• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2546-2554
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• 1996

In order to investigate the characteristics of sound-structure interaction problems, we modeled a rectangular cavity and the flexible wall of the cavity. Because the governing equations of motion are coupled through velocity terms, we could redefine them 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. As the result, comparisons of theory and experiment show good agreement. and using orthogonal polynomial functions which satisfy the boundary conditions in the Rayleigh-Ritz method show useful method for sound-structure interaction problems too.

• International Journal of Railway
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• v.6 no.4
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• pp.155-159
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• 2013

The purpose of this study was to develop a theoretical model to analyze the vibration of finite railways forced by distributed moving loads. The vibration characteristics of compliantly supported beam utilizing compressional damping model were investigated through the Rayleigh-Ritz method. The distributed moving load was analyzed as the cross correlation function on railways. This allowed the use of statistical characteristics for simulation of the moving train wheels on the rail. The results showed there is a critical velocity inducing resonant vibration of the rail. The mass spring resonance from the rail fastening systems exhibited significant influence on the resulting vibration response. In particular, the effect of the viscoelastic core damping was investigated as an efficient method for minimizing rail vibration. The decrease of the averaged vibration and rolling noise generation by the damping core was maximized at the mass-stiffness-mass resonance frequency.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.04a
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• pp.5-8
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• 2000

This paper presents the results of an elastic buckling analysis of orthotropic plate under in-plane linearly distributed forces. The analytical solution for the orthotropic plate whose boundaries were assumed to be simply supported was derived in the previous work. In this study the loaded edges of plate are assumed to be simply supported and other two edges are assumed to be fixed. For the buckling analysis Rayleigh-Ritz method is employed. Graphical form of results for finding the elastic buckling strength of orthotropic plate under in-plane linearly distributed forces is presented.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.703-711
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• 2018

In this paper is studied the effect of considering the theory of Timoshenko in the vibration of AFG beams that support ground masses. As it is known, Timoshenko theory takes into account the shear deformation and the rotational inertia, provides more accurate results in the general study of beams and is mandatory in the case of high frequencies or non-slender beams. The Rayleigh-Ritz Method is employed to obtain approximated solutions of the problem. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study. The incidence of the Timoshenko theory is analyzed for different cases of beam slenderness, variation of its cross section and compositions of its constituent material, as well as different amounts and positions of the attached masses.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.369-375
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• 2018

This paper presents the shear buckling analysis of symmetrically laminated cross-ply plates resting on Pasternak foundation under pure in-plane uniform shear load. The classical laminated plate theory is used for the shear buckling analysis of laminated plates. The Rayleigh-Ritz method with novel plate shape functions is proposed to solve the differential equations and a computer programming is developed to obtain the shear buckling loads. Finally, the effects of the plate aspect ratios, boundary conditions, rotational restraint stiffness, translational restraint stiffness, thickness ratios, modulus ratios and foundation parameters on the shear buckling of the laminated plates are investigated.

• Structural Engineering and Mechanics
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• v.48 no.2
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• pp.195-205
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• 2013

The buckling problem of linearly tapered micro-columns is investigated on the basis of modified strain gradient elasticity theory. Bernoulli-Euler beam theory is used to model the non-uniform micro column. Rayleigh-Ritz solution method is utilized to obtain the critical buckling loads of the tapered cantilever micro-columns for different taper ratios. Some comparative results for the cases of rectangular and circular cross-sections are presented in graphical and tabular form to show the differences between the results obtained by modified strain gradient elasticity theory and those achieved by modified couple stress and classical theories. From the results, it is observed that the differences between critical buckling loads achieved by classical and those predicted by non-classical theories are considerable for smaller values of the ratio of the micro-column thickness (or diameter) at its bottom end to the additional material length scale parameters and the differences also increase due to increasing of the taper ratio.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1790-1800
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• 2006

Dynamic behavior of flexural-torsional coupled vibration of rotating beams using the Rayleigh-Ritz method with orthogonal polynomials as basis functions is studied. Performance of various orthogonal polynomials is compared to each other in terms of their efficiency and accuracy in determining the required natural frequencies. Orthogonal polynomials and functions studied in the present work are: Legendre, Chebyshev, integrated Legendre, modified Duncan polynomials, the special trigonometric functions used in conjunction with Hermite cubics, and beam characteristic orthogonal polynomials. A total of 5 cases of beam boundary conditions and rotation are studied for their natural frequencies. The obtained natural frequencies and mode shapes are compared to those available in various references and the results for coupled flexural-torsional vibrations are especially compared to both previously available references and with those obtained using NASTRAN finite element package. Among all the examined orthogonal functions, Legendre orthogonal polynomials are the most efficient in overall CPU time, mainly because of ease in performing the integration required for determining the stiffness and mass matrices.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.611-617
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• 1986

In this paper, it is attempted to derive the minimum torque as the optimal value on each joint, which is applied during a PTP-motion in the range of working area of a supposed industrial robot. The rupposed industrial robot consits of 3-R joints prepared on three links, The optimizational analysis is performed by the formulation of a variational calculus process due to Rayleigh-Ritz method. That is, the torques of the inverse dynamic problem on joints in a arbitrary positions are computed by a generalized inertia matrix method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1165-1169
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• 2006

Vibration characteristics of a small stand alone W/T(wind turbine) system are experimentally and theoretically investigated. Vibration resonance of the tower-cable system is monitored and the data are analysed with the analytical results. To predict the resonance speed of the cable supported WIT. Rayleigh-Ritz method is applied to the tower-guy cable coupled system. Parametric study on the relation of the cable tension. cable elasticity and resonance frequency is carried out. Results of the study are utilized to design the stable structure of small size wind turbines which consist of a pivoted tower and guy cables.

• Journal of Industrial Technology
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• v.27 no.A
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• pp.47-53
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• 2007

A theoretical model based on Rayleigh-Ritz method is proposed to predict the resonance frequency of a W/T(Wind Turbine) tower structure supported by guy cables. In order to verify the validity of the theoretical model, a reduced W/T tower system is manufactured and tested. Frequency response and mode data are determined by modal testing and finite element analysis is performed to calculate the natural frequency of the tower model. Numerical and experimental results are compared with those by the theoretical analysis. Parametric study by the theoretical model shows how the cable tension and cable elasticity influence the resonance frequency of the W/T tower structure. Finally, vibration response under various rotating speed is investigated to examine the possibility of severe resonance.