• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.34 no.1
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• pp.57-65
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• 1992

The main purpose of this paper is to present both the natural frequencies and mode shapes of tapered beams under tensile axial force. The differential equation governing planar free vibration for tapered beams under tensile axial force is derived as nondimensional form. The three kinds of cross sectional shape are considered in differential equation. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. The hinged-hinged, hinged-clamped, clamped-clamped and constraints are applied in numerical examples. The lowest four nondimensional natural frequencies are reported as the function of nondimensional tensile axial force. The fundamental natural frequencies are presented when section ratios and nondimensional axial forces are varied. The effects of cross sectional shapes are reported and some typical mode shapes are also presented.

• Steel and Composite Structures
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• v.13 no.3
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• pp.225-238
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• 2012

Steel structural elements with web-tapered I cross section, are usually made of welded thin plates. Due to the nonrectangular shape of the element, thin web section may be obtained at the maximum cross section height. The buckling strength is directly influenced by lateral restraining, end support and initial imperfections. If no lateral restraints, or when they are not effective enough, the global behaviour of the members is characterized by the lateral torsional mode and interaction with sectional buckling modes may occur. Actual design codes do not provide a practical design approach for this kind of elements. The paper summarizes an experimental study performed by the authors on a relevant number of elements of this type. The purpose of the work was to evaluate the actual behaviour of the web tapered beam-columns when applying different types of lateral restraints and different web thickness.

• Smart Structures and Systems
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• v.19 no.6
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• pp.643-652
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• 2017

Pitched roof frames are widely used in construction of the industrial buildings, gyms, schools and colleges, fire stations, storages, hangars and many other low rise structures. The weight and shape of the gable frames with tapered members, as a familiar group of the pitched roof frames, are highly dependent on the properties of the member cross-sectional. In this work Enhanced Colliding Bodies Optimization (ECBO) is utilized for optimal design of three gable frames with tapered members. In order to optimize the frames, the design is performed using the AISC specifications for stress, displacement and stability constraints. The design constraints and weight of the gable frames are computed from the cross-section of members. These optimum weights are obtained using aforementioned optimization algorithms considering the cross-sections of the members and design constraints as optimization variables and constraints, respectively. A comparative study of the PSO and CBO with ECBO is also performed to illustrate the importance of the enhancement of the utilized optimization algorithm.

• Steel and Composite Structures
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• v.4 no.4
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• pp.281-301
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• 2004

The paper begins by presenting a unified variational approach to the lateral-torsional buckling (LTB) analysis of doubly symmetric prismatic and tapered thin-walled beams with open cross-sections, which accounts for the influence of the pre-buckling deflections. This approach (i) extends the kinematical assumptions usually adopted for prismatic beams, (ii) consistently uses shell membrane theory in general coordinates and (iii) adopts Trefftz's criterion to perform the bifurcation analysis. The proposed formulation is then applied to investigate the influence of the pre-buckling deflections on the LTB behaviour of prismatic and web-tapered I-section simply supported beams and cantilevers. After establishing an interesting analytical result, valid for prismatic members with shear centre loading, several elastic critical moments/loads are presented, discussed and, when possible, also compared with values reported in the literature. These numerical results, which are obtained by means of the Rayleigh-Ritz method, (i) highlight the qualitative differences existing between the LTB behaviours of simply supported beams and cantilevers and (ii) illustrate how the influence of the pre-buckling deflections on LTB is affected by a number of factors, namely ($ii_1$) the minor-to-major inertia ratio, ($ii_2$) the beam length, ($ii_3$) the location of the load point of application and ($ii_4$) the bending moment diagram shape.

• Structural Engineering and Mechanics
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• v.5 no.3
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• pp.257-268
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• 1997

The elastic deflections and Euler buckling loads are investigated for a class of tapered and initially curved cantilevered beams subjected to loading at the tip. The beam's width increases linearly and its depth decreases linearly with the distance from the fixed end to the tip. Unloaded, the beam forms a circular are perpendicular to the axis of bending. The beam's deflection responses, obtained by solving the differential equations in closed form, are presented in terms of four nondimensional system parameters: taper ratio ${\kappa}$, initial shape ratio ${\Delta}_0$, end load ratio f, and load angle ${\theta}$. Laboratory measurements of the Euler buckling loads for scale models of tapered initially straight, corrugated beams compared favorably with those computed from the present analysis. The results are applicable to future designs of the end structures of highway guardrails, which can be designed to give the appropriate balance between the capacity to deflect a nearly head-on vehicle back to its right-of-way and the capacity to buckle sufficiently that penetration of the vehicle may be averted.

• Geomechanics and Engineering
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• v.18 no.6
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• pp.615-626
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• 2019

Lightweight concrete (LWC) provides an attractive alternative to conventional piles by improving the durability of deep foundations. In this paper, the drivability of cylindrical and tapered piles made of lightweight and common concrete (CC) under hammer impacts was investigated by performing field tests and numerical analysis. The different concrete mixtures were considered to compare the mechanical properties of light aggregate which replaced instead of the natural aggregate. Driving tests were also conducted on different piles to determine how the pile material and geometric configurations affect driving performance. The results indicated that the tapering shape has an appropriate effect on the drivability of piles and although lower driving stresses are induced in the LWC tapered pile, their final penetration rate was more than that of CC cylindrical pile under hammer impact. Also by analyzing wave propagation in the different rods, it was concluded that the LWC piles with greater velocity than others had better performance in pile driving phenomena. Furthermore, LWC piles can be driven more easily into the ground than cylindrical concrete piles sometimes up to 50% lower hammer impacts and results in important energy saving.

• Transactions of Materials Processing
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• v.24 no.1
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• pp.37-43
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• 2015

The purpose of the current study is to improve the clinching joint strength of aluminum and fiber metal laminates (FMLs) comprised of three layers. The joining of FML and Al 5052 by a conventional clinching joint has some disadvantages such as necking of the upper sheet, lack of interlocking, defects caused by the vertical load, and especially loss of strength of the composite material due to the low ductility. In the current study, a tapered-hole clinching method is proposed as an alternative for the joining of Al 5052 and FMLs. A hole with a tapered shape is formed before the joining process. The design parameters were evaluated using the Taguchi method for the geometry of the tapered hole in order to determine the maximum separation load. The diameter of the punch corner, clearance, punch stroke and the tapered length were used as the main variables in the Taguchi method. In conclusion, the contribution ratio for each of the fours variable examined was 35.07%, 22.44%, 21.32% and 14.11%, respectively. In addition, the appropriate combination of the design parameters can make a 5% improvement in the vertical direction joint strength.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.145-150
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• 2000

Micro punching is one of general methods to fabricate simple holes such as permanent ink-jet printer nozzles. A thin punch, that is need for micro punching, usually has been obtained by mechanical machining. There are some method to obtain a thin punch from a cylindrical rod, e.g., microgrinding and WEDG (Wire Electro-Discharge Grinding). Inefficiently, only one punch can be obtained from these machining methods. In contrast with these methods, many punches can be fabricated simultaneously by electrochemical process. Electrochemical process has usually aimed to obtain very sharp probe for atomic force microscopy (AFM) or scanning tunneling microscopy (STM), and it has not been considered the whole shape of a probe in spite of good merits. In this paper, an ultrathin punch with a tapered shape and a cylindrical tip is newly fabricated by electrochemical process.

• Journal of the Korean Society of Propulsion Engineers
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• v.15 no.2
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• pp.8-14
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• 2011

In this paper, the combustion characteristics of hybrid rocket fuel with tapered grain port were investigated experimentally. The charging efficiency of convergent and divergent port shape fuel with $1^{\circ}$ taper angle was 6.8% higher than that of cylindrical port shape fuel. The regression rate was increased about 17.5% by using the convergent port shape fuel. On the other hand, in case of divergent port shape fuel, no notable difference of regression rate was observed when compared to that of the cylindrical port shape fuel. In the case of convergent port shape fuel, characteristic velocity and its efficiency were notably increased with respect to cylindrical port fuel. It was found that convergent port shape of hybrid rocket fuel can lead to a better option compared to the conventional cylindrical port in terms of combustion efficiency and performance improvement.