed. Therefore an analysis on the exact rigidity and the free vibration using the rigidity for the plate is performed in this paper.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.790-793
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• 2001

The characteristics of smart skin for wireless LAN system under compression load are investigated. The smart skin structure is composed of 3 layers of face material and 2 layers of core material. Theoretical formula for determining buckling load is derived by Rayleigh-Ritz method and compared with experimental result. The maximum length of specimen that buckling does not occur is determined by assuming that the compression load is sustained by only face material. In the experiment, if buckling occurs obviously then it follows the theoretical result well. In the process of buckling, the load supporting capability and the antenna property such as radiation pattern and reflection coefficient were examined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.10
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• pp.1666-1673
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• 1997

In order to investigate the characteristics of sound-structure interaction plate having a cut-out, we modeled a rectangular cavity and the flexible plate of the cavity. Because the particle velocity of air is the same as that of plate on the plate, we could easily redefine vibration equation using the velocity potential. We calculated the natural frequencies of plate using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz method. For the change of vibration characteristics, the effect of sound-structure interaction is more dominant than that of cut-out size.