• 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.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.685-691
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• 2017

The free transverse vibrations of axially functionally graded (AFG) cantilever beams with concentrated masses attached at different points are studied in this paper. The material properties of the AFG beam, consisting of metal and ceramic, vary continuously in the axial direction according to an established law form. Approximated solutions for the title problem are obtained by means of the Ritz Method. The influence of the material variation on the natural frequencies of vibration of the functionally graded beam is investigated and compared with the influence of the variation of the cross section. The phenomenon of dynamic stiffening of beams can be observed in various situations. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study.

• 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.

• Journal of Industrial Technology
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• v.29 no.A
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• pp.3-8
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• 2009

Vibration characteristics of a 6kW 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 and compared with the analytical results. To predict the resonance speed of the cable supported W/T, 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6A
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• pp.409-415
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• 2011

Optimization Analysis of angle-ply laminated shells, having one pair of opposite edges supported, are investigated on the basis of the first-order shear deformation theory. The equations of motion of the shell are solved by the use of ritz method. A range of results are presented for composite shells to show the effects of lamination angle and number of layers on natural frequency. In addition, an analysis of the strain energy distributions is used as an aid for the better understanding of the vibration characteristics of the shells.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.