• Structural Engineering and Mechanics
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• 제48권2호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.423-428
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• 2002

A numerical method is presented to obtain natural frequencies and mode shapes of tapered beams with static deflections due to self-weight. The differential equation governing the free vibrations of beam taken into account the static deflection due to self-weight is derived and solved numerically. The hinged-hinged, clamped-clamped and clamped-hinged and clamped-free end constraints are applied in the numerical examples. As the numerical results, the lowest three natural frequencies versus distributed slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with the effects of static deflection are presented in figures.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.493-500
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• 2001

The purpose of this paper is to investigate the natural frequencies and mode shapes of tapered beams with general boundary condition(translational and rotational elastic support) at one end and carrying a tip mass with translational elastic support at the other end. The beam model is based on the classical Bernoulli-Euler beam theory which neglects the effects of rotatory inertia and shear deformation. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies and the corresponding mode shapes are calculated over a wide range of section ratio, dimensionless spring constant, and mass ratio.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.125-138
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• 2018

This paper proposes a transfer matrix method for the bending vibration of two types of tapered beams subjected to axial force, and it is applied to analyze tapered beams with an edge or multiple edge open cracks. One beam type is assumed to be reduced linearly in the cross-section height along the beam length. The other type is a tapered beam in which the cross-section height and width with the same taper ratio is linearly reduced simultaneously. Each crack is modeled as two sub-elements connected by a rotational spring, and the method can evaluate the effect of cracking on the desired number of eigenfrequencies using a minimum number of subdivisions. Among the power series available for the solutions, the roots of the differential equation are computed using the Frobenius method. The computed results confirm the accuracy of the method and are compared with previously reported results. The effectiveness of the proposed methods is demonstrated by examining specific examples, and the effects of cracking and axial loading are carefully examined by a comparison of the single and double tapered beam results.

• 태양에너지
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• 제6권2호
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• pp.86-92
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• 1986

This paper presents the aerodynamic performances of horizontal axis wind turbines with non-twisted but taperd blades. Five configurations of blades, namely, one straight blade and four tapered blades with taper ratio of ranging from 0.1 to 0.7 have been simulated. The aerodynamic performances of the wind turbines have been determined over blade incidence angle of ranging from $2^{\circ}$ to $6^{\circ}$ and keeping same solidity and radius of them. The results are presented comparing straight blade from four tapered blades for maximum power coefficient and tip looses against variation of taper ratio. It also shows that the wind turbine with taper ratio of 0.5 has the highest maximum power coefficient than others. And wind turbines with taper ratio below 0.2 have lower values of maximum power coefficients than straight one. The tip loss of straight blade is the largest and reduces Slightly with the decrementation of taper ratio.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.949-954
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• 2006

The purpose of this paper is to investigate the stability of tapered columns with clamped one end and carrying a tip mass of rotatory inertia with translational elastic support at the other end. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck columns is derived using the Bernoulli-Euler beam theory. Both the divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter, mass ratio and spring stiffness.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 추계학술대회논문집
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• pp.802-807
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• 2003

The purpose of this paper is to investigate the free vibration characteristics of tapered beams with translational and rotational springs and tip masses at the ends. The beam model is based on the classical Bernoulli-Euler beam theory. The governing differential equation for the free vibrations of linearly tapered beams is solved numerically using the corresponding boundary conditions. Numerical results are compared with existing solutions by other methods for cases in which they are available. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the translational spring parameter, the rotational spring parameter, the mass ratio and the dimensionless mass moment of inertia.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.419-432
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• 2015

The free vibration of rotating Euler-Bernoulli beams with the thickness and/or width of the cross-section vary linearly along the length is investigated by using the Adomian modified decomposition method (AMDM). Based on the AMDM, the governing differential equation for the rotating tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and the closed form series solution of the corresponding mode shapes can be easily obtained simultaneously. The computed results for different taper ratios as well as different offset length and rotational speeds are presented in several tables and figures. The accuracy is assured from the convergence and comparison with the previous published results. It is shown that the AMDM provides an accurate and straightforward method of free vibration analysis of rotating tapered beams.

• Structural Engineering and Mechanics
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• 제32권6호
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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.

• 한국철도학회논문집
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• 제7권3호
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• pp.186-192
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• 2004

Using the finite element method, rail-wheel contact model has been analyzed for mechanical loads due to passengers and payload of the train. This paper presents an investigation on how tapered wheel and inclined rail surfaces affect the contact stress and displacement of rail-wheel contacting surface under mechanical loads. For a numerical analysis, the tapered faces of the wheel are considered as 2.5% and 5.5%. And two models of the tilted rail are also considered as 40：1 and 20：1 at the bottom of the rail. The computed results based on the contact stress and displacement FE analysis indicate that the tilting ratio of the rail, 20：1 with a tapered face of the wheel, 2.5% may be more stable compared to that of 40：1 tilting model and 5.5% tapered wheel face.